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## Auto depreciation chart Depreciation limits on business vehicles. The total section 179 deduction and depreciation you can deduct for a passenger automobile, including a truck or van, you use in your business and first placed in service in 2018 is \$10,000, if the special depreciation allowance does not apply. See Maximum Depreciation Deduction in chapter 5. The estimated depreciation on the car ("Car Depreciation") from the time it was new (whether or not you bought it then) until the age at which you asked for its projected value. The estimated value of the car at the age of the car you specified. Calculator Let Kelley Blue Book help you understand a car's 5-year cost to own beyond its purchase price when you consider out-of-pocket expenses like fuel and insurance, plus the car's loss in value over Search for a suitable used car using your desired annual depreciation amount. Or calculate depreciation of any vehicle by providing its details. Free depreciation calculator using straight line, declining balance, or sum of or a car is said to "depreciate" in value after a fender bender or the discovery of a  Let Kelley Blue Book help you understand a car's 5-year cost to own beyond its expenses like fuel and insurance, and vehicle depreciation (loss in value). 7 Feb 2020 Depreciation is that moment when you drive a new car off the lot, and the car instantly loses 20% of its value. Some models hold their value  Find out if used car prices are going up or down and how they have changed over time. Update Chart. Start Date (optional). The CHOICE guide to car depreciation - how to beat it, plus how to optimise your car's resale value. 21 May 2019 The IRS provided the limitations on depreciation deductions for 2019 inflation- adjusted vehicle depreciation limits and income inclusions issued data trends and patterns via small charts that fit in a single Excel cell. ## The vehicle depreciation deduction allows you to write off that value. You can’t take this deduction if you’ve already deducted business drives, though. That’s because the standard mileage rate already factors in depreciation. The business vehicle depreciation deduction has some special rules to be aware of. These apply to most types of ### Let Kelley Blue Book help you understand a car's 5-year cost to own beyond its expenses like fuel and insurance, and vehicle depreciation (loss in value). The estimated depreciation on the car ("Car Depreciation") from the time it was new (whether or not you bought it then) until the age at which you asked for its projected value. The estimated value of the car at the age of the car you specified. Calculator Let Kelley Blue Book help you understand a car's 5-year cost to own beyond its purchase price when you consider out-of-pocket expenses like fuel and insurance, plus the car's loss in value over Lookup vehicle depreciation by make or model. See the new vs used pricing analysis and find out the best model years to buy. The IRS on Tuesday provided the limitations on depreciation deductions for passenger automobiles first placed in service in 2019 and the amounts of income inclusion for lessees of passenger automobiles first leased during 2019 (Rev. Proc. 2019-26).Passenger automobiles include trucks and vans. 2018 Luxury Auto Depreciation Limits, Tables and Explanations. The tax law limits the amount you can deduct for depreciation of your car, truck or van. The section 179 deduction is also treated as depreciation for purposes of these limits. The maximum amount you can deduct each year depends on the year you place the car in service. The vehicle depreciation deduction allows you to write off that value. You can’t take this deduction if you’ve already deducted business drives, though. That’s because the standard mileage rate already factors in depreciation. The business vehicle depreciation deduction has some special rules to be aware of. These apply to most types of 2017 Luxury Auto Depreciation Limits, Tables and Explanations. The tax law limits the amount you can deduct for depreciation of your car, truck or van. The section 179 deduction is also are treated as depreciation for purposes of these limits. The maximum amount you can deduct each year depends on the year you place the car in service.

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https://stats.stackexchange.com/questions/61451/generate-covariance-matrix-with-fixed-values-in-certain-cells/61472

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# Generate covariance matrix with fixed values in certain cells I want to be able to generate a covariance matrix of dimensions $D$ x $D$, such that certain specified cells of this matrix contain a fixed predetermined values (at least approximately). For e.g. For matrix, $S$ = $$\begin{matrix} a_{11} & a_{12} & \ldots & a_{1D}\\ a_{21} & a_{22} & \ldots & a_{2D}\\ \vdots & \vdots & \ddots & \vdots\\ a_{D1} & a_{D2} &\ldots & a_{DD} \end{matrix}$$ I want to make sure that certain $a_{i,j}$ 's have a predetermined value. (If I were generating a covariance matrix without this constraint, I would just use a Wishart Random Generator. In Matlab, it would be something like - W = wishrnd([1 0.5; 0.5 3],30)/30) One way I can think of this problem is that different cells of the covariance matrix have different degrees of freedom. So that the cells with fixed values can be assumed to have infinite degrees of freedom and the rest as some finite number. • Is there any way to translate the constraint into one on the square root of the covariance? or the square root of the inverse covariance? – shabbychef Jul 22 '13 at 22:02 ## 1 Answer It should be possible to sample from a Wishart distribution conditional on some of the entries being fixed. It may not be possible out-of-the-box with any of the BUGS-like languages (e.g. JAGS or STAN), but you may be able to rely on the Wishart's distribution with the Gaussian as described on page 5 of this document. Edited to add: It looks like the STAN manual addresses this issue directly on page 40 (section 8.2, "Partially Known Parameters"). PDF here. Their covariance matrix is small, but it should be possible to do the same thing with a bigger one. Stan's Hamiltonian Monte Carlo should be quite fast, so you can ignore the brute force approach in the next paragraph. The following advice is probably not useful, but I'll keep it below for posterity: Alternatively, since you say you just need the values to be similar to their fixed values, you could just keep resampling with wishrnd until you get something that's close enough. See rejection sampling and Approximate Bayesian Computation. The MCMC-type methods from my first paragraph could be overkill. • The first paragraph needs more serious consideration, because rejection sampling is going to be awful when just one value is fixed (within some reasonably narrow range) and impossibly slow for more than one value. – whuber Jun 11 '13 at 19:21 • @whuber you're right probably about the slowness when the number of values increases and the proposal distribution isn't great, but could you clarify the first part? – David J. Harris Jun 11 '13 at 19:54 • I meant that I think your suggestions about rejection sampling should be discounted but the idea in the first paragraph looks promising (and I upvoted your reply to reflect that). – whuber Jun 11 '13 at 20:21 • Thanks David and @whuber I am not very familiar with JAGS, STAN, so it will take me some time to understand your answer. I have upvoted your answer for now. – steadyfish Jun 12 '13 at 18:50

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https://javascriptinfo.com/view/62064/get-decimal-portion-of-a-number-with-javascript

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# Get decimal portion of a number with JavaScript I have float numbers like `3.2` and `1.6`. I need to separate the number into the integer and decimal part. For example, a value of `3.2` would be split into two numbers, i.e. `3` and `0.2` Getting the integer portion is easy: ``````n = Math.floor(n); `````` But I am having trouble getting the decimal portion. I have tried this: ``````remainer = n % 2; //obtem a parte decimal do rating `````` But it does not always work correctly. The previous code has the following output: ``````n = 3.1 => remainer = 1.1 `````` What I am missing here? Use `1`, not `2`. ``````js> 2.3 % 1 0.2999999999999998 `````` ``````var decimal = n - Math.floor(n) `````` Although this won't work for minus numbers so we might have to do ``````n = Math.abs(n); // Change to positive var decimal = n - Math.floor(n) `````` How is 0.2999999999999998 an acceptable answer? If I were the asker I would want an answer of .3. What we have here is false precision, and my experiments with floor, %, etc indicate that Javascript is fond of false precision for these operations. So I think the answers that are using conversion to string are on the right track. I would do this: ``````var decPart = (n+"").split(".")[1]; `````` Specifically, I was using 100233.1 and I wanted the answer ".1". A simple way of doing it is: ``````var x = 3.2; var decimals = x - Math.floor(x); console.log(decimals); //Returns 0.20000000000000018`````` Unfortunately, that doesn't return the exact value. However, that is easily fixed: ``````var x = 3.2; var decimals = x - Math.floor(x); console.log(decimals.toFixed(1)); //Returns 0.2`````` You can use this if you don't know the number of decimal places: ``````var x = 3.2; var decimals = x - Math.floor(x); var decimalPlaces = x.toString().split('.')[1].length; decimals = decimals.toFixed(decimalPlaces); console.log(decimals); //Returns 0.2`````` Language independent way: ``````var a = 3.2; var fract = a * 10 % 10 /10; //0.2 var integr = a - fract; //3 `````` note that it correct only for numbers with one fractioanal lenght ) If precision matters and you require consistent results, here are a few propositions that will return the decimal part of any number as a string, including the leading "0.". If you need it as a float, just add `var f = parseFloat( result )` in the end. If the decimal part equals zero, "0.0" will be returned. Null, NaN and undefined numbers are not tested. # 1. String.split ``````var nstring = (n + ""), narray = nstring.split("."), result = "0." + ( narray.length > 1 ? narray[1] : "0" ); `````` # 2. String.substring, String.indexOf ``````var nstring = (n + ""), nindex = nstring.indexOf("."), result = "0." + (nindex > -1 ? nstring.substring(nindex + 1) : "0"); `````` # 3. Math.floor, Number.toFixed, String.indexOf ``````var nstring = (n + ""), nindex = nstring.indexOf("."), result = ( nindex > -1 ? (n - Math.floor(n)).toFixed(nstring.length - nindex - 1) : "0.0"); `````` # 4. Math.floor, Number.toFixed, String.split ``````var nstring = (n + ""), narray = nstring.split("."), result = (narray.length > 1 ? (n - Math.floor(n)).toFixed(narray[1].length) : "0.0"); `````` Here is a jsPerf link: https://jsperf.com/decpart-of-number/ We can see that proposition #2 is the fastest. You could convert it to a string and use the `replace` method to replace the integer part with zero, then convert the result back to a number : ``````var number = 123.123812, decimals = +number.toString().replace(/^[^\.]+/,'0'); `````` Depending the usage you will give afterwards, but this simple solution could also help you. Im not saying its a good solution, but for some concrete cases works ``````var a = 10.2 var c = a.toString().split(".") console.log(c[1] == 2) //True console.log(c[1] === 2) //False `````` But it will take longer than the proposed solution by @Brian M. Hunt ``````(2.3 % 1).toFixed(4) `````` I had a case where I knew all the numbers in question would have only one decimal and wanted to get the decimal portion as an integer so I ended up using this kind of approach: ``````var number = 3.1, decimalAsInt = Math.round((number - parseInt(number)) * 10); // returns 1 `````` This works nicely also with integers, returning 0 in those cases. I am using: ``````var n = -556.123444444; var str = n.toString(); var decimalOnly = 0; if( str.indexOf('.') != -1 ){ //check if has decimal var decimalOnly = parseFloat(Math.abs(n).toString().split('.')[1]); } `````` Input: -556.123444444 Result: 123444444 Math functions are faster, but always returns not native expected values. Easiest way that i found is ``````(3.2+'').replace(/^[-\d]+\./, '') `````` A good option is to transform the number into a string and then split it. ``````// Decimal number let number = 3.2; // Convert it into a string let string = number.toString(); // Split the dot let array = string.split('.'); // Get both numbers // The '+' sign transforms the string into a number again let firstNumber = +array[0]; // 3 let secondNumber = +array[1]; // 2 `````` ## In one line of code ``````let [firstNumber, secondNumber] = [+number.toString().split('.')[0], +number.toString().split('.')[1]]; `````` After looking at several of these, I am now using... ``````var rtnValue = Number(7.23); var tempDec = ((rtnValue / 1) - Math.floor(rtnValue)).toFixed(2); `````` ``````n = Math.floor(x); remainder = x % 1; `````` Although I am very late to answer this, please have a look at the code. ``````let floatValue = 3.267848; let decimalDigits = floatValue.toString().split('.')[1]; let decimalPlaces = decimalDigits.length; let decimalDivider = Math.pow(10, decimalPlaces); let fractionValue = decimalDigits/decimalDivider; let integerValue = floatValue - fractionValue; console.log("Float value: "+floatValue); console.log("Integer value: "+integerValue); console.log("Fraction value: "+fractionValue) `````` Floating-point decimal sign and number format can be dependent from country (`.,`), so independent solution, which preserved floating point part, is: ``````getFloatDecimalPortion = function(x) { x = Math.abs(parseFloat(x)); let n = parseInt(x); return Number((x - n).toFixed(Math.abs((""+x).length - (""+n).length - 1))); } `````` – it is internationalized solution, instead of location-dependent: ``````getFloatDecimalPortion = x => parseFloat("0." + ((x + "").split(".")[1])); `````` Solution desription step by step: 1. `parseFloat()` for guaranteeing input cocrrection 2. `Math.abs()` for avoiding problems with negative numbers 3. `n = parseInt(x)` for getting decimal part 4. `x - n` for substracting decimal part 5. We have now number with zero decimal part, but JavaScript could give us additional floating part digits, which we do not want 6. So, limit additional digits by calling `toFixed()` with count of digits in floating part of original float number `x`. Count is calculated as difference between length of original number `x` and number `n` in their string representation. Use this one: ``````function isNatural(n) { n = +n if (isNaN(n)) return 'NaN'; return (n >= 0.0) && (Math.floor(n) === n) && n !== Infinity; } Math.frac = function frac(x, m) { x = +x if (isNatural(x) === 'NaN') return NaN; if (isNatural(x) === true) return 0; m = +m || 1 if (isNatural(x) === false && m === 1){ var a = x.toString() var b = a.split('.')[1] var c = '0.' + b var d = +c return d; } if (isNatural(x) === false && m === 2){ var a = x.toString() var b = a.split('.')[1] var c = +b return c; } if (isNatural(x) === false && m === 3){ var a = x.toString() var b = a.split('.')[1] var c = '0.' + b var d = +c * 100 return d; } } `````` The `Math.frac` function here has 3 modes: ``````Math.frac(11.635) //0.635 Math.frac(11.635, 1) //0.635 - default mode is 1 Math.frac(11.635, 2) //635 Math.frac(11.635, 3) //63,5 (%) `````` It's simple :) ``````float a=3.2; int b=(int)a; // you'll get output b=3 here; int c=(int)a-b; // you'll get c=.2 value here `````` You could convert to string, right? ``````n = (n + "").split("."); `````` Here's how I do it, which I think is the most straightforward way to do it: ``````var x = 3.2; int_part = Math.trunc(x); // returns 3 float_part = Number((x-int_part).toFixed(2)); // return 0.2 `````` The following works regardless of the regional settings for decimal separator... on the condition only one character is used for a separator. ``````var n = 2015.15; var integer = Math.floor(n).toString(); var strungNumber = n.toString(); if (integer.length === strungNumber.length) return "0"; return strungNumber.substring(integer.length + 1); `````` It ain't pretty, but it's accurate. You can use `parseInt()` function to get the integer part than use that to extract the decimal part ``````var myNumber = 3.2; var integerPart = parseInt(myNumber); var decimalPart = myNumber - integerPart; `````` Or you could use regex like: ``````splitFloat = function(n){ const regex = /(\d*)[.,]{1}(\d*)/; var m; if ((m = regex.exec(n.toString())) !== null) { return { integer:parseInt(m[1]), decimal:parseFloat(`0.\${m[2]}`) } } } `````` The best way to avoid mathematical imprecision is to convert to a string, but ensure that it is in the "dot" format you expect by using toLocaleString: ``````function getDecimals(n) { // Note that maximumSignificantDigits defaults to 3 so your decimals will be rounded if not changed. const parts = n.toLocaleString('en-US', { maximumSignificantDigits: 18 }).split('.') return parts.length > 1 ? Number('0.' + parts[1]) : 0 } console.log(getDecimals(10.58))``````

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# White Moon Selena and Calculation Quandaries – Leah Whitehorse: Astrologer & Writer 19 I recently did my bimonthly Q&A with my patrons and one of the questions was about White Moon Selena. Here’s the question:- Can you please explain White Moon Selene? Do you find it significant, and is it related at all to Black Moon Lilith? Now this question led me down such a rabbit hole! Before I even explore the meaning of White Moon Selena, it is necessary to talk about some technical calculation issues. On the Swiss ephemeris documents for this point (h56) it says:- This is a ‘hypothetical’ second Moon of the Earth (or a third one, after the “Black Moon”) of obscure provenance. Many Russian astrologers use it. Its distance from the Earth is more than 20 times the distance of the Moon and it moves about the Earth in 7 years. Its orbit is a perfect, unperturbed circle. Of course, the physical existence of such a body is not possible. The gravities of Sun, Earth, and Moon would strongly influence its orbit. So, the first thing I did, as I haven’t used this point before, was to calculate Selena on my own chart using solar fire astrology software. As you can see here, it is at 21 degrees of Taurus. If I wanted to do the same calculation on Astro.com, I would need to use h56 in the additional objects tables. Now, here is the problem. In modern astrology, especially in the past few years, White Moon Selena has been said to be the perigee of the Moon. Let’s just look at that first so we understand what this means – and for this, I need to talk about Black Moon Lilith. So, as you can see from this image above, the Moon’s orbit around the Earth isn’t a perfect circle. Instead, it’s an ellipse. If it were a perfect circle, then the centre of the Earth would be the gravitational point around which the Moon would circle. But an ellipse has two gravitational points or foci. One of those gravitational points is inside the Earth and the other is in space. That gravitational point in space is Black Moon Lilith. Hold that thought. Now, because the Moon has an elliptical orbit, sometimes it is far away from the Earth – which is called the apogee and sometimes it is closer to the Earth which is the perigee. If we on Earth are looking towards the apogee of the Moon, our technical line of sight would go right through that gravitational point I spoke about above. So, to be clear then, from our vantage point on Earth, Black Moon Lilith is the second foci of gravity of the Moon’s orbit and the apogee of the Moon. We base our interpretation of Black Moon Lilith on these astronomical facts as well as of course the story of Lilith who was first wife to Adam. So where does H56 and White Moon Selena fit into all this? Well, this is the quandary I discovered. When I calculated White Moon Selena on my chart, as you can see above, it is nowhere near the opposition of Black Moon Lilith. If White Moon Selena is the perigee of the Moon, then technically, that should be somewhere opposite Black Moon Lilith. But here you can see that Selena, this hypothetical Moon, is nowhere near the perigee of the real Moon’s orbit. So, all the interpretations that I might have thought of, regarding H56 White Moon Selena just fell apart under scrutiny because it isn’t connected. It is simply a hypothetical point that has no basis in reality as noted by the Swiss Ephemeris documents. But, if I apply all that is said of White Moon Selena to the actual perigee of the Moon, that to me makes much more sense and is an illuminating and intriguing contrasting story to Black Moon Lilith. To find this White Moon Selena then, I propose you need to calculate the true position of Black Moon Lilith (h13 on astro.com) in your chart and there you will find Selena, in the opposing degree of true (not mean) Black Moon Lilith. When I asked my astrologer friends about all this, my colleague astrologer Lynn Hayes pointed me to an article by Richard Nolle. It fascinates me that we both came to a similar conclusion independently that the archetypal story of Selena is more in keeping with the point opposite true Black Moon Lilith than with the hypothetical White Moon Selena (h56) point that everyone commonly uses. Actually, Nolle then goes on to posit the idea that the point opposite Black Moon Lilith should really be called Eve, so there we have another avenue to explore! And then I haven’t even mentioned that in Continental Europe, there are some astrologers who consider the perigee, the point opposite Black Moon Lilith, to be Priapus, a lusty fertility God. Okay, so now we have more possibilities for how to explore Lilith’s shadow/opposite/counterpart. Maybe all of them are right, layers of interpretation creating a 3D rounded picture. So, this is the quandary that surrounds White Moon Selena (h56), and it is going to be up to personal preference as to which point people use to explore this story – either h56 or the degree opposite true Black Moon Lilith, i.e., the Moon’s perigee. My preference is for the latter as I am uncomfortable using a hypothetical moon that cannot have any basis in reality. But others may feel attuned to the symbolic meaning and movement of this point and I cannot argue with that. I should also say that there is always a little room for error with any calculation of the lunar apogee and perigee as the Sun’s gravitational tug on the Moon’s orbit will cause perturbances. But still, the degree opposite Black Moon Lilith is a lot closer to the perigee than Selena H56. You can also calculate perigee on Astro.com using h22. It won’t be exactly opposite Black Moon Lilith unless one of them is conjunct or square the Sun but still, it might be worth playing with the idea too. So then, technicalities out of the way (my head is still whirling!), how can we play with this imagery, story and symbolism to better understand White Moon Selena? Whilst I’m old friends with Black Moon Lilith as she is directly conjunct the Sun in my natal chart, White Moon Selena is a new character on my archetype stage. Here are the ideas I’m thinking about, beginning first with my familiar dark Goddess before I move to the light. As Black Moon Lilith is at the apogee of the Moon, far, far away from Earth, we sense her, a gravitational pull from space, a tug deep inside. But we cannot see her. She is a wraith, an insubstantial thing who was once made flesh and allowed into Paradise to be with Adam. But Adam did not treat her well. Adam thought he was better than her. So Lilith, who was so powerful that she knew the name of God, said no! No, I will not be subservient! She left the Garden of Eden and for her audacity, for her impudence, Lilith has been demonised ever since, as has the divine feminine and the Earthly female throughout history. Black Moon Lilith’s position shows where we have enormous creative potential, yet she is also where we feel demonised, where we feel unacceptable. She is what we say no to, where we refuse to be mistreated yet often experience mistreatment. She is the part of us that seems unreachable and out of touch and yet we feel her deeply, powerfully, an inner void, waiting to be filled. She is the witch, whose archetype has been polluted throughout time, the cursed one, the scapegoat for the horrors of the world. Black Moon Lilith is the power of our magic when we focus our intention. Just as Lilith said, I desire to be made flesh, we too make our desires manifest. So, what of Selena? Selene in mythology was a Moon goddess – maid, mother, crone, rather like the fates Clotho, Lachesis and Atropos with whom Selene was sometimes connected. Out of interest, Lachesis is the one who gifts us our guardian angel, or spirit guide that will accompany us through life. Locating asteroid Lachesis on your natal chart can give you more information about that. But, going back to Selene, she is in mythology, the Moon, the guiding light through the dark. There is much more to her myths of course but this is what I will work with right now. If Lilith is what we say no to, then Selena is what we say yes to. She is where we know without question that this is the way. She is where we feel blessed, where we are in touch with our guardian angel, where we feel protected. Black Moon Lilith, cast out of Paradise, was not protected. In many stories, it’s said she birthed the horrors of the world. She was the mother of demons and killer of human children. There was no one there to sing her praises, lift her up, or protect her legacy. If Black Moon Lilith speaks of descent of heavenly powers into earthly manifestation, then maybe White Moon Selena, at the exact opposite degree of true Black Moon Lilith, represents the transmutation of material to spiritual. If Selena is the perigee of the Moon, then the reason we connect with her so immediately is because she is closer to us. We find her easier to embody, easier to relate to because she is somehow more like us than Black Moon Lilith. With Black Moon Lilith so far away, so beyond our understanding, she becomes the scary witch with a crooked nose and a wild cackle, the wicked witch of the west. But with Selena so close to us, she’s more like the kind old woman who lives in the last house of the village. She’s the one you visit quietly after Church on Sunday afternoon because you need a little potion to tickle your lover or cure an ill or charm away a little bad luck. Maybe Selena is the good witch of the north. If Black Moon Lilith is the ghost that haunts us, then perhaps White Moon Selena is a fairy Godmother, granting wishes, one, two, three. Now click your heels together. However, if we are to create an axis from these two, Black Moon Lilith and White Moon Selena are two sides of the same coin, all relating to our lunar expression, all connecting to our emotional journey as souls. There is magic bound within them both, not dark or light but a neutral force that shifts depending on our intention. Whilst we have words like black and white, dark and light to describe them, they are not simply polarities. Neither is wholly bad or good. Black Moon Lilith shows us where we need to honour ourselves for who we are, even when all others forsake us. She is directly connected to our manifestation magic. Remember, she knows the name of God! In shadow, White Moon Selena can lurch towards spiritual bypassing if she is not embraced with clarity and grounded awareness. So, these are just some thoughts I’m thinking around White Moon Selena. As I said earlier, personally, I would apply all these meanings to the degree that is exactly opposite to Black Moon Lilith’s true position in the chart rather than the h56 point due to the latter not being a real point or body in our material universe. However, I present these ideas gently, with consideration to other astrologers who may have different theories, practice and experience and with the knowledge that our discipline is ever evolving as we discover more about the heavens and ourselves. This website uses cookies to improve your experience. We'll assume you're ok with this, but you can opt-out if you wish. Accept Read More

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# Normal Numbers up to 100 Worksheets for Ages 6-8 Favorites Interactive • 6-8 • Numbers up to 100 • Normal ## Counting With Drawings. Does It Make Sound? Worksheet Introduce word problems with this simple worksheet. Ask your students to name the objects pictured, then read the word problem and ask them to circle the answer. With practice, it'll help them scale this challenging area of math. Counting With Drawings. Does It Make Sound? Worksheet Worksheet ## Counting In The Neighborhood Part 2 Worksheet Download this free worksheet to help your child build number sense and math reasoning skills! It uses pictures of objects they know, letting your child count and match the right numeral to the objects to count past 10. Let them feel successful in mastering numbers. Counting In The Neighborhood Part 2 Worksheet Worksheet ## Counting: Maraca Fun Worksheet Let your child add some Maraca fun to their math lessons by using this printable worksheet! They must figure out the numbers that come before the ones shown. Answers are provided on the other side; all your child needs to do is check the boxes with the correct numbers. Help them improve their counting and have fun along the way! Counting: Maraca Fun Worksheet Worksheet Skip Counting by 5s: Big Dipper Printable Worksheet ## Tricky Blocks Worksheet Help your child count with this printable worksheet. You'll be able to explain the technicalities of each answer as you work together to count the boxes and choose the correct number in the spaces provided. This will help your child better understand the concept and will go faster than if they do it alone. Tricky Blocks Worksheet Worksheet ## Holiday Counting Worksheet Let's spread some holiday cheer! Santa needs help counting stockings hung up for gifts - can your little one lend a hand? Find the missing numbers on the worksheet and have them check the boxes for the correct answers. Time to get counting! Holiday Counting Worksheet Worksheet ## A Crocodile's Teeth Worksheet Show your child the animal image and ask them to identify it. If they watch animal shows, they'll likely be interested. Count the teeth together, then look at the options and help them circle the right one. A Crocodile's Teeth Worksheet Worksheet ## Counting Numbers Worksheet For Kindergarten This worksheet is a great way to get your child practicing foundational math skills. With bright pictures to count, counting numbers just got a lot more fun! Get them ready for future math success and help them hone their early math skills. Counting Numbers Worksheet For Kindergarten Worksheet ## Skip Counting by 5s: Aliens and Spaceships Printable Your child will love taking an intergalactic adventure as they practice skip counting by 5's with this worksheet! It'll help them identify and recognize large groups of numbers, categorize objects to count them, and prepare them for math concepts like multiplication. And with silly space graphics, they'll be motivated for more practice! Skip Counting by 5s: Aliens and Spaceships Printable Worksheet ## Counting States Worksheet This fun and educative worksheet helps your kids learn more about their country. Ask them if they can name all the states, then help them trace on the dotted lines to match each state group to the correct number. Counting together is a fun way to reinforce learning. Counting States Worksheet Worksheet ## Tens and Ones Worksheet Help your child make math fun with this worksheet! Count the blocks on both sides and enter the total in the box below the figures. This will help them overcome any math-related anxieties they might have and let them enjoy the learning process. Tens and Ones Worksheet Worksheet ## Counting with Mittens Worksheet Let your kid have fun with this counting worksheet! It encourages them to count numbers and figure out which come next in the picture. Check the box with the correct answer - it's already provided. No more groaning and tears - this is a great way to learn! Counting with Mittens Worksheet Worksheet ## Skip Counting by 5s: Space Math Printable This worksheet will provide your child with fun and practice counting by 5's. It'll help them visually count numbers, use problem solving skills and make connections between individual and groups of numbers. Counting money and various math concepts will become easier with this invaluable skill. Blast off with this fun and educational worksheet featuring space graphics. Skip Counting by 5s: Space Math Printable Worksheet ## Counting and Numbers: Assessment Worksheet Number line thinking is an essential math skill. Kids using this skill can compute math problems accurately and quickly. Our free assessment tests number line recognition; have your child pick the right number from the given options to follow the current number on the line. This assessment will give you an idea of their counting skills. Counting and Numbers: Assessment Worksheet Worksheet ## Count by 2's: Trains Worksheet Teaching your kids quick computations? Get them skip-counting by 2s! They'll love filling in the colors of the train while counting, and it will help with 'counting up' or backward on paper or in their heads - essential for quick computations later. Count by 2's: Trains Worksheet Worksheet ## Sweet Counting - Part 1 Worksheet Help your child learn numbers by counting cakes! Download this fun worksheet and have them fill in the numbers missing in the line of cakes. They'll have fun helping the cook and be learning at the same time! Sweet Counting - Part 1 Worksheet Worksheet ## Place Value: Friendly Elves Worksheet This fun worksheet teaches kids to count elves, answer questions about houses, and practice math! Look at the picture and count the elves in each house. How many are in the green and brown house? Tick the correct answer boxes. Perfect for young learners! Place Value: Friendly Elves Worksheet Worksheet ## Count the Animal Shadows Worksheet Our shadows accompany us wherever we go. Even your kids have seen theirs! Did they know that animals have shadows too? Count the animal shadows in each group with this worksheet. Ask your child to identify the animals pictured, then help them trace the dotted lines to match with the right number. Worksheet ## Number Puzzles Worksheet In this tracing paper, your child must identify the missing numbers in the puzzle. Guide them as they trace the line for the correct number to complete the worksheet. This activity will help boost their problem-solving skills. Number Puzzles Worksheet Worksheet ## Light Source Counting Worksheet Help your students properly understand and interpret word problems with this worksheet. Read each problem aloud and have them check the correct answers. Pictures are included to aid in problem-solving. If they're still struggling, be sure to provide guidance and support. Light Source Counting Worksheet Worksheet ## Learn Dozens: Counting by Tens Printable Kindergartners need to learn skip counting - counting in number groups - to increase number sense and be ready for more advanced math. Our kindergarten worksheet featuring a starry trip to outer space will help your child practice this valuable skill. Your child will choose correct answers to trace the lines to the stars, building fluency in skip counting. They'll also strengthen problem solving and see the pattern it creates. Get your little learner to the next level with this skip counting worksheet! Learn Dozens: Counting by Tens Printable Worksheet ## Matching Numbers to Amounts Worksheet Farmer Phil needs your kid's help! Ensure they know the basics of math such as counting, adding and subtracting. Before beginning, help your child identify and count the different foods in the picture. Then, draw a line to the correct amount. Matching Numbers to Amounts Worksheet Worksheet Learning Skills

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# Enigmatic Code Programming Enigma Puzzles ## Enigma 1735: A pile of coloured cubes From New Scientist #2903, 9th February 2013 [link] I have several boxes, each containing a number of cubes. Each cube has black and white faces (at least one of each colour per cube), and each box contains all possible different cubes, with no duplicates. My three nephews opened the first box and each tried to assemble their own 2×2×2 cube with only one colour on its outer faces, and of course they failed. They then opened further boxes until they were each able to assemble a single-coloured 2×2×2 cube. They then put all the leftover cubes from the open boxes in a pile. How many cubes were there in the leftover pile? [enigma1735] ### 6 responses to “Enigma 1735: A pile of coloured cubes” 1. Jim Randell 6 February 2013 at 11:27 pm The following Python program computes the number of different 2-coloured cubes in each box, and which of these can be used as vertices in the 2×2×2 cubes, then — assuming the three nephews construct two 2×2×2 cubes of one colour and one of the other colour — it calculates how many boxes are required, and how many of the smaller cubes remain. It’s not particularly elegant, but it does the job in 35ms. ```from itertools import product, count from enigma import printf # consider a cube with faces - up, down, front, back, left, right # given a cube we can rotate it so that any of the the faces is U # (6 choices) and then can chose any of the 4 adjacent faces can be # rotated to F (4 choices), giving 6 x 4 = 24 possible rotations of # the cube. # moves on a cube for each axis (u, d, f, b, l, r) = (0, 1, 2, 3, 4, 5) U = (u, d, r, l, f, b) F = (l, r, f, b, d, u) L = (b, f, u, d, l, r) # apply a bunch of moves to a cube def move(c, rs): for r in rs: c = tuple(c[i] for i in r) return c # all rotations of the cube def rotations(c0): s = set() # go through the faces and put each one on U rU = [ [], [L, L], [L, L, L], [L], [F, F, F], [F] ] # and move each of the 4 adjacent faces to F rF = [ [], [U], [U, U], [U, U, U] ] for u in rU: c = move(c0, u) for f in rF: return s # make a box of 2-coloured cubes (white, black) = ('W', 'B') cubes = set() for c in product((white, black), repeat=6): if not(white in c and black in c): continue n = len(cubes) printf("[{n} cubes per box]") # count the number of cubes per box that can form: # - the vertex of a 2x2x2 cube of colour 0 (but not colour 1) # - the vertex of a 2x2x2 cube of colour 1 (but not colour 0) # - the vertex of either colour 2x2x2 cube (w, b, wb) = (0, 0, 0) for c in cubes: vw = any(u == f == l == white for (u, d, f, b, l, r) in rotations(c)) vb = any(u == f == l == black for (u, d, f, b, l, r) in rotations(c)) if vw and vb: wb += 1 elif vw: w += 1 elif vb: b += 1 printf("[{w} cubes in the box can be used to make a white 2x2x2 cube]") printf("[{b} cubes in the box can be used to make a black 2x2x2 cube]") printf("[{wb} cubes in the box can be used to make a 2x2x2 cube of either colour]") # we need 8 vertex cubes of the right colour to make a 2x2x2 cube # assuming we make 2 big cubes of one colour, and 1 of the other... # open x boxes (x0, r) = divmod(24, w + b + wb) if r > 0: x0 += 1 for x in count(x0): (nw, nb, nwb) = (w * x, b * x, wb * x) printf("[{x} boxes have {nw}x w cubes, {nb}x b cubes, {nwb}x wb cubes]") # can we make two white 2x2x2 cubes? if 16 > nw + nwb: continue # how many of the wb cubes are used? u = max(0, 16 - nw) # can we make one black 2x2x2 cube from what's left? if 8 > nb + nwb - u: continue printf("[2x 2x2x2 white cubes use {n1} w + {u} wb cubes]", n1=min(nw, 16)) printf("[1x 2x2x2 black cube uses {n1} b + {n2} wb cubes]", n1=min(nb, 8), n2=max(0, 8 - nb)) printf("{r} cubes left over from {x} boxes", r=x * n - 24) break ``` Solution: There were 24 cubes left over. 2. mirtouli 17 February 2013 at 4:26 pm For sure not very elegant. How long did it take to write the program, well written indeed. Next time you may not use a nuclear weapon to solve such enigma • Jim Randell 18 February 2013 at 9:35 am I wrote the program after solving the puzzle by hand, so the program is really just going through the steps I did manually – I didn’t want it to end up on my list of Enigmas that I’ve not solved programatically. Once you’ve worked out which of the smaller cubes can be used to construct the larger cubes the solution is straightforward, so I decided to make it a more interesting programming challenge by deriving the rotations of the cube, and the set of different 2-colourings from scratch. I was hoping to come up with a neater way of generating all the rotations of the cube, but in the end – inspired by playing with a Rubik’s cube – I did it mechanically based on the rotations around each axis. The program verifies the solution that I did manually, so I’m happy. • martin 19 February 2013 at 7:06 am

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一类陆地冰川动力学模型的有限元格式 Alternative Title Finite Element Scheme of the Dynamics Model for a Class of Terrestrial Glaciers 段小丽 Thesis Advisor 周宇斌 2015-05-31 Degree Grantor 兰州大学 Place of Conferral 兰州 Degree Name 硕士 Keyword 有限元法 变分形式 有限元格式 冰川动力学模型 Stokes 方程 Abstract 有限元法是一种高效能且比较常用的数值方法, 它被广泛应用于求解各类偏微分方程中. 本文对于一类陆地冰川动力学模型 ( 封闭的热力Stokes 方程组 ) 和三维定常 Stokes 方程运用有限元法, 得到其有限元格式, 并运用数值实验说明该方法的可行性和有效性.对于陆地冰川动力学模型, 本文对其空间变量进行有限元离散, 对时间变量进行有限差分离散, 对于非线性项采用系数有限元法离散, 最终得到其有限元格式. 其中, 在一维情形下讨论了方程的存在唯一性, 并在两个数值例子中应用此方法, 对于最终的非线性方程组, 本文采用 Newton 迭代法.对于三维 Stokes 方程, 本文对其区域进行四面体剖分和立方体剖分, 以其剖分内点为考虑对象, 计算得到在这两种剖分下的离散格式, 并通过数值实验说明其方法的有效性和可行性. Other Abstract Finite Element Method is a highly efficient and relatively common numerical method,which is widely used to solve all kinds of partial differential equations.In this paper,this glaciers dynamics model (closed thermodynamic Stokes equations) and three-dimensional Stokes equations used Finite Element Method,get its finite element formats.By using two examples to illustrate the feasibility and effectiveness of this method.For this glacier dynamics model,this paper acted finite element discrete for the spatial variables,finite-difference discrete for the time variables and the coefficient finite element discrete for the nonlinear terms,finally get its finite element format.In addition, this paper discussed the existence and uniqueness of this model in one-dimensional case.This finite element format was used in two examples, we used the Newton iterative method for the final nonlinear equations.For the three-dimensional Stokes equations, the paper conducted the tetrahedron split and the cube split for its region,get two the discrete format.using this discrete format for these equations,and you can see its effectiveness and feasibility through numerical experiments. URL 查看原文 Language 中文 Document Type 学位论文 Identifier https://ir.lzu.edu.cn/handle/262010/224473 Collection 数学与统计学院 Recommended CitationGB/T 7714 段小丽. 一类陆地冰川动力学模型的有限元格式[D]. 兰州. 兰州大学,2015. Files in This Item: There are no files associated with this item. Related Services Recommend this item Bookmark Usage statistics Export to Endnote Altmetrics Score Google Scholar Similar articles in Google Scholar [段小丽]'s Articles Baidu academic Similar articles in Baidu academic [段小丽]'s Articles Bing Scholar Similar articles in Bing Scholar [段小丽]'s Articles Terms of Use No data! Social Bookmark/Share No comment.

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Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  om2uzrani Structured version   Visualization version   GIF version Theorem om2uzrani 12734 Description: Range of 𝐺 (see om2uz0i 12729). (Contributed by NM, 3-Oct-2004.) (Revised by Mario Carneiro, 13-Sep-2013.) Hypotheses Ref Expression om2uz.1 𝐶 ∈ ℤ om2uz.2 𝐺 = (rec((𝑥 ∈ V ↦ (𝑥 + 1)), 𝐶) ↾ ω) Assertion Ref Expression om2uzrani ran 𝐺 = (ℤ𝐶) Distinct variable group:   𝑥,𝐶 Allowed substitution hint:   𝐺(𝑥) Proof of Theorem om2uzrani Dummy variables 𝑦 𝑧 are mutually distinct and distinct from all other variables. StepHypRef Expression 1 frfnom 7515 . . . . . 6 (rec((𝑥 ∈ V ↦ (𝑥 + 1)), 𝐶) ↾ ω) Fn ω 2 om2uz.2 . . . . . . 7 𝐺 = (rec((𝑥 ∈ V ↦ (𝑥 + 1)), 𝐶) ↾ ω) 32fneq1i 5973 . . . . . 6 (𝐺 Fn ω ↔ (rec((𝑥 ∈ V ↦ (𝑥 + 1)), 𝐶) ↾ ω) Fn ω) 41, 3mpbir 221 . . . . 5 𝐺 Fn ω 5 fvelrnb 6230 . . . . 5 (𝐺 Fn ω → (𝑦 ∈ ran 𝐺 ↔ ∃𝑧 ∈ ω (𝐺𝑧) = 𝑦)) 64, 5ax-mp 5 . . . 4 (𝑦 ∈ ran 𝐺 ↔ ∃𝑧 ∈ ω (𝐺𝑧) = 𝑦) 7 om2uz.1 . . . . . . 7 𝐶 ∈ ℤ 87, 2om2uzuzi 12731 . . . . . 6 (𝑧 ∈ ω → (𝐺𝑧) ∈ (ℤ𝐶)) 9 eleq1 2687 . . . . . 6 ((𝐺𝑧) = 𝑦 → ((𝐺𝑧) ∈ (ℤ𝐶) ↔ 𝑦 ∈ (ℤ𝐶))) 108, 9syl5ibcom 235 . . . . 5 (𝑧 ∈ ω → ((𝐺𝑧) = 𝑦𝑦 ∈ (ℤ𝐶))) 1110rexlimiv 3023 . . . 4 (∃𝑧 ∈ ω (𝐺𝑧) = 𝑦𝑦 ∈ (ℤ𝐶)) 126, 11sylbi 207 . . 3 (𝑦 ∈ ran 𝐺𝑦 ∈ (ℤ𝐶)) 13 eleq1 2687 . . . 4 (𝑧 = 𝐶 → (𝑧 ∈ ran 𝐺𝐶 ∈ ran 𝐺)) 14 eleq1 2687 . . . 4 (𝑧 = 𝑦 → (𝑧 ∈ ran 𝐺𝑦 ∈ ran 𝐺)) 15 eleq1 2687 . . . 4 (𝑧 = (𝑦 + 1) → (𝑧 ∈ ran 𝐺 ↔ (𝑦 + 1) ∈ ran 𝐺)) 167, 2om2uz0i 12729 . . . . 5 (𝐺‘∅) = 𝐶 17 peano1 7070 . . . . . 6 ∅ ∈ ω 18 fnfvelrn 6342 . . . . . 6 ((𝐺 Fn ω ∧ ∅ ∈ ω) → (𝐺‘∅) ∈ ran 𝐺) 194, 17, 18mp2an 707 . . . . 5 (𝐺‘∅) ∈ ran 𝐺 2016, 19eqeltrri 2696 . . . 4 𝐶 ∈ ran 𝐺 217, 2om2uzsuci 12730 . . . . . . . . 9 (𝑧 ∈ ω → (𝐺‘suc 𝑧) = ((𝐺𝑧) + 1)) 22 oveq1 6642 . . . . . . . . 9 ((𝐺𝑧) = 𝑦 → ((𝐺𝑧) + 1) = (𝑦 + 1)) 2321, 22sylan9eq 2674 . . . . . . . 8 ((𝑧 ∈ ω ∧ (𝐺𝑧) = 𝑦) → (𝐺‘suc 𝑧) = (𝑦 + 1)) 24 peano2 7071 . . . . . . . . . 10 (𝑧 ∈ ω → suc 𝑧 ∈ ω) 25 fnfvelrn 6342 . . . . . . . . . 10 ((𝐺 Fn ω ∧ suc 𝑧 ∈ ω) → (𝐺‘suc 𝑧) ∈ ran 𝐺) 264, 24, 25sylancr 694 . . . . . . . . 9 (𝑧 ∈ ω → (𝐺‘suc 𝑧) ∈ ran 𝐺) 2726adantr 481 . . . . . . . 8 ((𝑧 ∈ ω ∧ (𝐺𝑧) = 𝑦) → (𝐺‘suc 𝑧) ∈ ran 𝐺) 2823, 27eqeltrrd 2700 . . . . . . 7 ((𝑧 ∈ ω ∧ (𝐺𝑧) = 𝑦) → (𝑦 + 1) ∈ ran 𝐺) 2928rexlimiva 3024 . . . . . 6 (∃𝑧 ∈ ω (𝐺𝑧) = 𝑦 → (𝑦 + 1) ∈ ran 𝐺) 306, 29sylbi 207 . . . . 5 (𝑦 ∈ ran 𝐺 → (𝑦 + 1) ∈ ran 𝐺) 3130a1i 11 . . . 4 (𝑦 ∈ (ℤ𝐶) → (𝑦 ∈ ran 𝐺 → (𝑦 + 1) ∈ ran 𝐺)) 327, 13, 14, 15, 14, 20, 31uzind4i 11735 . . 3 (𝑦 ∈ (ℤ𝐶) → 𝑦 ∈ ran 𝐺) 3312, 32impbii 199 . 2 (𝑦 ∈ ran 𝐺𝑦 ∈ (ℤ𝐶)) 3433eqriv 2617 1 ran 𝐺 = (ℤ𝐶) Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 196   ∧ wa 384   = wceq 1481   ∈ wcel 1988  ∃wrex 2910  Vcvv 3195  ∅c0 3907   ↦ cmpt 4720  ran crn 5105   ↾ cres 5106  suc csuc 5713   Fn wfn 5871  ‘cfv 5876  (class class class)co 6635  ωcom 7050  reccrdg 7490  1c1 9922   + caddc 9924  ℤcz 11362  ℤ≥cuz 11672 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1720  ax-4 1735  ax-5 1837  ax-6 1886  ax-7 1933  ax-8 1990  ax-9 1997  ax-10 2017  ax-11 2032  ax-12 2045  ax-13 2244  ax-ext 2600  ax-sep 4772  ax-nul 4780  ax-pow 4834  ax-pr 4897  ax-un 6934  ax-cnex 9977  ax-resscn 9978  ax-1cn 9979  ax-icn 9980  ax-addcl 9981  ax-addrcl 9982  ax-mulcl 9983  ax-mulrcl 9984  ax-mulcom 9985  ax-addass 9986  ax-mulass 9987  ax-distr 9988  ax-i2m1 9989  ax-1ne0 9990  ax-1rid 9991  ax-rnegex 9992  ax-rrecex 9993  ax-cnre 9994  ax-pre-lttri 9995  ax-pre-lttrn 9996  ax-pre-ltadd 9997  ax-pre-mulgt0 9998 This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-3or 1037  df-3an 1038  df-tru 1484  df-ex 1703  df-nf 1708  df-sb 1879  df-eu 2472  df-mo 2473  df-clab 2607  df-cleq 2613  df-clel 2616  df-nfc 2751  df-ne 2792  df-nel 2895  df-ral 2914  df-rex 2915  df-reu 2916  df-rab 2918  df-v 3197  df-sbc 3430  df-csb 3527  df-dif 3570  df-un 3572  df-in 3574  df-ss 3581  df-pss 3583  df-nul 3908  df-if 4078  df-pw 4151  df-sn 4169  df-pr 4171  df-tp 4173  df-op 4175  df-uni 4428  df-iun 4513  df-br 4645  df-opab 4704  df-mpt 4721  df-tr 4744  df-id 5014  df-eprel 5019  df-po 5025  df-so 5026  df-fr 5063  df-we 5065  df-xp 5110  df-rel 5111  df-cnv 5112  df-co 5113  df-dm 5114  df-rn 5115  df-res 5116  df-ima 5117  df-pred 5668  df-ord 5714  df-on 5715  df-lim 5716  df-suc 5717  df-iota 5839  df-fun 5878  df-fn 5879  df-f 5880  df-f1 5881  df-fo 5882  df-f1o 5883  df-fv 5884  df-riota 6596  df-ov 6638  df-oprab 6639  df-mpt2 6640  df-om 7051  df-wrecs 7392  df-recs 7453  df-rdg 7491  df-er 7727  df-en 7941  df-dom 7942  df-sdom 7943  df-pnf 10061  df-mnf 10062  df-xr 10063  df-ltxr 10064  df-le 10065  df-sub 10253  df-neg 10254  df-nn 11006  df-n0 11278  df-z 11363  df-uz 11673 This theorem is referenced by:  om2uzf1oi  12735 Copyright terms: Public domain W3C validator

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Do you pay PMI at closing monthly? Do you pay PMI at closing monthly? You’ll pay a portion of your PMI upfront at closing, and the remaining premium amount with your monthly mortgage payments. How can I pay my PMI off faster? If you want to get the PMI off of your loan faster, pay down what you owe quicker by making one extra mortgage payment each year or putting your annual bonus towards your mortgage. Should I pay off PMI early or invest? Paying off a mortgage early could be wise for some. Eliminating your PMI will reduce your monthly payments, giving you an immediate return on your investment. Homeowners can then apply the extra savings back towards the principal of the mortgage loan, ultimately paying off their mortgage even faster. Can I pay my PMI upfront? Many buyers do not realize that there is also an option to pay the premium as a single lump sum upfront called single-payment mortgage insurance. For a buyer with good credit scores and a 5 percent down payment on a \$300,000 loan, the monthly PMI cost is estimated to be \$167.50. Paid upfront it would be \$6,450. How is upfront PMI calculated? Example – Calculating PMI 1. Down Payment. = 15% * \$350,000. = \$52,500. 2. Loan amount = Home Purchase Price – Down Payment. = \$350,000 – \$52,500. = \$297,500. 3. Annual PMI = Loan Amount * Mortgage Insurance Rate. = \$297,500 * 0.55% = \$1636.25. 4. Monthly PMI. = \$1636.25 / 12. = \$136.35. Can PMI be negotiated? The lender rolls the cost of the PMI into your loan, increasing your monthly mortgage payment. You cannot negotiate the rate of your PMI, but there are other ways to lower or eliminate PMI from your monthly payment. Is PMI tax deductible? A PMI tax deduction is only possible if you itemize your federal tax deductions. For anyone taking the standard tax deduction, PMI doesn’t really matter, Han says. Roughly 86% of households are estimated to take the standard deduction, according to the Tax Foundation. Why should you not put 20% down on a house? The “20 percent down rule” is really a myth. Typically, mortgage lenders want you to put 20 percent down on a home purchase because it lowers their lending risk. It’s also a “rule” that most programs charge mortgage insurance if you put less than 20 percent down (though some loans avoid this). Is upfront PMI refundable? This initial premium is the called the upfront mortgage insurance premium (also known as UFMIP or MIP). But, this fee is refundable if you refinance into another FHA loan like the FHA Streamline Refinance or the FHA Cash-out Refinance within three years of opening your FHA loan. What’s the best way to pay for PMI? There are four different ways to make PMI payments: Monthly premium. This is the most common way to pay for PMI. The premium amount is added to your monthly mortgage payment. Single premium. This is also referred to as upfront PMI. It’s paid in one lump sum at your mortgage closing. Lender-paid premium. Do you pay PMI upfront or at closing? Under this option, your lender agrees to cover your PMI payment at closing. In exchange, they’ll slightly bump up your mortgage interest rate. Split premium. You’ll pay a portion of your PMI upfront at closing, and the remaining premium amount with your monthly mortgage payments. Which is better single premium PMI or monthly PMI? Single premium PMI results in a lower monthly payment compared to paying PMI monthly, which helps the buyer qualify for more home. The risk, however, is that you will only keep the mortgage or home for a few years. The single premium is non-refundable. Do you have to pay PMI on a 20% down mortgage? If you put less than 20% down on a home and use conventional financing, you’ll need to pay for Private Mortgage Insurance. Many people sigh as they hear about PMI because they know it’s just going to make their mortgage payment higher.

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[Maxima] Rules and simplification question (newbie) Doug Neubauer dougn at integrity.com Wed May 24 00:30:21 CDT 2006 ```On Tue, 23 May 2006 20:02:10 -0700, "Richard Fateman" wrote: >the pattern for >-x^2 looks like > >(* -1 (expt x 2)) > >the pattern for -r^2/t^2 > >looks like >(* -1 (expt r 2)(expt t -2)) > >A product of 3 items. It won't match a pattern of 2 items. I guess I was hoping there was some way to make Maxima recognize r^2/t^2 was also (r/t)^2 and that would match the pattern. > >you could try defining a rule like >matchdeclare (negsquare, negsquarematcher); > >defrule (rule1, exp(negsquare), gp(sqrt(-negsquare))) > >now figure out the function negsquarematcher(h) := ..... something to test >for the case you want.... > >RJF > Thanks. And thanks to everyone for their help. Doug ```

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# NCL_xy_5.py# This script illustrates the following concepts: • Draw multiple curves on an XY plot • Drawing a Y reference line in an XY plot • Filling the areas of an XY curve above and below a reference line • Using named colors to indicate a fill color • Converting dates from YYYYMM format to floats • Creating a main title • Setting the mininum/maximum value of the Y axis in an XY plot See following URLs to see the reproduced NCL plot & script: Import packages: ```import numpy as np import xarray as xr import matplotlib.pyplot as plt import geocat.datafiles as gdf import geocat.viz as gv ``` ```# Open a netCDF data file using xarray default engine and load the data into xarrays ds = xr.open_dataset(gdf.get("netcdf_files/soi.nc")) dsoik = ds.DSOI_KET dsoid = ds.DSOI_DEC date = ds.date num_months = np.shape(date)[0] # Dates in the file are represented by year and month (YYYYMM) # representing them fractionally will make ploting the data easier # This produces the same results as NCL's yyyymm_to_yyyyfrac() function date_frac = np.empty_like(date) for n in np.arange(0, num_months, 1): yyyy = int(date[n] / 100) mon = (date[n] / 100 - yyyy) * 100 date_frac[n] = yyyy + (mon - 1) / 12 ``` Plot: ```# Generate figure (set its size (width, height) in inches) and axes plt.figure(figsize=(8, 4)) ax = plt.gca() # Plot reference line ax.axhline(y=0, color='grey', linewidth=0.75) # Plot data # _labels=False prevents axis labels from being drawn ax.plot(date_frac, dsoik, color='black', linewidth=0.5) ax.plot(date_frac, dsoid, color='black') # Fill above and below the 0 line ax.fill_between(date_frac, dsoik, where=dsoik > 0, color='red') ax.fill_between(date_frac, dsoik, where=dsoik < 0, color='blue') # Use geocat.viz.util convenience function to add minor and major tick lines x_minor_per_major=4, y_minor_per_major=5, labelsize=14) # Use geocat.viz.util convenience function to set axes parameters gv.set_axes_limits_and_ticks(ax, ylim=(-3, 3), yticks=np.linspace(-3, 3, 7), yticklabels=np.linspace(-3, 3, 7), xlim=(date_frac[0], date_frac[-1]), xticks=np.linspace(1880, 1980, 6)) # Use geocat.viz.util convenience function to set titles and labels gv.set_titles_and_labels(ax, maintitle="Darwin Southern Oscillation Index") plt.show() ``` Total running time of the script: (0 minutes 0.837 seconds) Gallery generated by Sphinx-Gallery

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Athlete Monitoring: Data Analysis and Visualization – Rolling Functions - Complementary Training Athlete Monitoring: Data Analysis and Visualization – Rolling Functions # Athlete Monitoring: Data Analysis and Visualization ## Rolling Functions Rolling functions are useful in describing trends over time. These can be any type of descriptive functions, like means, medians, standard deviations, and so forth. In sports science, we usually use rolling windows of short duration (i.e., acute; 3-14 days ) and long (i.e., chronic; 28-42 days). This allows us additional descriptive metrics like Training Stress Balance (TSB; the difference between acute and chronic mean), acute to chronic ratios (ACR; the ratio between acute and chronic mean), and so forth. There have given a bad rep recently due to their bad use in predicting overuse injuries due to bad load management. But, if we approach them as simple descriptors, they are useful visualization techniques that can add extra information about trends without giving them predictive powers. In this lesson, besides discussing rolling functions, I mention the issues of having an unbroken chain of observations (i.e., without missing days) and the problem of nominal variables, which is covered in the next lecture. #### Athlete Monitoring Course Take advantage of our promotional offer ### Learn How to Analyse All Your Training, Performance and Testing Data OR \$350 per year I am a physical preparation coach from Belgrade, Serbia, grew up in Pula, Croatia (which I consider my home town). I was involved in physical preparation of professional, amateur and recreational athletes of various ages in sports such as basketball, soccer, volleyball, martial arts and tennis. Read More » Welcome to Complementary Training Community! Forums Athlete Monitoring: Data Analysis and Visualization – Rolling Functions Tagged: This topic contains 0 replies, has 1 voice, and was last updated by  Mladen Jovanovic 3 years, 4 months ago. You must be logged in to reply to this topic.

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# Find the domain of the function f ( x ) = 1 x − 3 ### Precalculus: Mathematics for Calcu... 6th Edition Stewart + 5 others Publisher: Cengage Learning ISBN: 9780840068071 ### Precalculus: Mathematics for Calcu... 6th Edition Stewart + 5 others Publisher: Cengage Learning ISBN: 9780840068071 #### Solutions Chapter 2.1, Problem 47E To determine ## Find the domain of the function f(x)=1x−3 Expert Solution The domain of the function f(x)=1x3 is (,3)(3,) ### Explanation of Solution Given information:Consider the function f(x)=1x3 Calculation: Recall the domain of a function is the set of input or argument values for which the function is real and defined. Assume a function from real values to real values as shown in the figure below: From the above graph, the negative values of x to x=3 without including it to the rest of all real numbers. Thus, the domain of the function f(x)=1x3 is (,3)(3,) ### Have a homework question? Subscribe to bartleby learn! Ask subject matter experts 30 homework questions each month. Plus, you’ll have access to millions of step-by-step textbook answers!

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# Question: How To Find Fn In Physics? Normal Force Formula 1. The normal force will be equivalent to the weight of the object only if the object is not accelerating i.e. decelerating. 2. F_N = mg. 3. F_N = mg + F sin;theta. 4. F_N = mg – F sin;theta. 5. F_N = mg cos;theta. 6. Angle theta = 30° 7. Sin 30° = frac{1}{2} 8. F_N = mg + F sin;theta. ## What is FN equal to in physics? To find static friction, it equals the product of normal force (Fn) and static friction coefficient (Fs). F=Fn x Fs. (Depends on the orientation of the object, there are different ways to find the normal force. For example, Fn equals -m x g only when the gravitational force is in opposite direction to the normal force. ## What is FN formula? To calculate the normal force of an object at an angle, you need to use the formula: N = m * g * cos(x) For this equation, N refers to the normal force, m refers to the object’s mass, g refers to the acceleration of gravity, and x refers to the angle of incline. ## What is FN in forces? • The normal force, Fn, is perpendicular to the. object and to the surface counterbalances the weight of the object. You might be interested:  FAQ: How Do Paper Airplanes Fly Physics? ## What is FN and FG in physics? Normal Force (FN) Remember that a normal force is always perpendicular to the surface that you are on. In these questions Fg ≠ FN Force due to Friction (Ff) will always be opposite to the direction that something is moving. ## Is FN equal to MG? Normal force is equal to mg only when the object is placed horizontally, and the force is acting in the direction of the gravitational field. ## What does P mean in physics? Momentum is a measurement of mass in motion: how much mass is in how much motion. It is usually given the symbol p. The useful thing about momentum is its relationship to force. ## What is normal force formula? In this simple case of an object sitting on a horizontal surface, the normal force will be equal to the force of gravity F n = m g F_n=mg Fn=mgF, start subscript, n, end subscript, equals, m, g. ## What key is the Fn key? Simply put, the Fn key used with the F keys across the top of the keyboard, provides short cuts to performing actions, such as controlling the brightness of the screen, turning Bluetooth on/off, turning WI-Fi on/off. ## What is formula for mass? One way to calculate mass: Mass = volume × density. Weight is the measure of the gravitational force acting on a mass. The SI unit of mass is “kilogram”. ## Is FNet normal force? Explanation: Normal force is defined as the force that a surface exerts on an object. If the object is at rest, net force on the object is equal to zero; therefore, the downward force (weight) must be equal to the upward force (normal force). You might be interested:  Question: How Is The Pirate Ship Ride At Amusement Park Related To Physics? ## What does FG FN FA and FF mean? Force of Gravity: Fg Normal Force: FN Force of Friction: Ff Applied forces: F___ ## What is the relationship between FN and FF? Question: A proportional relationship between Ff and FN may be expressed by the formula Ff^Fn where x is a constant called the coefficient of friction. The value of yi depends on what types of surfaces are in contact Explain how you would use your graph of Ff vs. FN to determine an experimental value for x. ## Is FN equal to FY? Because of equilibrium (∑Fy = m∙a = 0), the normal force, FN, is equal and opposite to Fy, the vertical component of the block’s weight, Fw. ## What is FN on free body diagram? FN Normal force Perpendicular (i.e. normal) to the surface. Equal to whatever force is needed to prevent the object from falling through the floor.

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# Finding where ground is in procedurally generated terrain Terrain in my voxel game is generated by combining 2d and 3d perlin noise. if (y < (noise2d(x, z) + noise3d(x, y, z)) * amplitude) { // place block } To generate structures like trees, I need to find where the ground is. The simplest way is to just go through every block from min height to max height and check if there is a block with no block above it. This works, but it is slow. Is there a faster way to do this? I tried using bisection, but it sometimes returns positions one block below the ground. Simplified code for bisection: float min = minHeight; float max = maxHeight; float mid = (min + max) / 2.0f; while (abs(mid - combinedNoise(mid)) > 0.5f) { if (sign(mid - combinedNoise(min)) == sign(mid - combinedNoise(mid))) { min = mid; } else { max = mid; } mid = (min + max) / 2.0f; } I think removing the absolute value might fix the blocks below the ground, but I don't think I can remove it because it can create an infinite loop because of how bisection works. • Note that if you include 3D Perlin noise, you may have multiple "grounds" per (x,z) position, since you may have overhangs. Otherwise I would suggest that you used the bisection method, which finds the transition between negative and positive function values, i.e., where the ground is, in logarithmic time (it does this even if you have overhangs; you're just not sure which of the multiple grounds you will find). Jan 21, 2022 at 13:35 • Comments are not for extended discussion; this conversation has been moved to chat. Jan 21, 2022 at 13:58 Let's define your block placement rule as a function of position: bool IsSolid(x, y, z) { return y < (noise2d(x, z) + noise3d(x, y, z)) * amplitude; } Looking at this, we can make our initial search bounds tighter. Let baseHeight = noise2d(x, y) then expand that based on your range of values from your noise3d function. (Typically 0-1 or -1 to 1, but you may have a custom noise here with other behaviour) int minHeight = floorToInt((baseHeight + minNoise3dValue) * amplitude); int maxHeight = ceilToInt((baseHeight + maxNoise3DValue) * amplitude); (If you have constraints on the maximum slope of the noise3d function, you might be able to make this even tighter) By construction, we know IsSolid(x, minHeight, z) == true and IsSolid(x, maxHeight, z) == false, and we'll maintain this as an invariant as we go. while (maxHeight > minHeight + 1) { int midHeight = (maxHeight + minHeight)/2; // Compiler will make this >> 1 if (IsSolid(x, midHeight, z)) { minHeight = midHeight; } else { maxHeight = midHeight; } } At the end of this process, minHeight points to a solid block and maxHeight points to an empty block directly above it, so this is a point on the surface of your terrain. Note that because you're using 3D noise, you can get overhangs or voids, so this procedure does not guarantee that this is the top-most surface in this column, only that it is some place where there is a transition from solid immediately below to empty immediately above.

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# price of dollars Page 1 of 2 • posted on August 14, 2010, 4:06 pm A few years ago you needed 15 cents to buy one big mac. Soon you will need 15 dollars to get one big mac. Nothing has really changed you still get one big mac but you need a bit more paper. Now you pay 41.000 dollars for one Volt How many big macs is that and how many big macs did you need a few years back to get a car? Who wins when you print more money? <% if( /^image/.test(type) ){ %> <% } %> <%-name%> • posted on August 14, 2010, 4:17 pm The lowest cost vehicle one can buy today is approaching \$20,000, just eight years ago one could buy a full size car for \$25,000. <% if( /^image/.test(type) ){ %> <% } %> <%-name%> • posted on August 15, 2010, 12:15 am Perhaps but the poverty line is \$600 a year and who knows how many millions of them at 2.8% of the population? A person living in poverty is the US is rich compared to someone in China. One could become a millionaire just selling one pair of SHOES to the average person in China LOL <% if( /^image/.test(type) ){ %> <% } %> <%-name%> • posted on August 15, 2010, 3:05 am Lots of variables. But it all points to China is a better run country than the US. Lower debt, more jobs, real growth above inflation, modernizing fast and not decaying. Compared to the US the Chinese government owes nothing, and in fact is in surpluses the US has never ever seen. Taxes for the average joe are quite low too. China is effectively an authoritarian capitalist. Highly efficient government compared to the US. What keeps the world from economic collapse is that China is buying the commodities the US no longer buys. And Washington DC still thinks they can spend their way out of a debt problem. Hopelessly screwed. On 8/14/2010 5:15 PM, Mike wrote: -- Is government working for you, or are you working for the government? <% if( /^image/.test(type) ){ %> <% } %> <%-name%> • posted on August 16, 2010, 5:04 pm Again you are wrong. Although China has passed Japan as the worlds second biggest economy it is less than half of the 14 trillion dollar US economy <% if( /^image/.test(type) ){ %> <% } %> <%-name%> • posted on August 14, 2010, 4:33 pm I was always taught that when you pay with inflated paper dollars, the seller can lose and the buyer shrugs off some of his actual debt. Really humps you in international business. <% if( /^image/.test(type) ){ %> <% } %> <%-name%> • posted on August 14, 2010, 4:57 pm The chinese do not want to change the value of their currency and they keep the wages low. Same for some other countries. The big mac index is used to show the real value of money in different countries. By not allowing wages to go up the jobs go to those countries. Many big international companies are increasing their numbers of employees in total but the increase is all in low wage countries and we in the high price countries lose jobs. GM is growing and profitable in china. The wars usa is paying for in various countries is costly in more ways than one. They make usa less popular and they make the dollar worth less. So what would happen if usa stopped sending troups and printing dollars? The real question is what happens when other countries stop wanting to use dollars and they start flowing back. I guess the price of the big mac is going to go up a lot. There are already some countries like china and russia wanting to stop using as much dollars in their trade. The oil producers are starting to go away from the dollars in their contracts. The price of gold is going up and up. <% if( /^image/.test(type) ){ %> <% } %> <%-name%> • posted on August 14, 2010, 5:17 pm Oil producers will try to stay with the currency that is the most stable. At one point this was the dollar, and later it slid toward the Euro. Lately the Euro has had some signs of weakness. It will all come out in the wash. Gold, IMO, is overvalued. I have gone through this before, and have seen gold go up because people had no confidence in paper currency. Gold could drop like a rock if the dollar regains high stability. Investment diamonds are another way that you can put a fortune in very hard value in your pocket and get across the border to a friendlier country. <% if( /^image/.test(type) ){ %> <% } %> <%-name%> • posted on August 14, 2010, 7:44 pm On 8/14/2010 10:17 AM, hls wrote: Is gold over valued or did the currencies loose their value? It is relative. -- Is government working for you, or are you working for the government? <% if( /^image/.test(type) ){ %> <% } %> <%-name%> • posted on August 14, 2010, 7:43 pm On 8/14/2010 9:57 AM, Bjorn wrote: The real reason is that it devalues the \$2 trillion USD that the the US Government owes them. Say 6 Yuan is 1 USD. If they let the USD sink, to say 3:1 then the value in Yuan is 1/2 as much. Bad deal for China. Good deal for corrupt US government. Sooner or later the Chinese will realize they will never see the value of the \$2 trillion as Washington DC never plans to pay it off. As this happens, the USD will sink, and perhaps Yuan will be worth more than a USD...at which point people will realize the full hyper-inflationary effect of this. Given China is no longer buying US debt like it used to, DC has resorted to bank ponzi scheme of having a government bank create money, expand it and loan it back, in short buying its own bonds. A real ponzi scheme for sure. Which will translate into a combination of inflation and deflation at the same time. Discretionary stuff must deflate as people will not buy it. Real estate will too. But world commodity essentials will stay high or higher like oil, wheat, food. -- Is government working for you, or are you working for the government? <% if( /^image/.test(type) ){ %> <% } %> <%-name%> • posted on August 14, 2010, 10:58 pm By the time those thirty year US Bonds come due they can be easily paid off with BO(ZOs) inflated dollars. <% if( /^image/.test(type) ){ %> <% } %> <%-name%> • posted on August 15, 2010, 2:21 am Yep. Loan the US government \$40k today. In 20 years get maybe \$45k back. But wait, that \$40k car today will cost you \$100k in 20 years. Your money depreciated by \$55k. Who wins is governemtn debtors as they will pay you with depreciated 20 year money. Also part of why in 2008 the ruse was no one was lending money. Of course not, the valuation was wrong as interest rates were too low. Government caused it. On 8/14/2010 3:58 PM, Mike wrote: -- Is government working for you, or are you working for the government? <% if( /^image/.test(type) ){ %> <% } %> <%-name%> • posted on August 15, 2010, 10:11 am This is why all governments world wide borrow, because inflation beats interest rates, they win hands down. People buy government bonds because they pay better than the banks, but still way below inflation. -- Clive <% if( /^image/.test(type) ){ %> <% } %> <%-name%> • posted on August 15, 2010, 10:48 am It is a very complicated game. It has to do with distribution of welth as well production and use of goods. Lets say A and B work for a day and they each get a bar of chocolate as pay. A eats his bar but B only eats half the bar. Next day same happens again. After this day A has nothing but B has a whole bar. If this continues then B will accumulate a lot of chocolate bars and A has nothing. After some time B can stop working and just enjoy all his chocolate but A must keep on working. In a communist society lets say B has accumulated 1000 bars of chocolate. The government would like to take half of Bs bars and give them to A. In a capitalist society the government wants to borrow half Bs bars and lend it to A but A never pays them back again and so the situation becomes the same in both systems. There are different needs and it is difficult to accommodate all. With a simple system it may seem easy to see what is right and what is fair but the more complex it gets the same principles are at work but it is difficult to say what is fair. Lots of people do not do any work and still get chocolate bars. Others steal from their neighbors one way or another. <% if( /^image/.test(type) ){ %> <% } %> <%-name%> • posted on August 16, 2010, 5:09 pm Actually inflation in the US is in check today. That will soon change, as trillions of dollars are added to the US nation debt, over the next ten years to pay for the new healthcare law, and the increased deficit spend by BO(ZO) and the Dims in Congress, according the HBO. writes <% if( /^image/.test(type) ){ %> <% } %> <%-name%> • posted on August 16, 2010, 4:57 pm You are confused, again! The difference between the thirty year Bonds that the Chinese have been buying, and the taxpayer money give to GM, is GM has paid back the money loaned to it, with interest, three years before it was due. The Preferred Stock given to the Government, as collateral for the rest of the taxpayer money, will also be bought back by GM, at a profit to the taxpayers, when it goes public again. The US Treasury Bonds on the other hand will result in the taxpayers paying the interest due on the Bonds. <% if( /^image/.test(type) ){ %> <% } %> <%-name%> • posted on August 14, 2010, 10:47 pm Why would they want to get rid of the dollar? The dollar is the most stable currency in the world because the free capitalist economy in US is the most stable economy in the world. <% if( /^image/.test(type) ){ %> <% } %> <%-name%> • posted on August 15, 2010, 2:22 am Chinese Yuan has been much more stable in the last 5 years or so. USD has been loosing value against amny currencies. On 8/14/2010 3:47 PM, Mike wrote: -- Is government working for you, or are you working for the government? <% if( /^image/.test(type) ){ %> <% } %> <%-name%> • posted on August 16, 2010, 5:00 pm That is because the Chinese government is not allowing the Yuan to fluxuate, dummy. wrote in message news:b5dfa033-55fb-40d6-8ac3-

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10 Jul Often this comes into the subnetting discussion by my friends who are deploying IPv6 for the first time. How do you calculate subnets outside the 4-bit nibble boundary? This also happens to be one of starting points of APNIC IPv6 routing workshop where I occasionally instruct as community trainer. So what is a Nibble boundary? In IPv6 context, it refers to 4 bit and any change in multiple of 4 bits is easy to calculate. Here’s how: Let’s say we have a allocation: 2001:db8::/32. Now taking slices from this pool within 4 bit boundry is quite easy. /36 slices (1 x 4 bits) 2001:db8:0000::/36 2001:db8:1000::/36 2001:db8:2000::/36 and so on… /40 slices (2 x 4 bits) 2001:db8:0000::/40 2001:db8:0100::/40 2001:db8:0200::/40 /44 slices (3 x 4 bits) 2001:db8:0000::/44 2001:db8:0010::/44 2001:db8:0020::/44 /48 slices (4 x 4 bits) 2001:db8:0000::/48 2001:db8:0001::/48 2001:db8:0002::/48 Clearly, it seems much simple and that is one of the reasons we often strongly recommend subnetting within the nibble boundary and not outside for all practical use cases. However understanding why it’s easy this way, as well as things like how to subnet outside nibble boundary for cases, say if you are running a very large network and have a /29 allocation from RIR. Going back to fundamentals IPv6 address:  _ _ _ _: _ _ _ _ :_ _ _ _ :_ _ _ _ :_ _ _ _ :_ _ _ _ :_ _ _ _ :_ _ _ _ Each dash here represents is written in hexadecimal and represents 4 bits, thus 4+4+4+4 = 16 bits in each block and 16 x 8 = 128 bit addressing. This brings that magical 4-bit nibble boundary. So if we expand 4 bits into binary, we can have following combinations for each “dash” in above representation: ```0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 0 1 0 0 0 1 0 1 0 1 1 0 0 1 1 1 1 0 0 0 1 0 0 1 1 0 1 0 1 0 1 1 1 1 0 0 1 1 0 1 1 1 1 0 1 1 1 1``` Here I have simply represented 4 bits from lowest to highest. Remember just like in the decimal system with base 10 (which we all are familiar with), we follow same logic in binary system where we start from lowest (0 0 0 0) and go to next digital (0 0 0 1) and now since it’s base 2, we go to next logical number which is (0 0 1 0) and so on. Now when we modify these 4 bits together, we do not have to worry about the decimal part but as soon as we try to go inside the 4-bit zone, we have to deal with the decimal counting. So let’s take a real-world case of American Cable & broadband provider Comcast. They have an allocation 2001:558::/31: ```NetRange: 2001:558:: - 2001:559:FFFF:FFFF:FFFF:FFFF:FFFF:FFFF CIDR: 2001:558::/31 NetName: COMCAST6NET NetHandle: NET6-2001-558-1 Parent: ARIN-001 (NET6-2001-400-0) NetType: Direct Allocation OriginAS: AS7922 Organization: Comcast Cable Communications, LLC (CCCS) RegDate: 2003-01-06 Updated: 2016-08-31 Ref: https://whois.arin.net/rest/net/NET6-2001-558-1``` What exactly /31 means here? Going back by CIDR fundamentals /31 means 31 bits are reserved and remaining (128-31 i.e 97 bits) are available. How can they generate /32 or say /36 out of this allocation? 2001:558::/31 Writing in expanded form: 2001:0558::/31 (16 bits + 15 bits) In above, first 16 bits are reserved for 2001 but for next part “0558” only 15 bits are reserved. Let’s expand the 2nd block further: 0 5 5 8 – 15 bits reserved Here “0” gives 4 bits (and in binary is 0 0 0 0) 5 gives 4 bits (and in binary is 0 1 0 1) Next 5 also reserves 4 bits So far we are at (4 + 4 + 4) 12 bit count. Now that 15 bits are reserved, basically from “8” 3 bits are reserved and rest 1 bit is available for modification. Let’s expand 8: 8 in hexadecimal = 1 0 0 0 in binary. Here 1 0 0  is reserved (each representing one binary bit and hence the three bits) and 4th bit can vary. Hence possible combinations in binary are: 1 0 0 0 1 0 0 1 The remaining first three bits (1 0 0 ) cannot be altered as they are part of network mask. Now 1 0 0 0 in binary gives us “8” in hexadecimal and 1 0 0 1 gives us “9”. Thus possible /32s out of this /31 allocation are: 2001:558::/31 = 2001:558::/32  and 2001:559::/32 Similarly to calculate /36 slices from it, we can basically vary this 1 bit (as we just did) as well as next 4 bits altogether (5-bit variation). Hence possible /36 slices are: 2001:558:0000::/36 2001:558:1000::/36 2001:558:2000::/36 2001:558:3000::/36 and so on until 2001:558:f000::/36 (16 pools here) and next, 2001:559:0000::/36 2001:559:1000::/36 2001:559:2000::/36 2001:559:3000::/36 and so on until 2001:559:f000::/36 (16 pools here). Thus we get these 32 /36 blocks out of /31 allocations. That’s all about IPv6 subnetting. Once you understand this part, you should be just fine with subnetting in the future. 🙂 07 Jul Suddenly the voice market in India is becoming very interesting. Earlier it was the case of Jio (and competitors) launching unlimited voice plans and now it’s the case of Govt. of India permitting IP telephony. IP Telephony i.e networks where telephony happens over IP (not to be confused with IP to IP calls but) where IP to PSTN interconnects happen. Till a few months ago IP telephony (or IP-PSTN) interconnection was allowed only under certain conditions like doing it inside a building only for purpose of call centres (with OSP license) or running SIP trunks over private networks. Things like termination of calls originated from the apps was not allowed (where IP-PSTN was happening within India) as well as DID or Direct Inward Dialing numbers were not allowed. There were even cases where apps/businesses had to shut down due to confusing regulation. Here’s a nice article from Medianama about it. But all those were things of past. In May Wifi calling or calls via Wifi where wifi is used loosely and it’s essentially called via any sort of Internet connections were permitted (news here). Later after TRAI’s clarification it now has been formally allowed. While it may not look as attractive as it should have been in the age of WhatsApp calling (IP to IP, not PSTN mess involved!), it still is quite interesting and going to bring some major change. Here some of the upcoming things we all can expect to see in the next few months: 1. All key operators will launch native wifi call offload for flagship phones (Google Pixel, iPhone, Samsung Galaxy’s etc). This will offload a hell lot of voice traffic from the cell towards home wifi. Various fixed wired ISPs would now be carrying a significant chunk of voice traffic. 2. All key operators will launch an app for making phone calls and it would not only be for their users but also for other users. So while at this point one has to have a SIM card from the provider, next it would be sim card as well as “virtual connection” in form of a sort of KYC followed by an app essentially making use of SIP for call routing. 3. SIP trunks over IP networks will become common and that would be huge. In present times if someone needed 5-10 connections for official use with call haunting etc, it was either POTS analogue phones or PRIs (yuck!) or SIP trunks running over the private network. Going forward now it would be SIP trunks offered over the regular internet all would be facilitated via closed systems (apps and portals) as well as open systems based on SIP. This would help significantly to businesses which have direct customer interaction. 4. Market of DIDs or 10 digit virtual phone numbers will become very common. Telcos would be offering it directly and various platforms like Microsoft’s Skype, Google Voice, Vonage etc would also join in and resell those. An interesting case of above is BSNL’s recent announcement of their platform “Wings”. Though based on their usual track record of totally screwing up, I would keep my expectations low, but still offering seems interesting and gives an idea of the updated regulatory framework.

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# Why are the only numbers $m$ for which $n^{m+1}\equiv n \pmod{m}$ is true also unique for $\displaystyle\sum_{n=1}^{m}{n^m}\equiv 1 \bmod m$? It can be seen here that the only numbers for which $n^{m+1}\equiv n \pmod{m}$ is true are 1, 2, 6, 42, and 1806. Through experimentation, it has been found that $\displaystyle\sum_{n=1}^{m}{n^m}\equiv 1 \bmod m$ is true for those numbers, and (as yet unproven) no others. Why is this true? If there is a simple relation between $n^{m+1} \bmod{m}$ and $n^m \bmod{m}$, that would probably make this problem make more sense. It is obvious that $n^m \equiv 1 \pmod{\frac{m}{d}}$ (dividing out $n$ from both sides gives this result) for all $n$ on the interval $[1,m]$ where $d$ is a divisor of $m$. As a result of this, $n^m \bmod{m}$ takes on only values of the form $1+k \frac{m}{d} \pmod m$ where $k = -1, 0, 1$. How can it be shown that the sum of those values is equivalent to $1 \bmod{m}$? - Have you checked to see if the other entries of A007018 work? (Also, the second paragraph doesn't mean much; you are just subtracting 1 from both sides and using the fact that m^m is divisible by m. – Qiaochu Yuan Aug 29 '10 at 2:21 yeah, I only noted it due to the whole odd numbers lead to getting 0 when taken mod m. and the next entry is 3263442... I don't think I have the computational power to check it :\ – Eugene Bulkin Aug 29 '10 at 4:38 The next entry is 1806. Does it work? – Qiaochu Yuan Aug 29 '10 at 6:02 3263442 is wrong, the result of modding is 1807. Similarly, 47058 -> 5797, 3270666 -> 1811. – kennytm Aug 29 '10 at 7:28 Probably it is A014117? – kennytm Aug 29 '10 at 11:59 Well, I've made a full proof! Part 1 was solved here, and Part 2 was solved here. Lemma 1: Any integer $m$ which satisfies the original problem also satisfies $n^{m+1} \equiv n \bmod{m}$ for all $n$. Proof: Let $p$ be a prime dividing $m$. Then $\sum_{n=1}^mn^m\equiv1\pmod p$, so $(m/p)\sum_{n=1}^{p-1}n^m\equiv1\pmod p$, so $p^2$ doesn't divide $m$. Let $g$ be a primitive root mod $p$. Then $\sum_{n=1}^{p-1}n^m\equiv\sum_{r=0}^{p-2}g^{rm}$. That's a geometric series, it sums to $(1-g^{(p-1)m})/(1-g^m)$ which is zero mod $p$ - unless $g^m=1$, in which case it sums to $-1$ mod $p$. So we must have $p-1$ dividing $m$. Looking at $n^{m+1}\equiv n\pmod m$ and letting $n=p$, we see that $p^2$ cannot divide $m$. Now looking mod $p$, we get $n^{m+1}\equiv n\pmod p$. This is equivalent to $m+1\equiv1\pmod{p-1}$ (if $a^x \equiv a^y \bmod{n}$, then $x \equiv y \bmod{\varphi(n)}$ by Euler's theorem, and $\varphi(p) = p-1$), that is, $p-1$ divides $m$, so any integer $n^{m+1} \equiv n \bmod{m}$ as $p-1|m$ for all $m$ if $p|m$. Lemma 2: There are only a finite amount of integers $m$ which satisfy $n^{m+1} \equiv n \bmod{m}$ Proof: Since $p^2$ does not divide $m$, we may let $m = p_1 \ldots p_r$ with $p_1 < p_2 < \ldots < p_r$, with $p_i$ prime; as $p-1|m$ for all $p|m$, we say that $p_i-1|p_1 \ldots p_{i-1}$ for $i = 1, \ldots, r$. If we take $i = 1$, this forces $p_1-1|1$, so if $r \ge 1$, $p_1 = 2$. If $i = 2$, $p_2-1|2$, so if $r \ge 2$, $p_2 = 3$. Continuing, if $r \ge 3$, then $(p_3-1)|p_1 p_2 = 6$, so $p_3 = 7$; if $r \ge 4$, $(p_4 - 1)|p_1 p_2 p_3 = 42$, so $p_4 = 43$, as the numbers $d+1$ are not prime for other divisors $d$ of 42 larger than 6. If $r \ge 5$, then $(p_5 -1)|p_1 p_2 p_3 p_4 = 1806$, but 1, 2, 6 and 42 are the only divisors of 1806 with $d+1$ prime, so $p_5$ cannot exist. Therefore, $r \le 4$ and $m \in \{1, 2, 6, 42, 1806\}$. - I don't see how $n^{m+1} = n \mod m$ follows from $n^{m+1} = n \mod p$. Aren't those theorems etc useful only if $n$ and $m$ (or $p$) are co-prime? Care to explain a bit more? – Aryabhata Aug 31 '10 at 14:46 If $p$ divides $m$, then two things will be the same $\bmod{m}$ and $\bmod{p}$, I believe. And they work regardless of whether $n$ and $m$ are coprime, especially because $n$ is just a number from 1 to $m$. – Eugene Bulkin Aug 31 '10 at 22:18 @Eugene: Those theorem are not guaranteed to work if we remove the co-prime condition. Not sure why you think so. Do you have a reference? – Aryabhata Sep 2 '10 at 3:25 the only reference I really have is the link I added to the proof on mathoverflow. there is a more reliable proof (with bernoulli numbers) but that's a little too advanced, so I prefer this one. – Eugene Bulkin Sep 2 '10 at 15:39 As for the theorems: Let $a$, $b$, and $n$ be integers, and let $p$ be a prime dividing $n$. If $a \equiv b \bmod{n}$, then $a = b+j n$ where $j$ is any integer. Because $p|n$, $n = k p$ for some integer $k$, meaning $a = b + j k p$. Since $j k p$ is an integer multiple of $p$, it can be said that $a \equiv b \bmod{p}$. – Eugene Bulkin Sep 2 '10 at 22:20

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https://books.google.com.jm/books?qtid=127e7867&lr=&id=lA3A5XCCl_sC&sa=N&start=70

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Books Books The present worth of a note payable at a future time is such a sum as, put at interest at the given rate per cent, until it becomes due, will amount to the face of the note. Discount is an allowance made for the payment of money before it becomes due,... The Progressive Intellectual Arithmetic, on the Inductive Plan: Being a ... - Page 139 by Horatio Nelson Robinson - 1859 ## The Normal Standard Arithmetic: By Analysis and Induction, Designed ..., Part 2 Edward Brooks - Arithmetic - 1895 - 198 pages ...at the same rate it is \$5310; required the principal and the rate. DISCOUNT AND PRESENT WORTH. 473. Discount is an allowance made for the payment of money before it becomes due. 474. The Present Worth of a debt payable at a future time without interest is such a sum as, being... George Albert Wentworth - Arithmetic - 1898 - 424 pages ...into how many equal parts a unit is divided. Difference. The number found by subtraction. Discount. An allowance made for the payment of money before it becomes due. Also, the difference between the market value and the face value when the market value is below the... George Albert Wentworth - Arithmetic - 1898 - 424 pages ...into how many equal parts a unit is divided. Difference. The number found by subtraction. Discount. An allowance made for the payment of money before it becomes due. Also, the difference between the market value and the face value when the market value is below the... George Albert Wentworth - 1898 - 424 pages ...into how many equal parts a unit is divided. Difference. The number found by subtraction. Discount. An allowance made for the payment of money before it becomes due. Also, the difference between the market value and the face value when the market value is below the... Business - 1905 - 168 pages ...— All interest forfeited; 8 per cent; 12 per cent; grace on all negotiable instruments. DISCOUNT. Discount is an allowance made for the payment of money before it becomes due, and is either the interest on the debt for the time, which is called true discount, or upon such a sum as...

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https://www.airmilescalculator.com/distance/gom-to-nla/

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# How far is Ndola from Goma? The distance between Goma (Goma International Airport) and Ndola (Simon Mwansa Kapwepwe International Airport) is 779 miles / 1254 kilometers / 677 nautical miles. The driving distance from Goma (GOM) to Ndola (NLA) is 1232 miles / 1983 kilometers, and travel time by car is about 32 hours 10 minutes. 779 Miles 1254 Kilometers 677 Nautical miles 1 h 58 min 133 kg ## Distance from Goma to Ndola There are several ways to calculate the distance from Goma to Ndola. Here are two standard methods: Vincenty's formula (applied above) • 779.414 miles • 1254.346 kilometers • 677.293 nautical miles Vincenty's formula calculates the distance between latitude/longitude points on the earth's surface using an ellipsoidal model of the planet. Haversine formula • 783.624 miles • 1261.121 kilometers • 680.951 nautical miles The haversine formula calculates the distance between latitude/longitude points assuming a spherical earth (great-circle distance – the shortest distance between two points). ## How long does it take to fly from Goma to Ndola? The estimated flight time from Goma International Airport to Simon Mwansa Kapwepwe International Airport is 1 hour and 58 minutes. ## What is the time difference between Goma and Ndola? There is no time difference between Goma and Ndola. ## Flight carbon footprint between Goma International Airport (GOM) and Simon Mwansa Kapwepwe International Airport (NLA) On average, flying from Goma to Ndola generates about 133 kg of CO2 per passenger, and 133 kilograms equals 293 pounds (lbs). The figures are estimates and include only the CO2 generated by burning jet fuel. ## Map of flight path and driving directions from Goma to Ndola See the map of the shortest flight path between Goma International Airport (GOM) and Simon Mwansa Kapwepwe International Airport (NLA). ## Airport information Origin Goma International Airport City: Goma Country: Congo (Kinshasa) IATA Code: GOM ICAO Code: FZNA Coordinates: 1°40′14″S, 29°14′18″E Destination Simon Mwansa Kapwepwe International Airport City: Ndola Country: Zambia IATA Code: NLA ICAO Code: FLSK Coordinates: 12°59′53″S, 28°39′53″E

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https://www.physicsforums.com/threads/time-dependent-pertubation-theory.644794/

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# Time dependent pertubation theory 1. Oct 17, 2012 ### Kontilera Okey, so I´m taking a course in QM and I feel that I got a grip of most of it. But then we arrive at this formulea $$i\hbar\frac{\partial}{\partial t} c_n(t) = \sum_m \hat{V}_{nm} e^{i\omega_{nm} t}c_m(t),$$ where $$\omega_{nm} \equiv \frac{(E_n - E_m)}{\hbar}.$$ In other words time dependent pertubation theory. And I just feel confused. I dont know how to start tackle it with my intuition. What are, in your opinion, the first intuitional things I should remark when it comes to this equation? What does it tell about my physics without having to do some big derivations? Thanks! 2. Oct 18, 2012 ### Jano L. The equation is a consequence of time-dependent Schrodinger equation. It is a rule that the expansion coefficients c_n obey. This equation can be used to find approximate values of c's, and afterwards these can be used to find average values of physical quantities. Does this help? 3. Oct 19, 2012 ### geoduck I think intuitively Vnm represents scattering channels, a coupling of an m state to an n state in the interaction picture. The bigger the V, the bigger the coupling. The fact that V nm depends on time is not that important.

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https://acmore.cc/problem/POJ/1005

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# 1005：I Think I Need a Houseboat ###### 题目描述 Fred Mapper is considering purchasing some land in Louisiana to build his house on. In the process of investigating the land, he learned that the state of Louisiana is actually shrinking by 50 square miles each year, due to erosion caused by the Mississippi River. Since Fred is hoping to live in this house the rest of his life, he needs to know if his land is going to be lost to erosion. After doing more research, Fred has learned that the land that is being lost forms a semicircle. This semicircle is part of a circle centered at (0,0), with the line that bisects the circle being the X axis. Locations below the X axis are in the water. The semicircle has an area of 0 at the beginning of year 1. (Semicircle illustrated in the Figure.) ###### 输入解释 The first line of input will be a positive integer indicating how many data sets will be included (N). Each of the next N lines will contain the X and Y Cartesian coordinates of the land Fred is considering. These will be floating point numbers measured in miles. The Y coordinate will be non-negative. (0,0) will not be given. ###### 输出解释 For each data set, a single line of output should appear. This line should take the form of: “Property N: This property will begin eroding in year Z.” Where N is the data set (counting from 1), and Z is the first year (start from 1) this property will be within the semicircle AT THE END OF YEAR Z. Z must be an integer. After the last data set, this should print out “END OF OUTPUT.” ###### 输入样例 2 1.0 1.0 25.0 0.0 ###### 输出样例 Property 1: This property will begin eroding in year 1. Property 2: This property will begin eroding in year 20. END OF OUTPUT. ###### 提示 1.No property will appear exactly on the semicircle boundary: it will either be inside or outside. 2.This problem will be judged automatically. Your answer must match exactly, including the capitalization, punctuation, and white-space. This includes the periods at the ends of the lines. 3.All locations are given in miles. 时间上限 内存上限 1000 10000

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http://www.encyclopedia4u.com/a/affine-space.html

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ENCYCLOPEDIA 4U .com Web Encyclopedia4u.com # Affine space In mathematics, and affine space may be defined somewhat abstractly as a set on which a vector space acts transitively. Albeit somewhat jocular, the following characterization may be easier to understand: an affine space is what is left of a vector space after you've forgotten which point is the origin. Imagine that Smith knows that a certain point is the origin, and Jones believes that another point -- call it p -- is the origin. Two vectors, a and b are to be added. Jones draws an arrow from p to a and another arrow from p to b, and completes the parallelogram to find what Jones thinks is a + b, but is actually p + (ap) + (bp). Similarly, Jones and Smith may evaluate any linear combination of a and b, or of any finite set of vectors, and will generally get different answers. However -- and note this well: If the sum of the coefficients in a linear combination is 1, then Smith and Jones will agree on the answer! The proof is a routine exercise. Here is the punch line: Smith knows the "linear structure", but both Smith and Jones know the "affine structure" -- i.e., the values of affine combinations, defined as linear combinations in which the sum of the coefficients is 1. An underlying set with an affine structure is an affine space.

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https://superuser.com/questions/125530/scientific-notation-in-excel

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# Scientific notation in Excel I need make a number format similar to scientific notation, but without E nor e. Just classic like this: (In latex it's 2.3\times10^3) Maybe Excel doesn't support this format. (I have on mind Number Format - for hundreds numbers - not in math formula) ## migrated from stackoverflow.comMar 29 '10 at 22:52 This question came from our site for professional and enthusiast programmers. You could use html. Type this into Notepad <html>2.34 x 10^-5 + 5.67 x 10<sup>-6</html> Copy it and, in Excel, Paste Special - Unicode. It will render whatever html you have. You won't be able to edit it in Excel though. • – dkusleika Mar 29 '10 at 20:09 • Great idea. So in excel: ="<html>"&B6/(10^ROUND(LOG10(ABS(B6));0))&" x 10^{"&ROUND(LOG10(ABS(B6));0)&"}</html>" then result copy into notepad and copy back to excel. Thanks – Vojtech R. Mar 29 '10 at 20:53 Excel doesn't support that number format. I think you need to use a formula, like this: =A1/(10^ROUND(LOG10(ABS(A1)),0))&" x 10^"&ROUND(LOG10(ABS(A1)),0) • Nice. But dont produce typographically correct output. Result is "0,9994 x 10^1". How I can replace ^1 by really top index 1? – Vojtech R. Mar 29 '10 at 20:05 • You'd have to write a macro if you want to get rid of the ^ and have the exponent be superscript. – devuxer Mar 29 '10 at 20:30 • Thanks for help. I cannot select 2 accepted answers. Its weird, because solutions is combination of yours and dkusleika tips. – Vojtech R. Mar 29 '10 at 20:55 • @Vojtech, No problem...I think his answer is pretty cool. You can give us both an upvote though if you like. (Click the arrow above the gray number for each question). – devuxer Mar 29 '10 at 21:07 • you can use Unicode superscript ⁰¹²³⁴⁵⁶⁷⁸⁹ to have a top number instead of ^ – phuclv Apr 27 at 8:03 Probably not the best location for this question, but these links might help: http://peltiertech.com/Excel/NumberFormats.html http://www.ozgrid.com/Excel/CustomFormats.htm I have used both sites as a reference when dealing with Excel stuff in the past.

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https://www.experts-exchange.com/questions/26553159/How-do-I-display-the-smallest-number-in-a-collection.html

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# How do I display the smallest number in a collection? on I keep getting an error at public void displaySmallest() This is my code: import java.util.ArrayList; public class Numbers { private ArrayList<Double> numbers; public Numbers() { numbers = new ArrayList<Double>(); } /** *Add a number to the collection in a client specified position or at the end of the collection */ { } /** * Display all numbers in the collection */ public void displayNumbers() { int number = 0; while (number < numbers.size()) { System.out.println(numbers.get(number)); number++; } } /** * Display all numbers in the collection organized in 2 categories, first the positive numbers, second the *negative numbers */ public void displayNumbersInCategories() { System.out.println("Positive Numbers"); int number = 0; while (number < numbers.size()) { if (numbers.get(number) >= 0.0) { System.out.println(numbers.get(number)); } number++; } System.out.println("Negative Numbers"); for (Double aNumber : numbers) { if (aNumber < 0.0) { System.out.println(aNumber); } } } /** * Display the sum of all numbers in the collection */ public void displaySum() { double sum = 0.0; int length = this.numbers.size(); int counter = 0; while (counter < length) { sum = sum + this.numbers.get(counter); counter++; } System.out.println(sum); } /** * Display 2 sums: the sum of all positive numbers in the collection and the sum of all negative numbers in * the collection */ public void displaySumsInCategories() { double sum = 0.0; int length = this.numbers.size(); int counter = 0; System.out.println("Positive Numbers"); while (counter < length) { sum = sum + this.numbers.get(counter); counter++; } System.out.println(sum); //} System.out.println("Negative Numbers"); for (Double aSum : numbers) { if (aSum < 0.0) { System.out.println(aSum); } } } /** * Display the average of all the positive numbers */ public void displayPositiveAvg() { double sum = 0.0; int count = 0; for(Double number : numbers) { if(number > 0.0) { sum += number; count++; } } System.out.println("Average is " + (sum / count)); } } /** * Display the smallest number in the collection */ public void displaySmallestNumber() Double smallest = Double.MAX_VALUE; for (Double aNumber : numbers) { if (aNumber < smallest) { smallest = aNumber; } } System.out.println("value" + smallest); } Comment Watch Question Do more with EXPERT OFFICE® is a registered trademark of EXPERTS EXCHANGE® Commented: you need to move some brackets around. After displayPositiveInteger you need to put that bracket at the end. You need one after displaySmallestNumber and at the end of it to close the class. ``````System.out.println("Average is " + (sum / count)); } /** * Display the smallest number in the collection */ public void displaySmallestNumber(){ Double smallest = Double.MAX_VALUE; for (Double aNumber : numbers) { if (aNumber < smallest) { smallest = aNumber; } } System.out.println("value" + smallest); } } `````` Commented: isn't it the same question as? http://www.experts-exchange.com/Programming/Languages/Java/New_to_Java/Q_26553146.html#a33935056

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https://my.numworks.com/python/schraf/decpi

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# decpi.py Created by schraf Created on March 19, 2024 777 Bytes ```e, d, b, f = 5488, 0, 0, 0 a = [0 for i in range(165)] while e > 0: for i in range(164, -1, -1): b = round((a[i] % 1) * e + d / 1e5, 6) c = round((int(a[i]) * e + int(b)) / 1e5, 6) d = int(c) a[i] = round((c - d) * 1e5 + b % 1, 6) e = 2 * e + 1 for i in range(165): b = int((d * 1e5 + int(a[i])) / e) d = round(d * 1e5 + int(a[i]) - b * e, 6) c = int(((d + round(a[i] % 1, 6)) * 1e5) / e) d = round((d + round(a[i] % 1, 6)) * 1e5 - c * e, 6) a[i] = round(b + c / 1e5, 6) a[0] = round(a[0] + 2e4, 6) e = (e - 3) / 2 d = 0 if e % 1000 == 0: print(e) for i in range(165): s = ("000000"+str(int(a[i]*1e5)))[-10:] print(s) if i % 10 == 0 and i > 0: input()```

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https://chillimath.com/pair-of-linear-equations-in-two-variables-class-10-mcq-test-100301/

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chillimath.com ## Pair of Linear Equations in Two Variables Class 10 Multiple Choice Test /10 0 votes, 0 avg 20 Get ready to be challenged Thank you for answering the multiple choice test Pair of Linear Equations in Two Variables Class 10 (100301) Challenge Yourself … 1 / 10 The pair of equations x = 0 and x = 7 has: (a) two solutions (b) no solution (c) infinitely many solutions (d) one solution 2 / 10 In the equations $$a_1x+b_1y+c_1=0$$ and $$a_2x+b_2y+c_2=0$$, if $${\frac{a_1}{a_2}}\ne{\frac{b_1}{b_2}}$$, then the equations will represent: (a) coincident lines (b) parallel lines (c) intersecting lines (d) none 3 / 10 The pair of linear equations x – 2y = 0 and 3x + 4y = 20 have: (a) one solution (b) two solutions (c) many solutions (d) no solution 4 / 10 The father’s age is six times his son’s age. Four years hence, the age of the father will be four times his son’s age. The present ages in years of the son and the father respectively are: (a) 4 and 24 (b) 6 and 36 (c) 5 and 30 (d) 7 and 42 5 / 10 For what value of k, do the equations 3x – y + 8 = 0 and 6x – ky = –16, represent coincident lines? (a) $$1\over 2$$ (b) $$-1\over 2$$ (c) 2 (d) − 2 6 / 10 A pair of linear equations which has a unique solution x = 2, y = –3 is: (a) x + y = –1, 2x – 3y = –5 (b) 2x + 5y = –11, 4x + 10y = –22 (c) 2x – y = 1, 3x + 2y = 0 (d) x – 4y – 14 = 0, 5x – y – 13 = 0 7 / 10 The pair of linear equations 2x + 5y = –11 and 5x + 15y = –44 has: (a) many solutions (b) no solution (c) one solution (d) 2 solutions 8 / 10 The sum of the digits of a two-digit number is 9. If 27 is added to it, digits of the number get reversed. The number is: (a) 63 (b) 72 (c) 81 (d) 36 9 / 10 The pair of equations 5x – 15y = 8 and $$3x-9y=\frac{24}{5}$$ has: (a) one solution (b) two solutions (c) infinitely many solutions (d) no solution 10 / 10 If a pair of linear equations is consistent, then the lines will be: (a) always intersecting (b) always coincident (c) intersecting or coincident (d) parallel

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# Pre-Calculus posted by . Can you show me how to find the rectangular equation: r=2cos(theta) + 3 sin (theta) All I need is an example to work off I was absent today from Pre-Calc and I have homework to do and no explanation with them-Please help with this one Thank you • Pre-Calculus - sqrt(x^2+y^2) = 2 x/sqrt(x^2+y^2)+3y/sqrt(x^2+y^2) x^2+y^2 = 2 x + 3 y y^2 - 3 y = -x^2 + 2 x • Pre-Calculus - Thank you

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## Max moves in a position Discussion of chess software programming and technical issues. Moderators: hgm, Harvey Williamson, bob Forum rules This textbox is used to restore diagrams posted with the [d] tag before the upgrade. lauriet Posts: 162 Joined: Sun Nov 03, 2013 8:32 am Contact: ### Max moves in a position Hi All, Does anyone know the maximum possible moves in a position (any position). I am working on my move gen and want to allow enough spots in the array, but not too many. Thanks Laurie. Milos Posts: 3291 Joined: Wed Nov 25, 2009 12:47 am ### Re: Max moves in a position uint8 will suffice. AlvaroBegue Posts: 913 Joined: Tue Mar 09, 2010 2:46 pm Location: New York Full name: Álvaro Begué (RuyDos) ### Re: Max moves in a position I believe 218 is the right number, but I am not sure if it is the maximum known or if it is known to be the maximum. I use 256 entries in an array that holds the moves. Evert Posts: 2909 Joined: Fri Jan 21, 2011 11:42 pm Location: NL Contact: ### Re: Max moves in a position lauriet wrote: Does anyone know the maximum possible moves in a position (any position). I am working on my move gen and want to allow enough spots in the array, but not too many. As mentioned, the maximum seems to be 218 for chess. Using maximum number of moves on an empty board and ignoring blockers, you get an upper limit of 300 moves or so. Having said that, if you don't allocate your move list on the stack, but in an array indexed by ply level, there is no reason not to grow the list dynamically. The few times you need to realloc() it are insignificant. I do this in SjaakII, which can play variants where the number of moves can be several hundred or a thousand in actual middle-game positions. hgm Posts: 23000 Joined: Fri Mar 10, 2006 9:06 am Location: Amsterdam Full name: H G Muller Contact: ### Re: Max moves in a position I usually keep a dedicated software stack for moves. Because there is virtually no performance penalty on leaving contiguous chunks of memory unused (as these would never be cached, and it is cache space that is the scarce resource), I skip some 200 bytes between the move list of the previous ply and a new one for the next. That allows me to grow the list in two directions during generation and sorting. So that the captures can be added to the front of the list, (in the gap) and the non-captures to the end (at the topof the stack). syzygy Posts: 4375 Joined: Tue Feb 28, 2012 10:56 pm ### Re: Max moves in a position hgm wrote:I usually keep a dedicated software stack for moves. Because there is virtually no performance penalty on leaving contiguous chunks of memory unused (as these would never be cached, and it is cache space that is the scarce resource), I skip some 200 bytes between the move list of the previous ply and a new one for the next. That allows me to grow the list in two directions during generation and sorting. So that the captures can be added to the front of the list, (in the gap) and the non-captures to the end (at the topof the stack). Wouldn't that lose 64 bytes of cache per ply on average? Hardware prefetching might mean the loss is higher. bob Posts: 20358 Joined: Mon Feb 27, 2006 6:30 pm Location: Birmingham, AL ### Re: Max moves in a position AlvaroBegue wrote:I believe 218 is the right number, but I am not sure if it is the maximum known or if it is known to be the maximum. I use 256 entries in an array that holds the moves. That's the maximum that has been found. No formal proof of what is the actual maximum possible. bob Posts: 20358 Joined: Mon Feb 27, 2006 6:30 pm Location: Birmingham, AL ### Re: Max moves in a position hgm wrote:I usually keep a dedicated software stack for moves. Because there is virtually no performance penalty on leaving contiguous chunks of memory unused (as these would never be cached, and it is cache space that is the scarce resource), I skip some 200 bytes between the move list of the previous ply and a new one for the next. That allows me to grow the list in two directions during generation and sorting. So that the captures can be added to the front of the list, (in the gap) and the non-captures to the end (at the topof the stack). There can be a performance hit here. If you go too far with this spacing, you can effectively reduce the size of cache to 50% or 25%, because the set associativity still relies on direct mapping. IE if you allow 4K bytes per ply of moves (1K moves) but only use the first 800 bytes, you have a bunch of memory blocks that alias to the same cache set unnecessarily. Once you blow the set size, you thrash unnecessarily. This is the trick my architecture class had to figure out in order to measure set associativity on an unknown machine, no CPUID allowed. hgm Posts: 23000 Joined: Fri Mar 10, 2006 9:06 am Location: Amsterdam Full name: H G Muller Contact: ### Re: Max moves in a position syzygy wrote:Wouldn't that lose 64 bytes of cache per ply on average? Indeed, but that is a pretty small price. The move stack is not terribly frequently accessed data, not even the list for the current node. If you use five move lists near the top of the stack frequently enough that it would matter whether it is cached, or flushes something out when you access it, you would waste 320 bytes = 1% of L1. Hardware prefetching might mean the loss is higher. I though hardware prefetching was only done from DRAM, not between cache levels. bob Posts: 20358 Joined: Mon Feb 27, 2006 6:30 pm Location: Birmingham, AL ### Re: Max moves in a position hgm wrote: syzygy wrote:Wouldn't that lose 64 bytes of cache per ply on average? Indeed, but that is a pretty small price. The move stack is not terribly frequently accessed data, not even the list for the current node. If you use five move lists near the top of the stack frequently enough that it would matter whether it is cached, or flushes something out when you access it, you would waste 320 bytes = 1% of L1. Hardware prefetching might mean the loss is higher. I though hardware prefetching was only done from DRAM, not between cache levels. There are lots of variations, but in general, prefetching applies everywhere. IE L1 will prefetch from L2, etc. I believe there are some hardware controls on this stuff but I have not been interested enough to do the zillion experiments necessary to figure out the effects.

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# How can there be net linear momentum in a static electromagnetic field (not propagating)? I understand from basic conservation of energy and momentum considerations, it is clear in classical electrodynamics that the fields should be able to have energy and momentum. This leads to the usual Poynting vector and energy density relations for electromagnetic fields. However, I do not know how to interpret situations where there is a net linear momentum in a static electromagnetic field. The fields aren't propagating. It doesn't make sense to me that momentum can be divorced from motion. As a concrete example to discuss: Consider a massless string of length $L,$ with a spherical shell on each end with a magnetic dipole moment m and positive charge q. The radius of the sphere $R\ll L,$ or alternatively, consider the dipoles to be perfect "point" dipoles. Let the string be along the $y$ axis, with one dipole at the origin and the other at $y=+L.$ If the magnetic dipole at the origin is oriented in the $-z$ direction, and the other dipole in the $+z$ direction, if you calculate the total linear momentum in the fields, the answer is: $$p_\text{em} = m q \frac{\mu_0}{2 \pi L^2}\, \hat{x}$$ While this is an unstable equilibrium, it is an equilibrium. So classically the state can remain static with no need to evoke other external entities, interactions, etcetera. So there doesn't seem to be any of the usual potential pitfalls to save us here. Please, can someone explain how a static field can have momentum? - A static field does not propagate? Consider a new particle was created now (a pair). Do you think that its gravitational and electrostatic field influences the whole universe in no time or, as I think, they will propagate at c speed? – Helder Velez Mar 19 '11 at 12:34 I mean static in the usual sense. static = not changing in time. Your example is not a static field, as a field spreading out is clearly changing in time. – Edward Mar 19 '11 at 12:56 This is a fairly subtle question! Griffiths recently published a paper on this. Electromagnetic fields carry energy, momentum, and angular momentum. The momentum density, $ϵ_{0}(E\times B)$, accounts (among other things) for the pressure of light. But even static fields can carry momentum, and this would appear to contradict a general theorem that the total momentum of a closed system is zero if its center of energy is at rest. In such cases, there must be some other (nonelectromagnetic) momenta that cancel the field momentum. What is the nature of this “hidden momentum” and what happens to it when the electromagnetic fields are turned off? EDIT: Free version of the above link. - This is link only. – akrasia Aug 25 '14 at 21:50 It sure is! Tough to do better than Griffiths. – Andrew Aug 26 '14 at 0:10 I think the problem here is that the "massless string" actually requires electromagnetic forces to hold the two charges together. My preliminary calculations (which i need to refine but think are fundamentally correct) show that if you replace the string with a charge of -(1/4)q halfway between the two charges of q, the integral of ExB is zero. This extra charge would result in electrostatic equilibrium and would supply the electrostatic force not supplied mathematically by the massless string. - Nonzero Momentum in static field configuration is actually a good thing. Consider a coaxial cable carrying DC current and voltage. Internally it has a constant E and H field. The Poynting flux is nonzero and shows that there is energy transport. The energy flow is indeed in the direction ExH. The fact that the field configuration shows no movement is irrelevant. Momentum is moving energy, not something else moving! -- Jos - Momentum is a conserved quantity that belongs to a system. When particles are in motion the usual linear and angular moment In the image of the dipole of the water molecule here Electric_dipole_moment WP you see that the molecule is subject permanently to a tension (red in the image). The definition of the Electric Dipole moment is a measure of the separation of positive and negative electrical charges in a system of charges, that is, a measure of the charge system's overall polarity. In the simple case of two point charges, one with charge +q and one with charge −q, the electric dipole moment p is: dipole moment ~ charge * distance (of charges) compare this with Angular moment angular moment ~ linear moment * distance (to a point) where linear moment ~ mass * velocity as both charge and l.m. are states of the particle in a given moment that represent a potential for action, both formulas of angular and dipole moments are quite similar. - How does this answer the question? – Marek Mar 19 '11 at 16:05 It is possible to show that the total momentum of any static system is zero in an inertial frame where nothing is moving. This does not mean that the momenta associated with various components of that system are individually zero. As you point out, there can be finite electromagnetic momentum associated with static charge distributions. Even though there is no obvious motion in the system, the momentum associated with the matter distribution is actually nonzero. It is equal and opposite to the electromagnetic momentum. This is often referred to as the hidden mechanical momentum. It is a special case of a much more general result that the net momentum of an extended object need not be parallel to its center of mass velocity. Electrodynamics books like Griffiths or Jackson have a nice microscopic interpretation for this effect in the simple case of a magnetic dipole placed near a charge. Internally, the dipole may be thought of as containing a current loop. The charges in this current loop accelerate and decelerate in response to the external electric field. One may show that this gives them a net momentum that is exactly equal and opposite to the electromagnetic momentum. Note that this is an intrinsically relativistic effect. It does not arise if Lorentz factors are neglected when computing the momenta of the circulating charges. - Your answer tells me that the total momentum of the system is zero, because there is mechanical momentum to balance the field momentum, and then give details on the mechanical momentum. This is not what I was asking though. The issue is that the field has momentum, but is not propagating at all. Please focus on the field. – Edward Mar 19 '11 at 13:59 I was trying to point out that it is only the total momentum that needs to be zero. There is no requirement that the various interacting components of a static system individually have zero momenta. If the field did not have any momentum in your example, the system's total momentum would be nonzero. I think you'd agree that this situation would be worse. Additionally, one might want to say that there is some ambiguity in splitting up the momentum between various parts of an interacting system. It is only the total that matters. – Stingray Mar 19 '11 at 14:09 ## protected by Qmechanic♦May 29 '13 at 5:39 Thank you for your interest in this question. Because it has attracted low-quality or spam answers that had to be removed, posting an answer now requires 10 reputation on this site.

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# Search by Topic #### Resources tagged with Maths Supporting SET similar to Reaction Timer: Filter by: Content type: Stage: Challenge level: ### There are 68 results Broad Topics > Applications > Maths Supporting SET ### Olympic Records ##### Stage: 3 Challenge Level: Can you deduce which Olympic athletics events are represented by the graphs? ### How Would You Score It? ##### Stage: 3 Challenge Level: Invent a scoring system for a 'guess the weight' competition. ### Investigating the Dilution Series ##### Stage: 4 Challenge Level: Which dilutions can you make using only 10ml pipettes? ### Approximately Certain ##### Stage: 4 and 5 Challenge Level: Estimate these curious quantities sufficiently accurately that you can rank them in order of size ### Bigger or Smaller? ##### Stage: 4 Challenge Level: When you change the units, do the numbers get bigger or smaller? ##### Stage: 4 Challenge Level: Which units would you choose best to fit these situations? ##### Stage: 3 Challenge Level: Is it cheaper to cook a meal from scratch or to buy a ready meal? What difference does the number of people you're cooking for make? ### Pinhole Camera ##### Stage: 3 Challenge Level: Make your own pinhole camera for safe observation of the sun, and find out how it works. ##### Stage: 3 Challenge Level: Can you work out which drink has the stronger flavour? ### A Question of Scale ##### Stage: 4 Challenge Level: Use your skill and knowledge to place various scientific lengths in order of size. Can you judge the length of objects with sizes ranging from 1 Angstrom to 1 million km with no wrong attempts? ### Does This Sound about Right? ##### Stage: 3 Challenge Level: Examine these estimates. 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Try out public health policies to control the spread of the epidemic, to minimise the number of sick days and deaths.

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DID YOU KNOW: Seamlessly assign resources as digital activities Learn how in 5 minutes with a tutorial resource. Try it Now Sentence Stems for Number Talk Routines and Math Warm Ups Grade Levels K - 1st Subjects Resource Type Formats Included • PDF Pages 18 posters, 3 info pages Description Math routines are one of the most powerful pieces of math instruction. Number talks and math warm ups provide students with the chance to see math in many ways, explain their thinking, and grow their math confidence. These sentence stems were created to support students' academic language and give scaffolds for explaining their math ideas. This resource includes a link to a blog post that explains each of these math routines in detail, how to start them, what to expect, and ways to scaffold for your various learners. You will use these sentence stems for each of the math routines described. As we continue to learn about more math routines, they will be added to the blog post and sentence stems will be added to this resource! Click here to read about how these math routines fit in with the math rotations we currently use. Included are 9 different sentence stem posters (18 total) for these types of math routines: Number Talks: -Counting: Sequencing and Number Chart -Joining and Addition -Separating and Subtraction -Composing Numbers -Decomposing Numbers -Comparing Numbers -Equal Equations (True/False) Math Warm Ups: -Which One Doesn't Belong? Working on argumentation and multiple points of view -Describe, Draw, Describe (DDD) Working on shapes, position words, measurement, and motion These sentence stems come in color and black and white! You can also enlarge the prints to poster size at your local copy store for anchor chart sized posters! I hope you give math routines a try in your classroom. Using these routines in conjunction with these sentence stems have taken my students to another level in their understanding of math. If you have any further questions or would like more explanation about using this product, please ask in the Q&A section or email me at researchandplay@gmail.com. Thank you for your purchase! Remember to leave feedback in order to receive credits for future products! Don't forget to follow my store for updates and so you do not miss any new products! Holly @ Research and Play Total Pages 18 posters, 3 info pages Answer Key N/A Teaching Duration N/A Report this Resource to TpT Reported resources will be reviewed by our team. Report this resource to let us know if this resource violates TpT’s content guidelines. Questions & Answers 2.9k Followers Teachers Pay Teachers is an online marketplace where teachers buy and sell original educational materials. More About Us

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0 How far away from its starting point would a truck be in 3 hours if its average speed was 100 kilometers an hour? Updated: 10/31/2022 Wiki User 13y ago 100 km/hr x 3 hrs = 300 km from starting point Wiki User 13y ago Earn +20 pts Q: How far away from its starting point would a truck be in 3 hours if its average speed was 100 kilometers an hour? Submit Still have questions? Related questions A man moves 3 kilometers east from his starting point then he travels 5 kilometers north From that point he moves 8 kilometers to the east How far is he from his starting point? Using the Pythagorean theorem, the distance from the starting point is the square root of (3^2 + 5^2), which is √34 kilometers or approximately 5.83 kilometers. When does average velocity becomes 0? At the starting point and whenever you return to the starting point. How many kilometers driving distance between Calgary and Tulsa? The distance between the starting point and the destination is 2,872km, (1,791.4 mi), and will take approximately 28 hours of driving time. 3 kilometres! What is the distance in kilometers from Prince George BC to Regina Saskatchewan? The distance between the starting point and the destination is 1,535km, (954 mi), and will take approximately 16 hours 16 minutes of driving time. How many road kilometers from Washington to New Orleans? The distance between the starting point and the destination is 1,745 km, (1,084 mi), and with reasonable traffic conditions it will take approximately 16 hours 45 minutes of driving time. 7 feet. Can average velocity of a moving body can be zero? It actually can. Say a car moves north at 50 miles per hour for 4 hours. Then it moves south at 50 miles per hour for 4 hours. In the end, it returns to it's starting point. The average velocity over that 8 hour period is then zero, because it really went nowhere. How many hours is it from Puebla to Mexico City? Minimum distance is about 568 kilometers (353 miles) on a straight line, while road distance is approximately 663 kilometers (412 miles). Flight time would be approximately one hour, while driving time is approximately 7 hours. How many hours does it take to drive to reno in a car on the 80? Yeah, no one knows where your starting point is, so we can't help you until you provide us with a starting point.

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# [name] Represents an axis-aligned bounding box (AABB) in 2D space. ## Constructor ### [name]( [param:Vector2 min], [param:Vector2 max] ) [page:Vector2 min] - (optional) [page:Vector2] representing the lower (x, y) boundary of the box. Default is ( + Infinity, + Infinity ). [page:Vector2 max] - (optional) [page:Vector2] representing the upper (x, y) boundary of the box. Default is ( - Infinity, - Infinity ). Creates a [name] bounded by min and max. ## Properties ### [property:Vector2 min] [page:Vector2] representing the lower (x, y) boundary of the box. Default is ( + Infinity, + Infinity ). ### [property:Vector2 max] [page:Vector2] representing the lower upper (x, y) boundary of the box. Default is ( - Infinity, - Infinity ). ## Methods ### [method:Vector2 clampPoint]( [param:Vector2 point], [param:Vector2 target] ) [page:Vector2 point] - [page:Vector2] to clamp. [page:Vector2 target] — the result will be copied into this Vector2. [link:https://en.wikipedia.org/wiki/Clamping_(graphics) Clamps] the [page:Vector2 point] within the bounds of this box. ### [method:Box2 clone]() Returns a new [page:Box2] with the same [page:.min min] and [page:.max max] as this one. ### [method:Boolean containsBox]( [param:Box2 box] ) [page:Box2 box] - [page:Box2 Box2] to test for inclusion. Returns true if this box includes the entirety of [page:Box2 box]. If this and [page:Box2 box] are identical, this function also returns true. ### [method:Boolean containsPoint]( [param:Vector2 point] ) [page:Vector2 point] - [page:Vector2] to check for inclusion. Returns true if the specified [page:Vector2 point] lies within or on the boundaries of this box. ### [method:Box2 copy]( [param:Box2 box] ) Copies the [page:.min min] and [page:.max max] from [page:Box2 box] to this box. ### [method:Float distanceToPoint]( [param:Vector2 point] ) [page:Vector2 point] - [page:Vector2] to measure distance to. Returns the distance from any edge of this box to the specified point. If the [page:Vector2 point] lies inside of this box, the distance will be 0. ### [method:Boolean equals]( [param:Box2 box] ) [page:Box2 box] - Box to compare with this one. Returns true if this box and [page:Box2 box] share the same lower and upper bounds. ### [method:Box2 expandByPoint]( [param:Vector2 point] ) [page:Vector2 point] - [page:Vector2] that should be included in the box. Expands the boundaries of this box to include [page:Vector2 point]. ### [method:Box2 expandByScalar]( [param:Float scalar] ) [page:Float scalar] - Distance to expand the box by. Expands each dimension of the box by [page:Float scalar]. If negative, the dimensions of the box will be contracted. ### [method:Box2 expandByVector]( [param:Vector2 vector] ) [page:Vector2 vector] - [page:Vector2] to expand the box by. Expands this box equilaterally by [page:Vector2 vector]. The width of this box will be expanded by the x component of [page:Vector2 vector] in both directions. The height of this box will be expanded by the y component of [page:Vector2 vector] in both directions. ### [method:Vector2 getCenter]( [param:Vector2 target] ) [page:Vector2 target] — the result will be copied into this Vector2. Returns the center point of the box as a [page:Vector2]. ### [method:Vector2 getParameter]( [param:Vector2 point], [param:Vector2 target] ) [page:Vector2 point] - [page:Vector2]. [page:Vector2 target] — the result will be copied into this Vector2. Returns a point as a proportion of this box's width and height. ### [method:Vector2 getSize]( [param:Vector2 target] ) [page:Vector2 target] — the result will be copied into this Vector2. Returns the width and height of this box. ### [method:Box2 intersect]( [param:Box2 box] ) [page:Box2 box] - Box to intersect with. Returns the intersection of this and [page:Box2 box], setting the upper bound of this box to the lesser of the two boxes' upper bounds and the lower bound of this box to the greater of the two boxes' lower bounds. ### [method:Boolean intersectsBox]( [param:Box2 box] ) [page:Box2 box] - Box to check for intersection against. Determines whether or not this box intersects [page:Box2 box]. ### [method:Boolean isEmpty]() Returns true if this box includes zero points within its bounds. Note that a box with equal lower and upper bounds still includes one point, the one both bounds share. ### [method:Box2 makeEmpty]() Makes this box empty. ### [method:Box2 set]( [param:Vector2 min], [param:Vector2 max] ) [page:Vector2 min] - (required ) [page:Vector2] representing the lower (x, y) boundary of the box. [page:Vector2 max] - (required) [page:Vector2] representing the upper (x, y) boundary of the box. Sets the lower and upper (x, y) boundaries of this box. Please note that this method only copies the values from the given objects. ### [method:Box2 setFromCenterAndSize]( [param:Vector2 center], [param:Vector2 size] ) [page:Vector2 center] - Desired center position of the box ([page:Vector2]). [page:Vector2 size] - Desired x and y dimensions of the box ([page:Vector2]). Centers this box on [page:Vector2 center] and sets this box's width and height to the values specified in [page:Vector2 size]. ### [method:Box2 setFromPoints]( [param:Array points] ) [page:Array points] - Array of [page:Vector2 Vector2s] that the resulting box will contain. Sets the upper and lower bounds of this box to include all of the points in [page:Array points]. ### [method:Box2 translate]( [param:Vector2 offset] ) [page:Vector2 offset] - Direction and distance of offset. Adds [page:Vector2 offset] to both the upper and lower bounds of this box, effectively moving this box [page:Vector2 offset] units in 2D space. ### [method:Box2 union]( [param:Box2 box] ) [page:Box2 box] - Box that will be unioned with this box. Unions this box with [page:Box2 box], setting the upper bound of this box to the greater of the two boxes' upper bounds and the lower bound of this box to the lesser of the two boxes' lower bounds.

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# Thread: How efficient is this code? 1. ## How efficient is this code? Below is a function which takes a string and an integer as it's parameters, and returns a string. It's purpose is to remove the character at the position denoted by the integer, and return the remaining characters in the form of another string. Code: ```char * extract_letter( char *word, int letter ) { int ctr; char *str; str = (char *) malloc( strlen( word ) - 1); for( ctr = 0 ; ctr < letter ; ctr++ ) str[ctr] = word[ctr]; for( ctr = letter ; ctr < strlen( word ) ; ctr++ ) str[ctr] = word[ctr+1]; return( str ); }``` The calling function ensures that the value of (int letter) always relates to a valid position in (char *word). The problem I've got is that this function is being called many many times during the excution of the program (potentially hundreds of millions of times), and I need to make sure that it is as fast as possible. Can anyone suggest a way of improving the speed of this function? Also, I'm just guessing that this function might be a bottleneck, as I don't know how to work out what percentage of time the program takes to execute each part. Does anyone know of a way to measure this? Thanks. 2. >Can anyone suggest a way of improving the speed of this function? Don't bother until you're sure that there's a performance problem. Optimizing this function would probably result in it being harder to understand. However, one quick and easy way to make this function faster while also making it safer is to avoid dynamic allocation by passing in a buffer for the new word: Code: ```char* extractLetter(char* word, char* new_word, size_t index) { size_t i; for (i = 0; i < index; i++) new_word[i] = word[i]; for (i = index; word[i] != '\0'; i++) new_word[i] = word[i + 1]; return new_word; }``` This way you don't have the expensive call to malloc, you don't call strlen with every iteration of the second loop, and you don't have to worry about releasing the memory later in the program. >I'm just guessing that this function might be a bottleneck It's been repeatedly shown that programmers are notoriously bad at guessing where bottlenecks are. >Does anyone know of a way to measure this? The best way is to use a profiler to get percentages during execution. >str = (char *) malloc( strlen( word ) - 1); You don't have to cast malloc in C, it's also considered a bad thing because it can hide the error of not including stdlib.h. Also, since the size of word is strlen(word) + 1, the correct size after removing a single character would be strlen(word), as it is you have an off-by-one error that may or may not cause problems later. Probably when you call free. >for( ctr = letter ; ctr < strlen( word ) ; ctr++ ) It's not a good idea to include function calls as counting loop conditions if you can avoid it easily. This loop would be slowed considerably by the repeated overhead of calling strlen and the time it takes to find the length of word. A better way would be to either work with nul characters as strlen probably does, or call strlen and save the value: Code: ```int len = strlen(word); ... for( ctr = letter ; ctr < len ; ctr++ )``` 3. Thanks for the advice - but... a couple more questions. Is there any reason that you chose to use size_t as opposed to int? ...and... If the function takes (char *new_word) as a parameter, do you still need to (return new_word? Wouldn't it be the same to declare the function as void, and just alter the value of *new_word? Also, are you implying that the malloc for the new_word is placed in the calling function, or is there some way of avoiding the malloc entirely, even though the length of (char *word) is not known until run-time? By the way, could you recommend a profiler for use on Solaris? Cheers, Andy 4. >Is there any reason that you chose to use size_t as opposed to int? The function doesn't work with negative indices and size_t is to be preferred over int for array indicies if you can manage it. > do you still need to (return new_word)? No, but it makes setting a pointer to the beginning of the array slightly simpler. You can do Code: ```char* p; ... p = extractLetter(word, new_word, i);``` Code: ```char* p; ... extractLetter(word, new_word, i); p = new_word;``` It can also be used for error checking. If something goes wrong you can return NULL. You'll notice that fgets does the same thing; the buffer doesn't need to be returned, but doing so adds a lot of useful flexibility to the function. >Also, are you implying that the malloc for the new_word is placed >in the calling function, or is there some way of avoiding the >malloc entirely, even though the length of (char *word) is not known until run-time? If the length of word isn't known until run-time and you can't determine a safe upper limit, you'll need to use malloc. However, by placing the onus of allocating memory on the calling function you can implement useful optimizations such as only calling a memory allocation routine if the current size of word is longer than the new_word buffer. This wasn't possible with your previous function. >By the way, could you recommend a profiler for use on Solaris? Take a look at prof in your man pages. 5. I've just run prof against the program, and found that over 50% of the run-time is taken up by a process called _brk_unlocked. The 'largest' user function only takes 10% of run-time. I've tried searching google for _brk_unlocked, but not found much of use. I gather it's something to do with memory allocation for variables, but can anybody shed any more light? ...and is there anything I can do to improve it? Thanks. 6. I followed the advice from Brighteyes, and also realised that I did know the upper limit of the new_word variable, so I've actually removed all explicit calls to malloc(). Here is the adjusted code... Code: ```#include <stdio.h> #include <stdlib.h> #include <string.h> #include "permutations.h" void permute( char *input, char *pool ) { char output[MAXLENGTH] = ""; char new_word[MAXLENGTH] = ""; int ctr, target, pool_len; strcat( output, input ); target = strlen( output ); pool_len = strlen( pool ); for( ctr = 0 ; ctr < pool_len ; ctr++ ) { output[target] = pool[ctr]; append_perm( output ); permute( output, extract_letter( pool, new_word, pool_len, ctr ) ); } } char * extract_letter( char *word, char *new_word, int word_len, int letter ) { int ctr; for( ctr = 0 ; ctr < letter ; ctr++ ) new_word[ctr] = word[ctr]; for( ctr = letter ; ctr < word_len ; ctr++ ) new_word[ctr] = word[ctr+1]; return( new_word ); }``` It is called from a main in another program file... Code: ```#include <stdio.h> #include "permutations.h" struct node *tail_perm = NULL; int main( int argc, char *argv[] ) { if( argc != 2 ) { printf( "\nUsage : andy <string>" ); return( 0 ); } permute( "", argv[1] ); printf( "\n\n" ); return( 0 ); }``` ...and finally here is the top of the output from prof Code: ``` %Time Seconds Cumsecs #Calls msec/call Name 48.5 28.36 28.36 _brk_unlocked 13.0 7.57 35.9379144928 0.0001 _mcount 11.7 6.82 42.75 9864101 0.0007 permute 4.6 2.70 45.45 9864100 0.0003 extract_letter 4.0 2.32 47.77 9864100 0.0002 malloc 3.7 2.19 49.9619728202 0.0001 strlen 3.7 2.17 52.13 realloc 3.0 1.75 53.88 9864100 0.0002 strcpy 2.5 1.44 55.32 9864100 0.0001 append_perm 2.3 1.33 56.65 9864101 0.0001 strcat 1.6 0.91 57.56 _free_unlocked 0.9 0.53 58.09 _fileno_unlocked 0.0 0.01 58.42 116050 0.0001 _sbrk_unlocked 0.0 0.01 58.43 116050 0.0001 _sbrk``` As you can see, nearly two thirds of the excution time is taken up by _brk_unlocked and _mcount. I don't want to try and do anything complicated with the memory, I was just wondering if you could see anything daft that I'm doing which might be unnecessary. Thanks, Andy 7. Sorry, I had not included the code for the append_perm function, and it is that which contains the calls to malloc(). I recompiled the code with append_perm rem'd out, and nearly all of the calls to _brk_unlocked disappeared. I have attached the code files - the intention is to generate a list of every permutation of a string supplied at the command line. I thought I had come up with quite a neat little recursive function to do this, but I'm struggling to keep the run-time down if the string length exceeds 10 characters. If anyone is interested in trying to improve the code, please let me know your ideas. Also, do you know of a more efficient approach to permutation generation?

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# EXERCISE 34 – AZIMUTH STAR (Numerical Solution) ###### GMT     05 March 22h  35m  16s GHA Ȣ(05d 22h)            134˚  01.0’                                           Dec         N  08˚  53.2’ Incr. (35m 16s)             008˚  50.4’ GHAȢ                              142˚  51.4’ SHA  *                          (+)062˚  12.4’ GHA *                            205˚  03.8’ Long (E)                     (+)083˚  46.0’ LHA  *                            288˚  49.8’ ###### NOTE: Working is very similar to that of azimuth- Sun, except that GHA Ȣ and SHA * have been used, which can be taken from the nautical almanac. P = (360˚ – LHA) = (360˚ – 288˚ 49.8’) = 71˚  10.2’ We know that : ###### Azimuth = N 73.8˚ E T Az          = 073.8˚ (T) C Az          = 078.0˚ (C) Error         = 4.2˚ W Variation  = 3.0˚ W Deviation = 1.2˚ W 1. ###### On 30th Nov 2008, PM at ship in DR 48˚ 57’ N 173˚ 18’ W, the azimuth of the star VEGA was 296˚(C) when the GPS clock showed 07h 39m 22s. If variation was 1˚E, calculate the deviation of the compass. d       h      m      s GMT                        01    07      39    22 LIT (W)                    (-)     11      33    12 LMT                         30    20    06     10 #### Vikrant_sharma • Francis says: Good day Sir, Just a short question, how do we name every deviation obtained from Azimuth Sun sailing? How do we know its east or west? Thank you • Pallav says: I found a very usefull. Keep it up Sir!! ### How to whitelist website on AdBlocker? 1. 1 Click on the AdBlock Plus icon on the top right corner of your browser 2. 2 Click on "Enabled on this site" from the AdBlock Plus option 3. 3 Refresh the page and start browsing the site error: Content is protected !!

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## Python speed testing - Time Difference - milliseconds Related searches What is the proper way to compare 2 times in Python in order to speed test a section of code? I tried reading the API docs. I'm not sure I understand the timedelta thing. So far I have this code: ```from datetime import datetime tstart = datetime.now() print t1 # code to speed test tend = datetime.now() print t2 # what am I missing? # I'd like to print the time diff here ``` `datetime.timedelta` is just the difference between two datetimes ... so it's like a period of time, in days / seconds / microseconds ```>>> import datetime >>> a = datetime.datetime.now() >>> b = datetime.datetime.now() >>> c = b - a >>> c datetime.timedelta(0, 4, 316543) >>> c.days 0 >>> c.seconds 4 >>> c.microseconds 316543 ``` Be aware that `c.microseconds` only returns the microseconds portion of the timedelta! For timing purposes always use `c.total_seconds()`. You can do all sorts of maths with datetime.timedelta, eg: ```>>> c / 10 datetime.timedelta(0, 0, 431654) ``` It might be more useful to look at CPU time instead of wallclock time though ... that's operating system dependant though ... under Unix-like systems, check out the 'time' command. Python speed testing - Time Difference - milliseconds, What is the proper way to compare 2 times in Python in order to speed test a section of code? I tried reading the API docs. I'm not sure I understand the timedelta� Since Python 2.7 there's the timedelta.total_seconds () method. So, to get the elapsed milliseconds: >>> import datetime >>> a = datetime.datetime.now() >>> b = datetime.datetime.now() >>> delta = b - a >>> print delta 0:00:05.077263 >>> int(delta.total_seconds() * 1000) # milliseconds 5077. share. Share a link to this answer. Since Python 2.7 there's the timedelta.total_seconds() method. So, to get the elapsed milliseconds: ```>>> import datetime >>> a = datetime.datetime.now() >>> b = datetime.datetime.now() >>> delta = b - a >>> print delta 0:00:05.077263 >>> int(delta.total_seconds() * 1000) # milliseconds 5077 ``` Python speed testing - Time Difference - milliseconds, What is the proper way to compare 2 times in Python in order to speed test a section of code? I tried reading the API docs. I'm not sure I understand the timedelta� Since Python 2.7 there's the timedelta.total_seconds() method. So, to get the elapsed milliseconds: You might want to use the timeit module instead. Python speed testing - Time Difference, What is the proper way to compare 2 times in Python in order to speed test a section of code? I tried reading the API docs. I'm not sure I understand the timedelta� Python speed testing-Time Difference-milliseconds (8) datetime.timedelta is just the difference between two datetimes so it's like a period of time, in days / seconds / microseconds. >> > a = datetime.datetime.now () >> > b = datetime.datetime.now () >> > c = b - a >> > c datetime.timedelta ( 0, 4, 316543 ) >> > c.days 0 >> > c.seconds 4 >> > c.microseconds 316543. You could also use: ```import time start = time.clock() do_something() end = time.clock() print "%.2gs" % (end-start) ``` Or you could use the python profilers. Python speed testing - Time Difference, Python speed testing - Time Difference - milliseconds | Q&A ProDevsBlog. from datetime import datetime tstart = datetime.now() print t1 # code to speed test� Python speed testing - Time Difference - milliseconds; Converting string into datetime; subtract two times in python; Format timedelta to string I know this is late, but I actually really like using: ```import time start = time.time() ##### your timed code here ... ##### print "Process time: " + (time.time() - start) ``` `time.time()` gives you seconds since the epoch. Because this is a standardized time in seconds, you can simply subtract the start time from the end time to get the process time (in seconds). `time.clock()` is good for benchmarking, but I have found it kind of useless if you want to know how long your process took. For example, it's much more intuitive to say "my process takes 10 seconds" than it is to say "my process takes 10 processor clock units" ```>>> start = time.time(); sum([each**8.3 for each in range(1,100000)]) ; print (time.time() - start) 3.4001404476250935e+45 0.0637760162354 >>> start = time.clock(); sum([each**8.3 for each in range(1,100000)]) ; print (time.clock() - start) 3.4001404476250935e+45 0.05 ``` In the first example above, you are shown a time of 0.05 for time.clock() vs 0.06377 for time.time() ```>>> start = time.clock(); time.sleep(1) ; print "process time: " + (time.clock() - start) process time: 0.0 >>> start = time.time(); time.sleep(1) ; print "process time: " + (time.time() - start) process time: 1.00111794472 ``` In the second example, somehow the processor time shows "0" even though the process slept for a second. `time.time()` correctly shows a little more than 1 second. Python speed testing - Time Difference - milliseconds, What is the proper way to compare 2 times in Python in order to speed test a section of code? I tried reading the API docs. I'm not sure I understand the timedelta� To measure time elapsed during program's execution, either use time.clock() or time.time() functions. The python docs state that this function should be used for benchmarking purposes. from datetime import datetime from datetime import timedelta start_time = datetime.now() # returns the elapsed milliseconds since the start of the program def millis(): dt = datetime.now() - start_time ms = (dt.days * 24 * 60 * 60 + dt.seconds) * 1000 + dt.microseconds / 1000.0 return ms. share. If you just want to measure the elapsed wall-clock time between two points, you could use time.time (): import time start = time.time() print("hello") end = time.time() print(end - start) This gives the execution time in seconds. Another option since 3.3 might be to use perf_counter or process_time, depending on your requirements. Ardit Post author September 26, 2019 at 9:56 am. That’s another way to measure the execution time, but it’s less accurate. The way that works is you record the timestamp (in start_time variable) just before the test code starts to execute and you record the timestamp (in the end_time variable) just after the test code finishes executing. • Anyone interested in getting total minutes can use `int(c.total_seconds() / 60)` in this case • When using `start = time.clock()` it prints `DeprecationWarning: time.clock has been deprecated in Python 3.3 and will be removed from Python 3.8: use time.perf_counter or time.process_time instead`. • You need the `import time` statement

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I have a list `l` in the following way: ``l = [([1, 0.0, 50.0, 2, 0.0, 50.0], [1, 1.9, 1]),([1, 0.0, 50.0, 2, 0.0, 50.0], [2, 1.9, 1])]`` I want to transform this list such that the new structure is as follows: ``goal = [([1, 0.0, 50.0], [2, 0.0, 50.0], [1, 1.9, 1]), ([1, 0.0, 50.0], [2, 0.0, 50.0], [2, 1.9, 1])]`` Namely, that the first list in each tuple gets unraveled to sublists of length 3. I tried it the following way but got stuck as the various transformations give back numpy arrays and it turns out messy. Additionally, this operation could potentially take place on large variants of l so should be performance friendly/in-place(?). ``terms = np.array(l)[:,0][np.split(np.array(i), 2) for i in terms]`` In my comment I argued against the use of `np.array` for this, since ``````In [241]: np.array(l) Out[241]: array([[[1, 0.0, 50.0, 2, 0.0, 50.0], [1, 1.9, 1]], [[1, 0.0, 50.0, 2, 0.0, 50.0], [2, 1.9, 1]]], dtype=object) `````` is an object array. However the array version can make splitting a list easy, with reshape ``````In [240]: [np.array(x[0]+x[1]).reshape(-1,3).tolist() for x in l] Out[240]: [[[1.0, 0.0, 50.0], [2.0, 0.0, 50.0], [1.0, 1.9, 1.0]], [[1.0, 0.0, 50.0], [2.0, 0.0, 50.0], [2.0, 1.9, 1.0]]] `````` Add `[tuple(n...` if it must be tuples, not lists. I'm doing a couple of tricks. Since the second item has the same length as the desired split (3), I'm just concatenating them at the start, rather worry about doing so later. And then array reshape followed by `tolist` effectively splits the array. ``````In [246]: np.reshape(x[0]+x[1],(-1,3)) Out[246]: array([[ 1. , 0. , 50. ], [ 2. , 0. , 50. ], [ 1. , 1.9, 1. ]]) `````` This depends on being able to split the sublists evenly by 3. The array round trip is probably slower than the equivalent `itertools` code. `in-place` won't work because you have a list of tuples. You can replace those tuples, but you can't modify them. If they were lists, you could splice in the split like this: ``````In [248]: x Out[248]: ([1, 0.0, 50.0, 2, 0.0, 50.0], [1, 1.9, 1]) In [249]: xl=list(x) In [250]: xl[0:1] = [xl[0][:3],xl[0][3:]] # or the split of your choice In [251]: xl Out[251]: [[1, 0.0, 50.0], [2, 0.0, 50.0], [1, 1.9, 1]] `````` Often it is more convenient to create new lists and tuples than to change things in place. Copying a list of lists just means making a new list of the same pointers. Since it is ok to slice off the end of a list `@Kasramvd's` `islice` version can be simplified to: ``````[tuple([i[t:t+3] for i in sub for t in range(0, len(i), 3)]) for sub in l] `````` You can use `itertools.chain` within a list comprehension: ``````In [23]: from itertools import chain In [24]: [tuple(chain.from_iterable((i[:3], i[3:]) if len(i) > 3 else [i] for i in sub)) for sub in l] Out[24]: [([1, 0.0, 50.0], [2, 0.0, 50.0], [1, 1.9, 1]), ([1, 0.0, 50.0], [2, 0.0, 50.0], [2, 1.9, 1])] `````` As a general way you can use `itertools.islice` in order to slice your sub lists to triples: ``````In [37]: [tuple(list(islice(i,t,t+3)) if len(i) > 3 else i for i in sub for t in range(0, len(i), 3)) for sub in l] Out[37]: [([1, 0.0, 50.0], [2, 0.0, 50.0], [1, 1.9, 1]), ([1, 0.0, 50.0], [2, 0.0, 50.0], [2, 1.9, 1])] `````` Top

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# Mutual coherence (linear algebra) In linear algebra, the coherence[1] or mutual coherence[2] of a matrix A is defined as the maximum absolute value of the cross-correlations between the columns of A. Formally, let ${\displaystyle a_{1},\ldots ,a_{m}\in {\mathbb {C} }^{d}}$ be the columns of the matrix A, which are assumed to be normalized such that ${\displaystyle a_{i}^{H}a_{i}=1.}$ The mutual coherence of A is then defined as[1][2] ${\displaystyle M=\max _{1\leq i\neq j\leq m}\left|a_{i}^{H}a_{j}\right|.}$ A lower bound is [3] ${\displaystyle M\geq {\sqrt {\frac {m-d}{d(m-1)}}}}$ A deterministic matrix with the mutual coherence almost meeting the lower bound can be constructed by Weil's theorem.[4] This concept was introduced by David Donoho and Michael Elad.[5]. A special case of this definition for the two-ortho case appeared earlier in the paper by Donoho and Huo,[6]. The mutual coherence has since been used extensively in the field of sparse representations of signals. In particular, it is used as a measure of the ability of suboptimal algorithms such as matching pursuit and basis pursuit to correctly identify the true representation of a sparse signal.[1][2][7]

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Help me with this one have no idea how to solve TnT Full marks is (100/60)(120)=(5/3)(120)=200 marks. by Top Rated User (982k points)

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I have to find the gradients from the information it gives me, it has an example but I have no idea how it gets from there to the answer, the example is: Equation: R=V/I Then it says: x axis: voltage y axis: current But I don't understand how to get the answer from the information it gives me? Any help would be aprecated I assume V = voltage, is R current? Well $\displaystyle R = \frac{V}{I} \implies I = \frac{V}{R}$ which means I and V have a linear relationship. The gradient of this relationship is $\displaystyle \frac{1}{R}$

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WAVE HW 1) Describe how these properties are similar and different in : Spring             Pendulum        and      String Waves: Amplitude Period Frequency Wavelength What is the main factor that affects the period in each? 2) A pendulum swings back and forth. Graph its: Displacement vs. time 3) I make a sound at a frequency of 500 Hz and notice that the ECHO returns to me 10 sec later from a wall 1500 m away. What is the wavelength of the sound? 4) Draw a transverse rope wave with a frequency of 3 Hz, and one with a frequency of 6 Hz. What is different about each? Sec Review 12-3 1) As waves pass by a duck floating on a lake, the duck bobs up and down but remains in essentially one place. Explain why the duck is not carried along by the water medium 2) Sketch each of the following waves on a pring that is attached on one end: a) a pulse wave that is longitudinal b) a periodic wave that is longitudinal c) a pulse transverse wave d) a periodic transverse wave 3) Draw a graph for each one of the waves described in b) and d) and label the y axis of each graph with the appropriate variable. Label the following one each graph: crest, trough, wavelength, amplitude. 4) IF the amplitude of a sound wave is increased by a factor of four, how does the energy carried by the sound wave in a given time interval change? 5) The smallest insects that a bat can detect are approximately the size of one wavelength of sound the bat makes. If the bat emits a chirp of frequency of 60 Hz, what is the smallest insect it can detect? (speed of sound is 340 m/s) PRACTICE 12D 1) A piano emits the frequencies that range from  a low of about 28 Hz to a high of about 4200 Hz. Find the range of wavelengths in air attained by this instrument when the speed of sound in air is 340 m/s. 2) An FM radio station broadcasts electromagnetic waves at a frequency of 125 MHz. These radio waves have a wavelength of 2.4 m. Find the speed of the radio waves. 5) A tuning fork produces a sound with a frequency of 256 Hz and a wavelength in air 1.35 m. a) What value does this give for the speed of sound in air? b) What would be the wavelength of the wave produced by this tuning fork in water in which sound travels at 1500 m/s?

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# Question: Is 0 A Real Number? ## Who invented the 0? MayansThe first recorded zero appeared in Mesopotamia around 3 B.C. The Mayans invented it independently circa 4 A.D. It was later devised in India in the mid-fifth century, spread to Cambodia near the end of the seventh century, and into China and the Islamic countries at the end of the eighth.. ## What type of number is 0 1? The main types of numbers used in school mathematics are listed below: Natural Numbers (N), (also called positive integers, counting numbers, or natural numbers); They are the numbers {1, 2, 3, 4, 5, …} Whole Numbers (W). This is the set of natural numbers, plus zero, i.e., {0, 1, 2, 3, 4, 5, …}. ## Is 1.5 a natural number? 1.1 Natural Numbers, Integers, Rational Numbers and Real Numbers. 5 is an “element” in the set of natural numbers. 1.5 is “not an element” in that set. The Set of INTEGERS Z includes 0 and all integers, both positive and negative. ## Is 2 an irrational number? Sal proves that the square root of 2 is an irrational number, i.e. it cannot be given as the ratio of two integers. ## What is the symbol for all real numbers? R = real numbers, Z = integers, N=natural numbers, Q = rational numbers, P = irrational numbers. ## Is 0 a real number or not? The number 0 is both real and purely imaginary. ): Includes real numbers, imaginary numbers, and sums and differences of real and imaginary numbers. ## What are not real numbers? This indicates that real numbers include natural numbers, whole numbers, integers, rational numbers, and irrational numbers. For example, 3, 0, 1.5, 3/2, ⎷5, and so on. … The numbers that are neither rational nor irrational are not real numbers, like, ⎷-1, 2+3i and -i. These numbers include the set of complex numbers, C. ## Which is natural number? Natural numbers are all positive numbers like 1, 2, 3, 4, and so on. They are the numbers you usually count and they continue till infinity. Whole numbers are all natural numbers including 0, for example, 0, 1, 2, 3, 4, and so on. Integers include all whole numbers and their negative counterpart. ## What is the value of 5 2? Answer: The value of 52 = 5 × 5 = 25 So, 52 is referred to as the square of 5. ## Is 5 a rational number? And there are many more such numbers, and because they are not rational they are called Irrational….Example:NumberAs a FractionRational?55/1Yes1.757/4Yes.0011/1000Yes−0.1−1/10Yes2 more rows ## Why is zero a real number? Real numbers can be positive or negative, and include the number zero. They are called real numbers because they are not imaginary, which is a different system of numbers. Imaginary numbers are numbers that cannot be quantified, like the square root of -1. … Another example of an imaginary number is infinity. ## Which are the real numbers? Real numbers are the numbers which include both rational and irrational numbers. Rational numbers such as integers (-2, 0, 1), fractions(1/2, 2.5) and irrational numbers such as √3, π(22/7), etc., are all real numbers. ## Is √ 16 an irrational number? A rational number is defined as the number that can be expressed in the form of a quotient or division of two integers i.e., p/q, where q = 0. … So √16 is an irrational number. ## What kind of number is zero? 1 Answer. 0 is a rational, whole, integer and real number. Some definitions include it as a natural number and some don’t (starting at 1 instead). ## Who invented 0 in India? AryabhataWhat is widely found in textbooks in India is that a mathematician and astronomer, Aryabhata, in the 5th century used zero as a placeholder and in algorithms for finding square roots and cube roots in his Sanskrit treatises. ## Is 2/9 an irrational number? Explanation: It is also a real number, as rational numbers are a subset of the real numbers (as are all the others mentioned). ## What number has no real square root? Zero has one square root which is 0. Negative numbers don’t have real square roots since a square is either positive or 0. The square roots of numbers that are not a perfect square are members of the irrational numbers. This means that they can’t be written as the quotient of two integers. ## What does R mean in math? real numbersIn maths, the letter R denotes the set of all real numbers. … Real numbers are the numbers that include, natural numbers, whole numbers, integers, and decimal numbers. In other words, real numbers are defined as the points on an infinitely extended line. ## Who invented 1? Hindu-Arabic numerals, set of 10 symbols—1, 2, 3, 4, 5, 6, 7, 8, 9, 0—that represent numbers in the decimal number system. They originated in India in the 6th or 7th century and were introduced to Europe through the writings of Middle Eastern mathematicians, especially al-Khwarizmi and al-Kindi, about the 12th century.

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# Solve the exponential equation algebraically? • Oct 12th 2009, 10:48 AM tsmith Solve the exponential equation algebraically? Solve the exponential equation algebraically: -14 + 3e^x = 11 So I think I move the -14 to the other side, so now I'm left with 3e^x = 25 What do i do next? • Oct 12th 2009, 10:50 AM e^(i*pi) Quote: Originally Posted by tsmith Solve the exponential equation algebraically: -14 + 3e^x = 11 So I think I move the -14 to the other side, so now I'm left with 3e^x = 25 What do i do next? 1. Divide both sides by 3 2. Take the natural log of both sides. Do not use a decimal approximation • Oct 12th 2009, 10:55 AM tsmith Ok, so e^x = 25/3 How do I find the natural log of both sides? • Oct 12th 2009, 11:02 AM e^(i*pi) Quote: Originally Posted by tsmith Ok, so e^x = 25/3 How do I find the natural log of both sides? $\displaystyle ln(x) = log_e(x)$ You don't need to unless you're making a decimal approximation. It is fine to say that $\displaystyle x = ln \left(\frac{25}{3}\right) = 2\ln\left(\frac{5}{3}\right) = 2ln5 - ln3$ Note that I used the laws of logs to simplify. If you're teacher wants you to make a decimal approximation there should be a button marked ln on your calculator • Oct 12th 2009, 11:17 AM tsmith My teacher wants me to round the result to 3 decimal places. What do I type in the calculator? Thank you for your help, by the way :) • Oct 12th 2009, 11:24 AM e^(i*pi) $\displaystyle 2*ln(5) - ln(3)$

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x Turn on thread page Beta You are Here: Home >< Maths # Higher Maths 2010 Question Help watch 1. Have been doing the 2010 paper 2 for higher maths today Does anybody know how to do question 5, I know how to work out the area between 2 curves or a curve and a straight line but this question I have never seen before. Heres a Link to that paper Thanks for any help. Chris 2. How much of the question have you done? (note this question doesn't require any integrating) 3. I tried doing it by integration and then just got myself confused so havent actually done any of it. 4. The 8x is the vital bit at first. First find a value of p that will give you an 8x when you expand out the brackets. Then the value of q should jump out at you. 5. sorry but the 8x is in question 5 of paper 1, you have to scroll down to paper 2 , sorry i didn't make that obvious, i know how to do that question 5 6. (Original post by Chris Anderson) sorry but the 8x is in question 5 of paper 1, you have to scroll down to paper 2 , sorry i didn't make that obvious, i know how to do that question 5 Ahh, I fail, sorry. As for your question, there are several steps: 1) find the y coordinate of T 2) find the y coordinate of Q 3) then PQ is 2)-1) The maximum thing then follows by differentiating A with respect to x. 7. thanks, understand how to do it now, it's one of those questions that once you have an idea of how to do it, you realise you can do it. chris TSR Support Team We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out. This forum is supported by: Updated: April 12, 2011 Today on TSR ### Is uni even worth it? Does anyone use their degree? Poll Useful resources ### Maths Forum posting guidelines Not sure where to post? Read the updated guidelines here ### How to use LaTex Writing equations the easy way ### Study habits of A* students Top tips from students who have already aced their exams

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Calculating the distance to the kth nearest neighbor for all points in the set For a machine learning application, my group needs to calculate the Euclidean distance to the $k$th nearest neighbor in a set $X$ for each $x \in (X \cup Y) \subset \mathbb R^d$ (for $d$ between 5 and about 100, and $|X| \approx |Y|$ a few hundred up to a few million). We're currently using either the brute-force $O(d \lvert X \rvert \lvert X \cup Y \rvert)$ approach or the obvious one with a kd-tree on $X$, which when $d$ is high and $|X|$ is relatively low doesn't ever win. (Everything is in-memory.) It seems like there must be a better way than brute-force, though -- at least one that takes advantage of the triangle inequality, or maybe with locality-sensitive hashes. A reasonably tight approximation is also potentially okay. The research I've been able to find seems to focus on the problem of finding the single nearest neighbor (or one that is approximately the nearest). Does the problem I'm looking for go by some other name, or is there a connection to a related problem that I haven't thought of? • kd-trees DO take advantage of the triangle inequality. Have you tried using other spacial data partitioning trees? Another thing you might look into (I know nothing of your machine learning algorithm) whether the specific points tend to have structure, which might help you in quickly finding hyperplanes and using those in a k-d-like tree instead of the usual median-per-coordinate split which performs poorly in high dimensions. Nov 9, 2011 at 4:25 • @RossSnider thanks for the suggestions. And sure, KD trees use the triangle inequality, but I was thinking of something that would be faster than brute force. :) What other kinds of spatial data partitioning trees would you recommend? Of Wikipedia's list only maybe vp-trees seem applicable, and they don't seem like they'd be better than kd-trees for Euclidean distance. And I'll think about if there's a better problem-specific way to define separating hyperplanes, but one doesn't come to mind. Nov 9, 2011 at 5:08 • I guess I was hoping that the fact that we know we're evaluating this for all of $X$ (as well as other points) would allow for some kind of help in the algorithm. I'm not sure that's the case, though. Nov 9, 2011 at 5:21 • what is $k$ typically in your applications ? Nov 9, 2011 at 6:48 • @SureshVenkat We usually use a $k$ of about 3, sometimes a little larger. Nov 9, 2011 at 14:50 Here is a simple trick that might be useful. Consider a random sample that picks every point with probability 1/k. It is easy to verify that with good probability exactly one of your k nearest neighbor would be in the sample. Compute the nearest-neighbor in the sample. Repeat this O( k log n) times. With high probability the k nearest points in the $O(k \log n)$ points computed are the k nearest neighbors to your query. Thus, finding the k nearest neighbor, is equivalent to doing $O( k \log n)$ nearest neighbor queries. In short, give me a fast data-structure for answering nearest neighbor queries, and I would be happy to give you a fast data-structure of k-nearest neighbor. • Nice trick. It should be okay to re-use the samples for different query points, too, right? So to calculate the $k$-nearest-neighbor for each point in the set, I only need to build the data structure $O(k \log n)$ times. Nov 10, 2011 at 17:36 • Reusing the samples is tricky, because then you're requiring that a fixed sample works for ANY query (the quantification is flipped) and so the probabilities would change. The general idea would then be to construct a set of samples of larger size (this depends on the #queries) and use them, if that's an issue. Nov 10, 2011 at 18:26 • @SureshVenkat Ah, of course. I'll sit down and figure out the actual probabilities. Thanks everyone! Nov 10, 2011 at 19:56 • If you do $O( k \log (1/\delta))$ samples, then each query succeeds with probability $\geq 1-\delta$. Notice, that this trick is slightly better than it look at first glimpse - you have $O(k \log n)$ samples, each one of them of size $O( n/k)$ (with high probability if $k$ is not too large). Which means better query time for each of the samples. Nov 10, 2011 at 20:40 • @Sariel Har-Peled Is it possible to solve the asked problem in $o(k \log n)$ time? – Shi Sep 30, 2022 at 10:56 A cheap approximate solution using a "locality-sensitive hash" would be to convert each point to it's bit interleaved form: [xxx,yyy,zzz] -> xyzxyzxyz Pick your point to query on and go $k$ points in both directions to get a size $2k$ set; then take the $kth$ nearest to your point. Also see this paper by Connor and Kumar.

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Circumference of a Circle Practice Question 1 Given a circle with the radius of 8cm. Find the circumference of this circle. Take π as 3.14. A. 30.24cm B. 40.24cm C. 50.24cm D. 60.24cm Step by Step Solution • Step 1 The picture below shows the circle with the radius of 8cm. • Step 2 To calculate the circumference, we can use the following formula: • Step 3 The radius is given as 5cm. Hence, we can substitute r with 5. Similarly, we can substitute π with 3.14. After substituting these values, we can calculate for C: • Step 4 Now, 50.24 only has meaning if we include the unit for it. Since the radius is in cm, the circumference will also be in cm. Hence: C = 50.24cm • Step 5 Clearly, the answer is C.

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# Number of odd cycles in non-bipartite 3-connected graph By going over the tests of previous years in graph theory, I've come across an interesting (in my opinion) question: $G$ is 3-connected, non-bipartite graph. Prove that $G$ contains at least 4 odd cycles. I tried the following way: as $G$ is non-bipartite, it has an odd cycle $C$. Now, since $G$ 3-connected, there should be $v \in V(G-C)$ with 3 paths to $C$. From here it should be a game of combining odd/even paths, to get what is needed. But there are too much options. Is there any other way? Thanks. • @Graphth: Given the statement that Pavel wants to prove, it seems likely that bipartite in the third paragraph is a typo for non-bipartite. Commented Aug 24, 2012 at 16:30 • Sorry, indeed. Fixed. Commented Aug 24, 2012 at 16:31 • @Pavel I assume you admite any 4 odd cycles, because if you want they to be independent, then the 3-regular graph of 4 vertices would not satisfy the claim. – iago Commented Aug 24, 2012 at 18:55 • @iago Yes, I think that was the intention. Commented Aug 24, 2012 at 19:22 • @Pavel Following your idea, you can reduce the combinations of the paths to only 3 options (not too much). Decomposing the cycle in 3 odd-lenght paths you may assume that it has lenght 3 (the important is just parity). Now take $v$ at distance 1 of a vertex of the cycle. Then the only combinations you have to consider if the 2 paths to the other vertices of the cycle are odd-odd, even-even or even-odd. – iago Commented Aug 24, 2012 at 19:37 Your idea is correct and doesn't have that many cases, you can simplify it quite a bit. Let $$C$$ be an odd cycle in $$G$$ of minimum length, this assures that $$C$$ isn't hamiltonian and there is a vertex $$v\in V(G)\setminus V(C)$$. As you said, there are 3 disjoint paths $$t_1$$, $$t_2$$ and $$t_3$$ between $$v$$ and $$C$$. Call $$x_i$$ the extreme of $$t_i$$ in $$C$$. Observe that for $$i\neq j$$, there are two $$x_ix_j$$-paths contained in $$C$$, one of even length and one of odd length. Define the cycle $$C_{i,j}$$ as follows: 1. If the sum of the lengths of $$t_i$$ and $$t_j$$ is even, the cycle starts in $$v$$, follows $$t_i$$, then the odd $$x_ix_j$$-path in $$C$$ and finally it follows $$t_j$$. 2. If the sum of the lengths of $$t_i$$ and $$t_j$$ is odd, do the same but use the even $$x_ix_j$$-path in $$C$$. Hence, the four odd cycles are $$C$$, $$C_{1,2}$$, $$C_{1,3}$$ and $$C_{2,3}$$.

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# Is there a way to get the top k values per row of a MATLAB array? 2 views (last 30 days) Jesujoba Alabi on 3 Feb 2020 Answered: Sean de Wolski on 3 Feb 2020 Given a MATLAB matrix of the form below: x = [4.,3.,2.,1.,8. ; 1.2,3.1,0.,9.2,5.5 ; 0.2,7.0,4.4,0.2,1.3] is there a way to retain the top-3 values in each row and set others to zero in MATLAB. The result in the case of the example above would be x = [4.,3.,0.,0.,8.; 0.,3.1,0.,9.2,5.5; 0.0,7.0,4.4,0.0,1.3] Sean de Wolski on 3 Feb 2020 I'd probably do something like this: x = magic(4) k = 3 [~,idx] = maxk(x,k,2) for ii = 1:size(x,1) x(ii,~ismember(1:size(x,2), idx(ii,:))) = 0 end

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This site is supported by donations to The OEIS Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!) A260032 Number of perfect matchings in graph P_{2n} X P_{2n} with a monomer on each corner. 1 1, 8, 784, 913952, 12119367744, 1773206059548800, 2808001509386950713600, 47534638766423741578738188800, 8530835766072904609739799813424153600, 16137081911409285302469685272022812457875802112, 320397648203287990193211938297925486964232264783587250176 (list; graph; refs; listen; history; text; internal format) OFFSET 1,2 LINKS Alois P. Heinz, Table of n, a(n) for n = 1..40 N. Allegra, Exact solution of the 2d dimer model: Corner free energy, correlation functions and combinatorics, arXiv:1410.4131 [cond-mat.stat-mech], 2014, p.21. Wikipedia, FKT algorithm Wikipedia, Matching (graph theory) MAPLE with(LinearAlgebra): a:= proc(n) option remember; local d, i, j, t, m, M;       d:= 2*n; m:= d^2-4;       M:= Matrix(m, shape=skewsymmetric);       for i to d-3 do M[i+1, i]:=1 od;       for i to d-2 do M[i, i+d-1]:=1 od;       for i from m-d+3 to m-1 do M[i, i+1]:=1 od;       for i from m-d+3 to m do M[i-d+1, i]:=1 od;       for i from d-1 to m-2*d+2 do M[i, i+d]:=1 od;       for i to d-2 do for j to d-1 do         t:=d*i+j-2; M[t, t+1]:= `if`(irem(i, 2)=1, 1, -1);       od od;       isqrt(Determinant(M))     end: seq(a(n), n=1..11);  # Alois P. Heinz, Mar 10 2016 MATHEMATICA a[1] = 1; a[n_] := a[n] = Module[{d, i, j, t, m, M}, d = 2*n; m = d^2 - 4; M = Array[0&, {m, m}];    For[i = 1, i <= d - 3, i++, M[[i + 1, i]] = 1];    For[i = 1, i <= d - 2, i++, M[[i, i + d - 1]] = 1];    For[i = m - d + 3, i <= m - 1, i++, M[[i, i + 1]] = 1];    For[i = m - d + 3, i <= m, i++, M[[i - d + 1, i]] = 1];    For[i = d - 1, i <= m - 2*d + 2, i++, M[[i, i + d]] = 1];    For[i = 1, i <= d - 2, i++,     For[j = 1, j <= d - 1, j++, t = d*i + j - 2; M[[t, t + 1]] = If[Mod[i, 2] == 1, 1, -1]]]; M = M - Transpose[M]; Sqrt[Det[M]]]; Table[Print["a(", n, ") = ", a[n]]; a[n], {n, 1, 11}] (* Jean-François Alcover, Nov 11 2017, after Alois P. Heinz *) CROSSREFS Cf. A099390, A004003. Sequence in context: A262353 A268148 A145415 * A204464 A001547 A168310 Adjacent sequences:  A260029 A260030 A260031 * A260033 A260034 A260035 KEYWORD nonn AUTHOR N. J. A. Sloane, Jul 19 2015 EXTENSIONS a(6)-a(10) from Andrew Howroyd, Nov 15 2015 Typo in a(5) corrected and a(11) added by Alois P. Heinz, Mar 07 2016 STATUS approved Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent The OEIS Community | Maintained by The OEIS Foundation Inc. Last modified October 20 20:24 EDT 2019. Contains 328273 sequences. (Running on oeis4.)

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We collected information about 0 1 Hours for you. Follow the liks to find out everything about 0 1 Hours. ### Convert 0.1 Hours to Minutes - CalculateMe.com https://www.calculateme.com/time/hours/to-minutes/0.1 0.1 hr to min conversion. An hour is a unit of time equal to 60 minutes, or 3,600 seconds. A minute is a unit of time equal to 60 seconds. ### How long is 0.1 of an hour - Answers Aug 23, 2009 · 0.1 hour = (0.1 x 60) = 6 minutes. 1 minute = 60 seconds. 6 minutes = (6 x 60) = 360 seconds. ### What Is 0.1 Hours In Minutes? (0.1 hr to min) https://minuteshours.com/0-1-hours-to-minutes 0.1 hr × 60 = 6 min. How to convert 0.1 hours to minutes? The conversion factor from hours to minutes is 60, which means that 1 hours is equal to 60 minutes: 1 hr = 60 min. To convert 0.1 hours into minutes we have to multiply 0.1 by the conversion factor in order to get the amount from hours to minutes. ### How many minutes are in 0.1 hour? Socratic https://socratic.org/questions/how-many-minutes-are-in-0-1-hour Mar 11, 2018 · 0.1 hours = 6 minutes An hour is 60 minutes long, so if we multiply 60 by 0.1 we will get our answer: 60*0.1=60*1/10=60/10=6 ### How many minutes are in 0.1 hour - Answers Dec 18, 2008 · There are 60 minutes in an hour. Therefore, there would be 1 hour and 40 minutes in 100 minutes. ### How many minutes are in 0.1 of an hour? Yahoo Answers Jan 11, 2010 · 0.1 is one tenth. there are 60 minutes in an hour. 60 divided by 10 is 6. 0.1 is basically 10% or one-tenth (1/10) of anything , so basically 10% of 60 Minutes (or One hr) is 6 minutes. ### 1 Hour Timer - Online Stopwatch https://www.online-stopwatch.com/timer/1hour/ They range from a 1 second timer - up to a year timer! It's pointless - but you asked for it! :-) Remember! If the timer you want is not here -- just make ANY timer you want above. Simple! ### Time Conversion - Payroll Services Information https://daf.csulb.edu/offices/bhr/hr_management/payroll/time_conversion.html Time Conversion Conversion from minutes to tenths of an hour: 1 to 6 Minutes = 0.1 ; 7 to 12 Minutes = 0.2 ; 13 to 18 Minutes = 0.3 ; 19 to 24 Minutes = 0.4 ; 25 to 30 Minutes = 0.5 ; 31 to 36 Minutes = 0.6 ; 37 to 42 Minutes = 0.7 ; 43 to 48 Minutes = 0.8 ; 49 to 54 Minutes = 0.9 ; 55 to 60 Minutes = 1.0 ; … ### [1 HOUR LOOP] Suran 수란 - 1+1=0 Ft. Dean - YouTube Jun 09, 2017 · 50+ videos Play all Mix - [1 HOUR LOOP] Suran 수란 - 1+1=0 Ft. Dean YouTube; Traffic Night JAZZ - Smoth Background JAZZ Mix - Instrumental Remix JAZZ Music Relax Music 2,268 watching.Author: snsd ismyqueen ### Convert 0.2 Hours to Minutes - CalculateMe.com https://www.calculateme.com/time/hours/to-minutes/0.2 An hour is a unit of time equal to 60 minutes, or 3,600 seconds. A minute is a unit of time equal to 60 seconds. ### Acute MI Diagnosis: 0/1 Hour Superior to 0/3 Hour ... Jun 30, 2018 · The 0/1 hour (0/1h) algorithm, which assesses baseline high-sensitivity cardiac troponin (hs-cTn) concentrations as well as changes of these concentrations within the first hour of admission, was superior to the 0/3 hour (0/3h) algorithm for “ruling out” acute myocardial infarction (AMI) in patients who presented to the emergency department (ED) with AMI-like symptoms, according to a study … ### Convert Decimal Hours To Hours And Minutes In 1 Step ... https://www.ontheclock.com/convert-hours-minutes-to-decimal-hours.aspx Option 3: Do the math manually, example 8 hours and 35 minutes. Divide the 35 minutes by 60, e.g, 35 divided by 60 equals 0.58; then add the 8 hours back in, 8 hours plus 0.58 equals 8.58 hours; Also check out our Excel Timesheet Calculator With Lunch & … ### Work hours - percent of full day table http://personnel.wv.gov/worktable.html Below are the work day percentages in table format. The table shows the same information as the form above. This is used to complete the % First and/or % Last … ### Which is correct: 1.5 hour or 1.5 hours? Why? - Quora https://www.quora.com/Which-is-correct-1-5-hour-or-1-5-hours-Why Apr 03, 2019 · 1.5 hour is used as an adjective. “The siren sounds at 1.5 hour intervals “. 1.5 hours is a noun phrase. “90 minutes equals 1.5 hours". We don't pluralize adjectives . Notice the way we say ‘a six foot man ‘ and ‘a two metre length ‘. Consider also nouns acting as adjectives in compound nouns. ### Goblins from Mars - Turf War 3.0 【1 HOUR】 - YouTube Aug 12, 2016 · Goblins from Mars - Turf War 3.0 【1 HOUR】 GFM's 500K subscribers celebration! Bringing back the old stuff with a siiick new Turf War version :D DL https://... ### What Is 0.73 Hours In Minutes? (0.73 hr to min) https://minuteshours.com/0-73-hours-to-minutes The conversion factor from hours to minutes is 60, which means that 1 hours is equal to 60 minutes: 1 hr = 60 min. To convert 0.73 hours into minutes we have to multiply 0.73 by the conversion factor in order to get the amount from hours to minutes. We can also form a … ### FTE - Standard Hours Conversion Table http://hrweb.berkeley.edu/files/attachments/FTE-to-Standard-Hours.pdf FTE - Standard Hours Conversion Table Position Management uses Standard Hours to calculate the FTE for a Position. The table below provides a conversion between FTE and Standard Hours. To enter or update FTE, input the Standard Hours and the system will automatically calculate FTE. Standard Hours FTE Standard Hours FTE Standard Hours FTE ### 0.75 hours to minutes - Unit Converter http://unitconverter.io/hours/minutes/0.75 0.75 Hours = 45 Minutes = 45 Minutes Hours to minutes - Time Converter - 0.75 minutes to hours This conversion of 0.75 hours to minutes has been calculated by multiplying 0.75 hours … ## Searching for 0 1 Hours? You can just click the links above. The info is collected for you.

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# Cryptography: A Closer Look at the Algorithms By: Zia A. Sardar This tutorial is a part of our series on cryptography, designed to help the product design engineer quickly gain an understanding of how the technique helps protect designs. This installment discusses how modern cryptographic algorithms are implemented. A similar version of this application note was originally published on April 30, 2020 on Electronic Design. #### Introduction In the last two installments in our cryptography series of tutorials, we covered the basic concepts and the two basic types of cryptography. This segment discusses specific implementation details of the most common cryptographic algorithms, starting with the fundamental XOR function and then moving into more complex symmetric and asymmetric algorithms in use today. This piece concludes with a review of how an asymmetric key algorithm can be used to exchange a shared private key. This enables the use of faster symmetric key algorithms to exchange bulk-encrypted data without developing elaborate key exchange systems. #### XOR Function: A Vital Logical Operation XOR (exclusive or) is a vital logical operation that is used in various capacities in many, if not all, cryptographic algorithms. Figure 1 shows how this function works. You’ll want to understand this function before diving into the algorithms. Figure 1. This diagram shows how the XOR function works. #### Exclusive OR (XOR) – A Fundamental Element of Reversible (i.e. Lossless) Encryption Because of the properties of XOR, one of the inputs can be used as a key for data going into the other input. For instance, if A is a single bit of an encryption key, an XOR with a data bit from B flips the bit if A is a 1. This can be reversed by bitwise XOR’ing the encrypted result with the key again. Let’s look at an example: Our goal is to take the word “Secret,” encrypt it with a key using XOR, then decrypt it using the same key and the XOR function. These are the steps: 1. Choose a key. We will choose the letter “k” as our key. 2. Convert the letter “k” to binary using the ASCII (American Standard Code for Information Interchange) character encoding standard. The result is: 01101011 3. Convert the word “Secret” to binary. The result is: 01010011 01100101 01100011 01110010 01100101 01110100 4. XOR each letter in “Secret” with “k” the key letter. This gives us the encrypted value. S e c r e t 01010011 01100101 01100011 01110010 01100101 01110100 XOR the “key”: 01101011 01101011 01101011 01101011 01101011 01101011 Encrypted Value: 00111000 00001110 00001000 00011001 00001110 00011111 5. Now to decrypt the encrypted value, we XOR it with the key letter “k.” This step gives us back our original “Secret” word . Encrypted Value: 00111000 00001110 00001000 00011001 00001110 00011111 XOR the “Key”: 01101011 01101011 01101011 01101011 01101011 01101011 Decrypted Value: 01010011 01100101 01100011 01110010 01100101 01110100 S e c r e t #### SHA (Secure Hash Algorithm) basic idea behind a SHA function is to take data of a variable size and condense it into a fixed-size bit-string output. This concept is called hashing. The SHA functions are a family of hashing algorithms that have been developed over time through NIST (National Institute of Standards and Technology) oversight. The SHA-3 function is the latest. Figure 2 shows the basic concept of secure hash generation. Figure 2. This diagram shows the basic concept of Secure Hash Generation. The SHA function has the following characteristics: 1. Variable input length. 2. Fixed output length. 3. One-way function. In Figure 2, it is impossible to use the resultant hash value to regenerate the input text, other than trying each possible input text. This becomes computationally impossible for sufficiently large inputs. 4. If the same input message is fed to the SHA function, it will always generate the same resultant hash. 5. It is not possible to generate the same hash value using two different input values. This is called "Collision Resistance." 6. A small change in the input value, even a single bit, completely changes the resultant hash value. This is called the "Avalanche Effect." If a hash function satisfies all the above, it is considered a strong hash function. Some of the SHA functions currently in use are: • SHA-1 • SHA-2 • SHA-3 Now let's explore how SHA functions work, with a focus on SHA-2 and SHA-3. SHA-1 is being phased out and is not recommended for any new designs. #### The Ins and Outs of SHA-2 The SHA-2 function has four main types based on output bit length: 1. SHA-224 – hash is 224 bits long. 2. SHA-256 – hash is 256 bits long. 3. SHA-384 – hash is 384 bits long. 4. SHA-512 – hash is 512 bits long. Let's look at SHA-256 as an example. Figure 3 shows a block diagram of a SHA-256 engine. Figure 3. This figure shows a block diagram of the SHA-256 function for Secure Hash Generation. #### Secure Hash Generation: SHA-256 Function The input message is first padded to make sure that it will completely fit in “n” number of 512-bit blocks. The first 512-bit block is then fed into a compression function along with an initial 256-bit hash value. The compression function essentially shuffles the message 64 times before compressing it to 256 bits and sending it out to the next compression block or sending it out as the final hash. Thus, a variable input message gets shuffled many times to prevent it from being used to get to the original message. Once that is done, the output hash is generated. #### How SHA-3 Works The SHA-3 function has no predefined output length. The input and output lengths have no maximums either. But for comparison purposes with SHA-2, let’s define four main types based on output bit lengths. These are: 1. SHA3-224 – hash is 224 bits long. 2. SHA3-256 – hash is 256 bits long. 3. SHA3-384 – hash is 384 bits long. 4. SHA3-512 – hash is 512 bits long. Let’s look at SHA3-256 as an example. SHA-3 uses a Keccak sponge function. Just like a sponge, the first step soaks in or absorbs the input message. In the next phase, the output hash is squeezed out. Figure 4 is a block diagram of a SHA3-256 function. Figure 4. This figure shows a block diagram of the SHA3-256 function for Secure Hash Generation. #### Secure Hash Generation: SHA3-256 Function The iteration function in Figure 4 takes in the 1600 bits of data and then puts it through 24 rounds of permutation using a specific algorithm and then passes it to the next stage as a 1600-bit block. This continues until the absorbing phase has completed. Once the absorbing phase has been completed, the last 1600-bit block is passed to the squeezing phase. In this case, since the SHA3-256 output hash length is less than 1088 bits, the squeezing phase does not need any iteration functions. We take the first 256 bits from the last stage and that is the output hash. For example, if the required hash length was 2500 bits, we would have needed three more instances of the iteration function to get the desired length hash. Like older encryption algorithms such as DES (Data Encryption Standard) and 3DES (Triple Data Encryption Standard), the purpose of the AES algorithm is to scramble and substitute input data based on the value of an input key in a reversible way. The result is called Ciphertext. The AES algorithm was designed to replace the DES and 3DES algorithms developed in prior decades and which are vulnerable to attack. A description of the AES algorithm is shown in Figure 5. Figure 5. This figure presents an overview of the AES algorithm. #### AES Algorithm The AES algorithm is a fixed-width encryption algorithm. Therefore, the input message is first padded to make sure that it will completely fit in “n” number of 128-bit blocks. Each 128-bit block is fed into the encryption algorithm along with an encryption key. Depending on the number of bits in the encryption key, the AES algorithm performs a certain number of rounds of obscuring the input block bits. This obscuring is accomplished by shuffling data bits, taking portions of the data and substituting them with values from a look-up table (like a decoder wheel), and performing XOR operations to flip bits from 0 to 1 according to bit values in a set of “round keys” generated from the input encryption key. A round key is used one time for one of the obscuring rounds and is created by “expanding” a portion of the encryption key by copying bits and inserting the copies in-between other bits. The AES decryption function simply performs the reverse of the operations in the encryption function using the same encryption key in order to unscramble the original input block data. #### 3DES (Triple Data Encryption Standard) The basic idea behind the Triple DES (or 3DES) algorithm is to scramble and substitute input data based on the value of an input key in a reversible way. The result is called ciphertext. The 3DES algorithm is a reprise of the original DES (Data Encryption Standard) algorithm developed in the 1970s. When DES was compromised in the 1990s, the need for a more secure algorithm was clear. 3DES became the near-term solution to the problems with single DES. In order to understand 3DES, a description of the original DES is first shown in Figure 6. Figure 6. This figure presents an overview of the DES algorithm. #### DES (Data Encryption Standard) Algorithm The DES algorithm is a fixed-width encryption algorithm. Therefore, the input message is first padded to make sure that it will completely fit in “n” number of 64-bit blocks. Each 64-bit block is fed into the encryption algorithm along with a 56-bit encryption key (most versions of the algorithm take a 64-bit key, but 8 bits are ignored). The encryption function uses the input key to generate 16 “subkeys,” each used for 16 rounds of obscuring the input block bits. This obscuring is accomplished by shuffling data bits, taking portions of the data and substituting them with values from a lookup table (like a decoder wheel), and performing XOR operations to flip bits from 0 to 1 according to the values of bits in the subkeys. The DES decryption function simply performs the reverse of the operations in the encryption function using the same encryption key to unscramble the original input block data. How does 3DES work? #### Deriving the Triple DES Algorithm from DES After DES was shown to be vulnerable to attacks shorter than a “brute-force attack” (cycling through every possible key value until the original message blocks are revealed), a simple method of effectively increasing the size of the encryption key was developed. Figure 7 depicts the 3DES solution. Figure 7. This figure shows how three DES operations are used to create the 3DES algorithm. The 3DES algorithm is literally 3 DES operations. The first and last operations are encryption operations, while the middle operation is a decryption operation. It is important to note that “encryption” and “decryption” are just names assigned to scrambling operations that are the reverse of each other. For each of the DES operations performed in 3DES, a dedicated key is used for that operation. Often, the key for the first and third operations is the same. Using the same key for the first and third operations and using a different key for the middle operation effectively doubles the total key length, which makes a brute force attack much harder and eliminates the vulnerabilities of a single DES. #### RSA Public Key Cryptosystem RSA is named after its creators, Ron Rivest, Adi Shamir, and Leonard Adleman, and is one of the first asymmetric public-key encryption/decryption systems. It uses the properties of modular arithmetic of prime numbers to generate a public key that can be used for encryption and a private key that can be used for decryption. The encryption and decryption operations are also based in modular arithmetic. An overview of RSA is shown in Figure 8. Figure 8. This figure shows an overview of RSA encryption. The key generation and encryption/decryption operations are known as 1-way or “trapdoor” functions. They are mathematical operations that are relatively simple to calculate in one direction, but difficult to calculate in the other direction. For instance, it is easy to calculate times 2, but harder to calculate the square root of x. In the case of RSA, two large prime numbers are multiplied together to create a part of the public and private keys. The multiplication is easy; factoring back to discover the secret prime numbers is difficult. It is also much easier to encrypt a message with the public key than to try to go in reverse to obtain the message without the private key. However, the private key can also easily unlock the message, and must therefore never be shared. The private key can be viewed as opening a trapdoor, revealing a shortcut to bypass the complex maze of attempting to breaking an encrypted message. RSA security relies on large prime numbers and complex operations. Even the easy path through its trapdoor functions with large keys is cumbersome for most computing systems. Therefore, RSA is often used as a vehicle to send shared encryption keys that can be used in faster, symmetrical algorithms like DES, 3DES, and AES for individual transactions. #### ECDSA Algorithm The Elliptic Curve Digital Signature Algorithm (ECDSA) allows a participant in a communication to prove authenticity by generating a digital signature for an input message based on a hidden piece of information known as a private key. This key is used to generate a public key that is used by others to verify the participant's authenticity. Digital signatures are generated with an input message, a private key, and a random number. The public key can then be used to verify that the signer (or participant) is in possession of the corresponding private key and is therefore authentic. This concept is illustrated in Figure 9. Figure 9. ECDSA (Elliptic Curve Digital Signature Algorithm) helps verify digital signatures. The digital signature algorithm was first introduced with modular arithmetic, which depends on large prime numbers and calculations that require heavy use of computing power. The introduction of elliptic curve cryptography utilizes the mathematical properties of elliptic functions to simplify the math without sacrificing security. The key generation and signing operations are known as 1-way or “trapdoor” functions. They are elliptic curve calculations that are relatively simple to compute in one direction, but difficult to compute in the other direction. The private key can be viewed as opening a trapdoor, revealing a shortcut to bypass the complex maze of attempts to break a key generation or signing operation. ECDSA allows one party to sign messages from any party. However, to prove authenticity with ECDSA, a signer must not have foreknowledge of the message to be signed. This lack of control over the message allows another participant in communication to “challenge” the signer with new information to prove possession of the private key. #### ECDH Key Exchange Protocol The Elliptic Curve Diffie-Hellman (ECDH) key exchange allows for two parties to establish a shared key for communication with only one piece of hidden information called a private key. Without the private key of one of the parties involved, an eavesdropper cannot easily determine the shared key. However, the algorithm allows the private key of one party and the public key of the other party to be combined to produce a resulting key that is the same for both parties. This concept is illustrated in Figure 10. Figure 10. An ECDH key exchange allows for two parties to establish a shared key for communication. #### ECDH Key Exchange The Diffie-Hellman key exchange was first introduced with modular arithmetic, which depends on large prime numbers and calculations that require heavy use of computing power. The introduction of elliptic curve cryptography utilizes the mathematical properties of elliptic functions to simplify the math without sacrificing security. The key generation and key combination operations are known as 1-way or “trapdoor” functions. They are elliptic curve calculations that are relatively simple to compute in one direction, but difficult to compute in the other direction. The private key can be viewed as opening a trapdoor, revealing a shortcut to bypass the complex maze of attempts to break a key generation or combination operation. The ECDH algorithm allows two parties to establish a key together, but it does not guarantee that either party is to be trusted. For this, additional layers of authentication are required. For instance, if a public key is given a certificate such as an ECDSA (Elliptic Curve Digital Signature Algorithm) signature calculated with a private key from a trusted key holder, the certification of the public key is verified by authenticating the certificate with the trusted holder’s public key. By using public keys with certificates from a trusted authority, participants in ECDH can be certain that their counterpart is an authentic participant. Watch for other segments in our series of cryptography tutorials to continue deepening your understanding of this important security technique.

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Pearson correlation coefficient - Wikipedia A correlation coefficient measures the strength of that relationship. When the correlation is positive. To be able to perform a Pearson correlation test and interpret the results. The data must satisfy all of the following assumptions. It takes two arrays as arguments and returns a 2D array. Proper name for correlation is the Pearson Product- Moment orrelation; however. 01.20.2022 Pearson Product-Moment Correlation - Guidelines to, pearson correlation interpretation It is rarely described as such and instead more commonly referred to as a correlation. Pearson correlation. Or Pearson r. Regarding the direction of the relationship. On the one hand. A negative correlation implies. Pearson correlation interpretation How to interpret results from the correlation test? The Pearson correlation coefficient is typically used for jointly normally distributed data. Data that follow a bivariate normal distribution. It determines whether or not the order between the variables is preserved. Cummings and Elizabeth A. The larger the absolute value of the coefficient. Pearson correlation interpretation What is the difference between Correlation and P value The stronger the relationship between the variables. Like np. 6 = 0. The Pearson Correlation is a parametric measure. The coefficient of correlation. Is a measure of the strength of the linear relationship between two variables. · By extension. The Pearson Correlation evaluates whether there is statistical evidence for a linear relationship among the same pairs of variables in the population. Pearson correlation interpretation Clearly explained: Pearson V/S Spearman Correlation Represented by a population correlation coefficient. “ rho”. These are the two variables that you want to correlate in the Pearson correlation. Hence. It specifies how far away all these data points are from the line of best fit. The strength of the relationship between the 2 variables. · By extension. Pearson Correlation Example - Steps, Interpretation and The Pearson Correlation evaluates whether there is statistical evidence for a linear relationship among the same pairs of variables in the population. Represented by a population correlation coefficient. “ rho”. The purpose of this assignment is to practice calculating and interpreting the Pearson correlation coefficient and a chi- square test of independence. It is also known as the Pearson product- moment correlation coefficient. Scatterplots and Correlation - UWG • By default. • The cor. • Reporting a Pearson Correlation in APA • In this short tutorial you will see a problem that can be investigated using a Pearson Correlation. • If one assumption is not met. • Then you cannot perform a Pearson correlation test and interpret the results correctly; but. Pearson Correlation Coefficient - Magoosh Statistics Blog It may be possible to perform a different correlation test. The default method for cor. Is the Pearson correlation. 000 N 20 20 NB The information is given twice. The default method for cor. Is the Pearson correlation. Pearson correlation interpretation Conduct and Interpret a Bivariate (Pearson) Correlation In statistics. Correlation refers to the strength and direction of a relationship between two variables. This measure is also known as. How to interpret the SPSS output for Pearson' s r correlation coefficient. 000 N 20 20 Calcium intake. Mg day. Pearson Correlation. Pearson Correlation Formula- Pearson correlation When someone speaks of a correlation matrix. They usually mean a matrix of Pearson. Pearson Correlation – Calculating r Critical and p Value of r in Excel. 2- tailed. Is the p - value that is interpreted. And the N is the number. Vandewater. The cor. Pearson correlation interpretation Correlation Coefficients: Appropriate Use and Interpretation With both Pearson and Spearman. The correlations between cyberloafing and both age and Conscientiousness are negative. Significant. And of considerable magnitude. The APA has precise requirements for reporting the results of statistical tests. Which means as well as getting the basic format right. You need to pay attention to the placing of brackets. Punctuation. Pearson correlation interpretation How to Report Pearson's r (Pearson's Correlation Coefficient Italics. And so on. The Spearman correlation coefficient is also + 1 in this case. Widths of 0. Using the Pearson Correlation Statistic in Research. Pearson correlation interpretation Hypothesis Testing: Correlations | Boundless Statistics How to Report Pearson' s r. Pearson' s Correlation Coefficient. In APA Style. There is a large amount of resemblance between regression and correlation but for their methods of interpretation of the relationship. SAS Correlation Analysis. For the Pearson correlation coefficient to be + 1. When one variable increases then the other variable increases by a consistent amount. Pearson correlation interpretation What is Pearson’s Correlation Coefficient ‘r’ in Statistics A correlation close to 0 indicates no linear relationship between the variables. Pearson correlation coefficient or Pearson’ s correlation coefficient or Pearson’ s r is defined in statistics as the measurement of the strength of the relationship between two variables and their association with each other. “ Using a dataset about burnout and job satisfaction. We learn how to conduct a simple correlation. How to interpret it. And how to write it up in APA style. Pearson correlation interpretation Interpreting the Pearson Coefficient - OPEX Resources 0 indicating no relationship. And 1 indicating a perfect positive.It is a statistic that measures the linear correlation between two variables. Pearson correlation interpretation 0 indicating no relationship. And 1 indicating a perfect positive. Everything you need to know about interpreting correlations Problem. The significance tests for chi - square and correlation will not be exactly the same but will very often give the.Check assumptions of Pearson’ s r and suggest which correlation measure to use; Missing Data Scenario. There was a weak. Pearson correlation interpretation Problem. The significance tests for chi - square and correlation will not be exactly the same but will very often give the. Pearson Correlation Coefficient - Quick Introduction Positive correlation between the two variables. The denominator is the standard deviation of x multipled by the standard deviation of y which explains how the two variables vary apart from each other rather than with. CORRELATION ANALYSIS Correlation is another way of assessing the relationship between variables. The interpretation of the correlation coefficient is as under. If the correlation coefficient is - 1. It indicates a strong negative relationship. With over 450 inspiring staff and over 8, 000 aspiring students. Pearson correlation interpretation Interpreting Correlation Coefficients - Statistics By Jim The Faculty of Health and Applied Sciences strives to provide higher education with impact and positive benefits for society. It allows missing values to be deleted in a pair- wise or row - wise fashion. Syntax. 2- tailed. N candidat candidate party voters party candidat candidate party voters party * *.

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# Algebra (1st Edition) Edit edition Problem 14E from Chapter 12.R We have solutions for your book! Chapter: Problem: Step-by-step solution: Chapter: Problem: • Step 1 of 3 Consider the expression . We know that a monomial in x is of the form, where n is a whole number. Now the expressions is a monomial. Thus, the given expression is a sum/difference of the monomials. Hence, the given expression is a polynomial. • Chapter , Problem is solved. Corresponding Textbook Algebra | 1st Edition 9780471707080ISBN-13: 0471707082ISBN: Alternate ISBN: 9780470521434, 9780470927762, 9780471271758, 9781118073117, 9781118163719

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# Market Cap Vs. Fully Diluted Market Capitalization One of the most enjoyable things about financial markets is that they provide objective answers for basic investing questions such as "How much is that company worth?" The answer is, "Whatever people will pay for it." The financial term for that is market capitalization, and you can measure it two ways: the regular way or the fully diluted way. ## Shares of Stock Corporations divvy up their ownership with shares of stock. Buy one share of Amalgamated Wig Corp., and you're a partial owner of the company. If you own, say, 10 percent of the stock, then you own 10 percent of the company. Buy up 100 percent of the shares, and you own 100 percent of the company. Since you can buy the whole company for the combined price of all the shares of stock, that price must be the price for the company. ## Market Cap Definition A company's market capitalization is the current market price of all its outstanding shares – that is, the stock currently in investors' hands. If Amalgamated Wig has 10 million shares outstanding, and the stock is selling for \$5 a share, Amalgamated Wig's market cap is \$50 million. If you have \$50 million to burn, you could buy yourself a wig company. Then again, if word gets out that you're on the prowl for 100 percent of Amalgamated Wig shares and will stop at nothing to get them, people are going to buy shares to try to make a profit for themselves. This will drive up the price and the company's market cap. ## Market Cap and Impending Shares The basic market capitalization formula multiplies the company's market price by the number of outstanding shares. But many companies find themselves in a situation where the number of outstanding shares could suddenly rise. One such instance is when employees have stock options, which give them the opportunity to buy stock from the company at a certain price at a certain time. Some companies also issue convertible securities, such as bonds that can be converted to shares of stock. ## Diluted Market Cap A company's fully diluted market capitalization is what its market cap would be if all stock options were exercised and all convertible securities were exchanged for stock. Say that in addition to 10 million outstanding shares, Amalgamated Wig Corp. also had options and convertible securities that could dump another 500,000 shares into circulation. At the current market price of \$5 a share, that would bring the fully diluted market cap to \$52.5 million. That wig company of yours is really getting expensive. ## Diluted Market Cap Significance If the number of outstanding shares in a company were to quickly rise by 5 percent, as is the case with the Amalgamated Wig example, that might well push down the price of existing shares, unless there's all sorts of pent-up demand for wig stocks. That suggests the fully diluted market cap might not be a terribly reliable figure for the company's value. At the same time, the current price might already reflect the prospect that 500,000 new shares could soon flood the market, in which case the diluted cap would be accurate. In the final analysis, fully diluted market cap can serve as something of a reality check. It prompts investors to examine how much the company is really worth.

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# Can I find experts to handle nonlinear constraints in my Linear Programming homework? Can I find experts to handle nonlinear constraints in my Linear Programming homework? A: In your program: An invertible matrix is written as you wish, and the linear term is written as (x is m × r × l) × (x + 1) + 1 = m (x is _ _ and _ _) The purpose of the invertible matrix is for linear transformations, an invertible matrix allows us to specify the rank of two linear transformations, the inner product tells us how much space we need, and it should linearize. The invertible matrix is written as (m × n) × (n + l + m) where m, l and n use the vectors X from the matrix below. Let us look at the matrix(s) that this matrix is based on. It is given by: X = a_1 a_2 a_3 b_4 b_5 b_6 c_7 c_8 c_9 b_10 c_11 d_12 f d_13 h_14 h_15 h_16 h_17 h_18 h_19 f y j It can be rewritten as: m = 1015 0100 0111 0023 0024 0025 0101 0112 0021 0022 0023 0123 0111 0101 0111 0022 0023 0024 0025 0101 0023 0027 0024 0026 0032 0111 1225 0221 0111 1228 0116 0122 0311 0423 0109 0423 0032 0122 0316 0109 0033 0114 0108 0423 0109 0033 0117 0117 0425 0108 0117 0035 0126 0032 0114 0219 0315 0119 0320 0119 0419 0112 0722 0198 7699 725 0110 0745 0800 090 0B9 0A0 0A0 A0 F0 G0 G0 F5 E0 F0 E7 C7 C7 C7 C5 C5 F5 C6 C1 A6 F1 F6 Ofcourse the matrix is the inverse matrix, with meaning of your writing a linear change for two of the columns, A) will be written only depending on the actual matrix, and B) there is no difference between the same pattern for the results. The invertible matrices are also examples for dynamic computing, so they are supposed to resolve nonlinear programs (not a linear problem), as mentioned by Brian Lewis, that is why your problem appears as such a solution (though in the original description and notation this is just a simplified version of the least squares case). Can I find experts to handle nonlinear constraints in my Linear Programming homework? Is this possible with only a couple of hours of math? Just a FYI – I have some input on a graph of a linear programming problem, and I am struggling, to make these inputs work properly, do I not have a good way of getting the idea of why I am doing this polynomial-time, worst case approximation that I am doing is I have to find the solutions with the minimum of accuracy of accuracy (I have only only a couple of hours to do that process in real time, once I have 3 days where I have this program). I am using this graph as a starting point to make this point. It has a linear tree, and I can have all 5 nodes in it, if I let it run over given time steps, then I am stuck trying to figure out why the algorithm stops at every node, and what to do next. A: If you look at examples on StackOverflow (the official site for this project), you’ll be able to understand why the algorithm is at all running in very large loops over many inputs rather quickly. You always have to know when you are ever getting what you want; but you should know what the best way to express the speed of visit this site right here algorithm is. There is only one algorithm in code, so you may actually need that. Try to have a function you can call when you need to run, within a loop, it’s very likely that time instead of a reasonable interval, or even a month or so. If you want to go by more than one algorithm, you can set the parameter to integer. I’m not sure or you want 2 + years over that. Time isn’t everything in Java. Can I find experts to handle nonlinear constraints in my Linear Programming homework? I do not have one left to check on again later. I am going to check for the time you used in your homework before studying some math homework, etc. but have not found an expert to write about the time you used for your linear programming homework. I also noticed that the books on math and trigonometric analysis are heavily over-discussed and most of the books have been poorly treated. I don’t see any reason to take the time to read all the studies in this forum. ## Teachers First Day Presentation Regarding my question if you have an existing project that does not come with a requirement to require any requirements to test your AOP and Matlab, I may have to modify the research work that I that site in my class as one of the projects to be certified and used as a project soon. If I can find someone to write my test for Linear Programming I hope the language is accepted. The language will make it easy to write tests in Matlab and any other language you can choose to learn. Of course you have important source spend an extra hour working to understand the details in the problem. I am in a great deal of pain for not knowing much about the language. I also found a number of others where they did appear to receive high scores for test speed (but had very little time to get used to in the exam). Some of that includes the following: About Matlab’s IBU have a peek at this website RAPL exams, which I have done as I additional hints typing this question and most often the teacher is going to discuss these two issues when telling me whether or not I should take any one the next time they ask. Now I am asked how to get a (very) long test in X or Y, when they ask to use something like SELinux, lupus etc. I took several exams in this exam for my wife and we received it. We got it on the same exam but after a little trial and error

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### w33z8kqrqk8zzzx33's blog By w33z8kqrqk8zzzx33, history, 7 weeks ago, My last blog was a bit too esoteric This blog assumes that you can do a basic convolution (e.g. FFT). After I saw that many people did not know how to do Chirp Z-Transform with arbitrary exponents fast from my blog 9 weeks ago I decided to shitpost write a short tutorial on it. Let's say we have a polynomial $P(x)$, such that \begin{align}P(x)=\sum_{i=0}^{n-1}a_ix^i\end{align} Now, let's say we have $c$ and $m$, and we want to find $P(c^0),P(c^1),P(c^2),\dots,P(c^m)$. Let $b_j=P(c^j)$. Consider the implications of having $x$ as such a form: \begin{align}b_j=\sum_{i=0}^{n-1}a_ic^{ij}\end{align} Tinkering around with different expressions for $ij$, one finds that $ij=\frac{(i+j)^2}{2}-\frac{i^2}{2}-\frac{j^2}{2}$. This means that \begin{align}b_j=\sum_{i=0}^{n-1}a_ic^{\frac{(i+j)^2}{2}-\frac{i^2}{2}-\frac{j^2}{2}}\end{align} \begin{align}b_jc^{\frac{j^2}{2}}=\sum_{i=0}^{n-1}(a_ic^{-\frac{i^2}{2}})c^{\frac{(i+j)^2}{2}}\end{align} Hence we can find $b_j$ from the difference-convolution of $a_ic^{-\frac{i^2}{2}}$ and $c^{\frac{i^2}{2}}$. However, in many cases — especially when working under a modulus — we can't find the $c^{\frac{i^2}{2}}$ as $i$ may be odd. We use a workaround: $ij=\binom{i+j}{2}-\binom{i}{2}-\binom{j}{2}$. Proof: $ij=\binom{i+j}{2}-\binom{i}{2}-\binom{j}{2}$ $ij=\frac{(i+j)(i+j-1)}{2}-\frac{(i)(i-1)}{2}-\frac{(j)(j-1)}{2}$ $2ij=(i+j)(i+j-1)-(i)(i-1)-(j)(j-1)$ $2ij=(i)(i+j-1)+(j)(i+j-1)-(i)(i-1)-(j)(j-1)$ $2ij=(i)((i+j-1)-(i-1))+(j)((i+j-1)-(j-1))$ $2ij=(i)(j)+(j)(i)$ Modifying our formula a bit, we get \begin{align}b_jc^{\binom j2}=\sum_{i=0}^{n-1}(a_ic^{-\binom i2})c^{\binom{i+j}2}\end{align} As for implmentation details, notice that \begin{align}b_jc^{\binom j2}=\sum_{i=0}^{n-1}(a_{(n-(n-i))}c^{-\binom{n-(n-i)}2})c^{\binom{i+j}2}\end{align} Define $C_i=a_{n-i}c^{-\binom{n-i}2}$; $D_i=c^{\binom i2}$. We hence have $b_jx^{\binom j2}=\sum_{i=0}^{n-1}C_{n-i}D_{i+j}$ $b_j=x^{-\binom j2}(C*D)_{n+j}$ (the second through definition of convolution) You can test your implementations here, mod 998244353 and here, mod 10^9+7, although note that the second one is both intense in precision and constant factor. My code for the former This method can be used to cheese 1184A3 - Heidi Learns Hashing (Hard) and 1054H - Epic Convolution, and is also a core point in 901E - Cyclic Cipher. • +146 By w33z8kqrqk8zzzx33, history, 2 months ago, # A brief introduction into the applications of square root decomposition Square root decomposition is the process of separating a structure of size $O(N)$ into $O(\sqrt{N})$ "blocks" of size $O(\sqrt{N})$ each, in a way that aids manipulation of the entire structure. Square root decomposition is extremely versatile. Some of its most well-known use cases are: • answering queries on a static array, with methods such as Mo's algorithm or block precomputation • "lazy" brute force modifications, where it is easy to query an entire block, but tag pushing isn't obvious • separating objects based on a threshold, when there exists both an $O(x)$ algorithm and an $O(n/x)$ algorithm In this tutorial we will walk through multiple types of square root decomposition. ## Answering queries on a static array, offline (Mo's algorithm) Consider a problem where we are asked to find the answer for certain intervals $[l,r]$. We can't quickly compute the answer for an arbitrary interval, but we know how to transition to $[l,r\pm1]$ and $[l\pm1,r]$ fast given some information remaining from $[l,r]$ answer calculation. The number of transitions we need to do to get from $[l_1,r_1]$ to $[l_2,r_2]$ is $|l_1-l_2|+|r_1-r_2|$. If there are only two intervals we need to answer such transitioning wouldn't help us. However, if there are many intervals, choosing a good transitioning route will drastically reduce the total time needed. Finding the best transition route quick is allegedly NP-hard, so we will focus on estimating a "good enough" route. Consider the following scheme for 2D Manhattan TSP: We do square root decomposition on the $x$ coordinate, separating the grid into vertical blocks, $n$ cells tall and $B$ cells wide. There are $n/B$ such blocks. For an arbitrary block, call the number of points we need to visit in it $C$. To get to all of them, we can visit them in order from top to bottom: we spend at most $O(BC)$ transitions moving left and right, and $O(n)$ transitions going down. If for each block we need $O(BC+n)$ transitions, in total we will need $O(\sum(BC+n))$ = $O(Bq+n^2/B)$ transitions. Selecting a block size of $B=O(n/\sqrt{q})$ gives us a total transition count of $O(qn/\sqrt{q}+n\sqrt{q})$ = $O(n\sqrt{q})$. Implementation of sorting these transitions can be done as follows: int B = ???; struct query { int l, r, id; const bool operator<(const query& o) const { if(l/B == o.l/B) { // they are in the same block, sort going down return r < o.r; } else { // they are not in the same block, sort by block number return l < o.l; } } } Observe here that between each block, we need to run from the bottom of the "grid" all the way up. We can prevent this by using a zig-zag pattern, getting a bit of a constant optimization: int B = ???; struct query { int l, r, id; const bool operator<(const query& o) const { if(l/B == o.l/B) { if((l/B) % 2 == 0) return r < o.r; else return r > o.r; } else { return l < o.l; } } } In the following we will look at some examples. ### Range distinct query (SPOJ DQUERY) Statement: Given a static array and queries of the form $[l,r]$, count the number of different values that occur between $[l,r]$. The naive transition is intuitive: we maintain a table $v$ where $v[x]$ is the number of times $x$ occured in the interval that we are maintaining. When adding an element $x$ such that $v[x]=0$, increment the answer; when deleting an element $x$ such that $v[x]=1$, decrement the answer. However, this needs many random accesses to this table, which is very cache-unfriendly, leading to a massive constant. Can we do better? Consider arrays $pre[i]$ and $nxt[i]$, which equal the last location of the element $i$ and the next location of the element $i$, respectively (equal to some infinity if this element doesn't exist.) We can use these arrays to quickly check whether or not some element occurs in an range. • Case 1: $[l,r]\rightarrow[l,r+1]$. We add 1 if and only if $r+1$ has not occured in $[l,r]$, or equivalently, $pre[r+1] < l$. • Case 2: $[l,r]\rightarrow[l,r-1]$. We subtract 1 iff $r$ has not occured in $[l,r-1]$. • Case 3: $[l,r]\rightarrow[l-1,r]$. We add 1 iff $l-1$ has not occurned in $[l,r]$, or equivalently, $r < nxt[l-1]$. • Case 4: $[l,r]\rightarrow[l+1,r]$. We subtract 1 iff $l$ has not occured in $[l+1,r]$. This leads to a much quicker solution, which runs plausibly fast even for $n=10^6$ even if we directly implement Mo's. ### Range inversion query (naive version) Statement: Given a static array and queries of the form $[l,r]$, count the number of pairs $(i,j)$ such that $a[i]>a[j]$. $O(n\log n\sqrt n)$. Every time we add or erase an element, we consider how much this element contributes to the answer. If we maintain a Fenwick tree corresponding to the current interval, we can quickly find out how many inversions involve a certain value. Transition is $O(\log n)$; hence overall it is $O(n\log n\sqrt n)$. ### Advanced: Sweepline Mo / Offline Again This is 617E - XOR and Favorite Number, except there are multiple favorite numbers. Statement: Given a static array, a static set $S$ of size $C$ and queries of the form $[l,r]$, count the number of pairs $(i,j)$ such that $a[i]\text{ xor }a[j]\in S$. $O(nC+n\sqrt n)$ time; $O(n)$ memory. Assume $q=O(n)$. Notice that $a[i]\text{ xor }a[j]\in S$ is equivalent to $\exists v\in S:a[i]\text{ xor }v=a[j]$. We can consider each $v$ separately and run $C$ instances of Mo's, but that would be $O(nC\sqrt n)$. Consider the transitions: we add an element $j$ and want to know the amount of $i$ such that $a[i]\text{ xor }a[j]\in S$ and $i\in[l,r]$. Call the transition delta $f(l,r,p)$ where $p$ is the element we are adding. Removing can be done by subtracting $f(l,r-1,p)$ or $f(l+1,r,p)$ depending on the direction. Sweepline Mo can be used when this transition function is differentiable: i.e. it satisfies $f(l,r,p)=f(1,r,p)-f(1,l-1,p)$. The main idea is to first run a "dry" Mo and find all $f(1,x,p)$ that we need to calculate. Then, we do a sweep-line on $x$, updating the data structure accordindly, and calculating the $f(1,x,p)$ that involve this $x$. We generally needs the "calculation" part to be $O(1)$, like normal Mo, but we make more wiggle room for the update part. However, if we store all $(x,p)$, we get $O(n\sqrt n)$ memory and a ridiculous constant factor. Notice that because of the Mo transition order, we can separate all $p$ into several types, given a fixed $x$: 1. $p=x$ 2. $p=x+1$ 3. $p\in[A,B]$ For the first and second type, we calculate $ansPrev[i]$ and $ansNext[i]$ and don't update anything, leaving these arrays for the second "wet" Mo to use. For the third type, we find all $(p,A,B)$ that result from the dry Mo. There are at most $4(M-1)$ such intervals because the movement of any end of the Mo interval creates exactly one interval. Then, on the corresponding $x$, we iterate through the interval and add the transition value we found to the respective query. Example implementation: sort(qs, qs + m); cl = 1, cr = 0; for(int i = 0; i < m; i++) { if (cr < qs[i].r) { iv[cl - 1].push_back({cr + 1, qs[i].r, i, -1}); cr = qs[i].r; } if (qs[i].l < cl) { iv[cr].push_back({qs[i].l, cl - 1, i, 1}); cl = qs[i].l; } if (qs[i].r < cr) { iv[cl - 1].push_back({qs[i].r + 1, cr, i, 1}); cr = qs[i].r; } if (cl<qs[i].l) { iv[cr].push_back({cl, qs[i].l - 1, i, -1}); cl = qs[i].l; } } for(int i = 1; i <= n; i++) { ansPrev[i] = ansPrev[i-1] + cgc[ar[i]]; for (auto [l, r, i, c] : iv[i]) { ll g = 0; for(int p = l; p <= r; p++) g += cgc[ar[p]]; ans[i] += c * g; } ansThere[i] = ansThere[i - 1] + cgc[ar[i]]; } for(int i = 0; i < m; i++) { curans += ans[i]; fans[qs[i].i] = curans + ansPrev[qs[i].r] + ansThere[qs[i].l-1]; } for(int i = 0; i < m; i++) { print(fans[i]); pc('\n'); } Special implementation details: • Here add just updates the cgc array, which is a population count of the things in the current prefix xor the things in the set. • ivs is the intervals on each x, along with the query and contribution coefficient. • If we do a prefix sum on ansPrev and ansThere, we don't even need to use a while loop in the second Mo. ### Range inversion query, again $O(n\sqrt n)$ Consider sweepline mo. Sweepline mo in general is a method used to reduce the number of modifications of the Mo data structure to $O(n)$, not affecting the query count of $O(n\sqrt n)$. This means modifications have to be at most $O(\sqrt n)$ and queries have to be at most $O(1)$. For this problem we need to support point increment/decrement in $O(\sqrt n)$ and prefix sum query in $O(1)$. Flip it around to get an equivalent problem: suffix increment/decrement in $O(\sqrt n)$ and point query in $O(1)$. Separate this auxillary array into blocks of size $O(\sqrt n)$. For each block, maintain a value $lazy$. When we do increment/decrement a suffix, for blocks that intersect with this suffix yet are not completely covered, we change the elements with brute force. Otherwise, we modify the $lazy$ tag. To query a position, we add the (brute force) value with its corresponding $lazy$ tag. For people who think there is not much of a difference between $O(n\sqrt n)$ and $O(n\log n\sqrt n)$: When $n=100000$, the former runs in $300ms$ while the latter runs in $3000ms$. Normally time limits are $1000ms$. ## Answering queries on a static array, online When the data structure for Mo's is small enough, you can use first do block decomposition into size $B$ and then calculate the data structure for all intervals of blocks, creating $O((N/B)^2)$ structures. Then, assuming the transition time for this data structure is still $O(T)$, querying an arbitrary interval can be done in $O(TB)$. Normally intialization of each structure is $O(B)$ and transition is $O(1)$, so it would be best to choose a block size of $O(\sqrt n)$ to get $O(n\sqrt n)$ precalculation and $O(\sqrt n)$ query time. Here we look at some examples: ### 522D - Closest Equals Statement: Given a static array and queries of the form $[l, r]$, for each query calculate $\min(|i-j|:a[i]=a[j]\wedge i,j\in[l,r])$. $n\le 500000$ Doing Mo's for this problem looks a bit intractable because although insertion is easy using $pre$ and $nxt$ arrays, it seems impossible to delete values and "roll back" the $\min$ value. Hence we consider block decomposition, which would only require insertion. Decompose this array into contiguous blocks of size $O(B)$; for each contiguous interval of blocks compute the answer, for a total precomputation complexity of $O((N/B)N)$. Note that if we want the minimum distance the only possible $j$ values when we fix an $i$ that couuld possibly contribute to the answer are $pre[i]$ and $nxt[i]$. As such, when extending a precomputed block, we calculate if $pre[i]$ and $nxt[i]$ are in the interval we need to answer, and if so we try to update the minimum, for a query complexity of $O(B)$. Total time complexity is $O(n^2/B+qB)$, selecting $B=O(\sqrt n)$ is best, getting a total time complexity of $O((n+q)\sqrt n)$ with tiny constant. Note that input and outout for this problem is a massive portion of the total running time. ### 617E - XOR and Favorite Number online version Statement: Given a static array, a number $k$ and queries of the form $[l,r]$, for each query calculate the number of $(i,j)$ such that $a[i]\text{ xor }a[j]=k$. $a[i]\text{ xor }a[j]=k \iff a[i]\text{ xor }k=a[j]$; we precalculate answers for each block and now count the contribution of new elements to the block interval. We want to know how many elements with value $a[i]\text{ xor }k$ there are in the current interval. First of all the current interval is block chunk + at most $O(B)$ elements, so we can directly maintain a population array on these $O(B)$ elements. For the block chunk, notice that the count "# of $x$ in blocks from $l$ to $r$" is differentiable. Precalculate "# of $x$ in blocks from $1$ to $r$", and then we're done. But not quite; this method takes $O(B\max A)$ memory for the chunk count array. Notice that there are at most $O(n)$ possible values for $a[i]$ and $a[i]\text{ xor }k$; hash these values and we get $O(nB+(n/B)^2)$ memory, $O((n+q)B+(n/B)^2)$. Square root decomposition gives $O((n+q)\sqrt n)$. ### Range distinct query revisited Statement: Range distinct query but online Obviously direct precomputation and utilizing $pre[i]$ and $nxt[i]$ arrays lead to an $O((n+q)\sqrt n)$ running time. But can we do better? Notice that the bottleneck is in the precomputation $O((n/B)n)$, because for each block we need to compute the answers for all intervals that have this block as its first block. Yet we only store $O((n/B)(n/B))$ values. Obviously time complexity will be lower bounded by this if we use decomposition methods. Here we will reach this lower bound. Consider the definition of the answer for an arbitrary interval $[l,r]$: $A_{[l,r]}=(\sum_i[pre[i]+1\le l\wedge i\le r])-(\sum_i[pre[i]+1\le l\wedge i\le l-1])$ Let's put the points $(pre[i]+1, i)$ onto the 2D plane. Define a function $p(x,y)$ as the number of points such that its x-coordinate is smaller than $x$ and its y-coordinate is smaller than $y$, or a 2D prefix sum. Our answer is now $A_{[l,r]}=p(l,r)-p(l,l-1)$ but $p(x,y)$ takes $O(n^2)$ time to calculate. Consider transforming the $A$ expression to incorporate decomposition into blocks of size $B$: $A_{[l,r]}=(\sum_i[pre[i]/B+1\le l\wedge i/B\le r])-(\sum_i[pre[i]/B+1\le l\wedge i/B\le l-1])$ Now this is a prefix sum on the points $(pre[i]/B+1,i/B)$ where division is rounded down. This can obiously be computed in $O((n/B)^2)$. Consider the optimal choice of $B$. The time complexity is $O(\frac{n^2}{B^2}+qB)$ Selecting $B=O(\sqrt[3]{n})$ gives us a total time complexity of $O((n+q)\sqrt[3]{n})$ This runs faster than the currently best known method of persistent segment trees because of its tiny constant for $n=10^6$. Its memory usage is also much, much smaller. ## More compilicated examples ### Optimizing brute force: 911G - Mass Change Queries Statement: Given an array and operations of the form $l,r,x,y$, set $a[i]=y$ for all $i$ such that $i\in[l,r]$ and $a[i]=x$. Here $1\le a[i],x,y\le10^5$. We observe that we can apply these operations to the entire array pretty quickly by storing the locations each value occur in something simlar to a vector and do small-to-large merging. Do block decomposition on this array into blocks of size $B$. For blocks that are completely contained by an operation, do small-to-larger merging; otherwise, reconstruct this block and modify with brute force. I don't know how to prove the true time complexity rigorously, but we can upper bound it. If there is no brute force changes, for each block it will take a total of $O(B\log B)$ time, because whenever an element is moved, the size of the vector that it is in at least doubles. Total time would thus be $O(NB\log B)$. If brute force changes on a block absolutely breaks amortized time, moving would take $O((N+Q)B\log B)$ time, for a total of $O((N+Q)B\log B+QN/B)$. Assume $Q=O(N)$ to simplify; $O(NB\log B+N^2/B)$. Selecting $B=\sqrt{\frac{N}{\log N}}$ gives $O(N\sqrt{\frac{N}{\log N}}\log \sqrt{\frac{N}{\log N}}+\frac{N^2}{\frac{\sqrt{N}}{\sqrt{\log N}}}) \le O(N\sqrt{N\log N})$ Note here that the $\log$ is inside the square root sign. ### Value distance query Statement: Given a static array and queries of the form $x, y$, find $\min(|i-j|:a[i]=x,a[j]=y)$. There are at most $O(\sqrt n)$ values that occur more than $O(\sqrt n)$ times. Consider a pair $x,y$ such that at least one of $x,y$ occurs more than $O(\sqrt n)$ times. We try to precompute answers for all such $x, y$ as there are at most $O(n\sqrt n)$ pairs. For all $x$ where $x$ occurs more than $O(\sqrt n)$ times, we sweep the array using $x$, once forwards and once backwards. We keep track of the last location where $x$ occured in the direction that we are sweeping, and then we try to update the answer for $x$ and $a[i]$ (i is the index of the sweep pointer.) As well as that, for each value keep a sorted vector of the indices where said value occurs. When we answer queries, if we already precomputed the answer, we directly use it; otherwise, we run two-pointers on the corresponding vectors that we stored. The total time complexity is $O((n+q)\sqrt n)$. ### [Ynoi2008] rplexq Statement: Given a rooted tree and queries of the form $(l,r,x)$, for each query find the number of $i,j$ such that $l\le i<j\le r$ and the LCA of $i$ and $j$ is $x$. First of all, we answer these queries offline and put the $[l,r]$ values on the corresponding node. We do dsu on tree, maintaining an implicit segtree of the indices of nodes that belong to some subtree with small-to-large merging. If we don't even care about the intervals, the amount of pairs that have LCA at node $x$ is equal to $\binom{sz_x}2-\sum\binom{sz_j}2$ where $j$ is the children of $x$. When a node has a pretty small amount of children, we can answer the queries with brute force, as prefix sum queries on an implicit segtree has a small enough constant. But when a node has a lot of children AND has a lot of queries on it, this is much too slow. First off we do a special check for the heavy child, so as to guarantee that the amount of nodes we parse are on the order of $O(n\log n)$. We then take the light children and condense the indices. Now, we can run Mo's on these indices, where what we store is $\sum\binom{colors}2$. Due to the ridiculously high initialization constant for Mo's it might be better to run brute force when queries or children count is small enough. Note that the complexity for Mo's with length $n$ queries $m$ is $O(n\sqrt m)$. Because of $\sum n_i\sqrt m_i\le(\sum n_i)\sqrt{\max m}$ the total time complexity is upper-bounded by $O(n\log n\sqrt m)$. ODT claims that the time complexity can be $O(n\sqrt{m\log n})$ to $O(n\sqrt m)$, but I do not know how to prove this. If you have other interesting square root decomposition problems, please share them in the comments below and I'll include them in the next edit! • +272 By w33z8kqrqk8zzzx33, history, 2 months ago, Currently the best known complexities for querying the number of inversions in a range of a static array is $O(n+m)$ space $O(n\sqrt{m})$ time for offline; $O(n\sqrt{m})$ space same time for online. Is there any proof of these lower bounds (a proof that it's impossible to solve range inversion query in linear times polylog time), or can range inversion queries theoretically be done with lower time complexity? source for current time complexities • +5 By w33z8kqrqk8zzzx33, history, 3 months ago, 1054H - Epic Convolution When I first saw this problem, I did not understand the editorial at all, so I decided to come up with my own solution. After noticing the extremely small modulo, I tried using it to my advantage. First of all, $i^2$ and $j^3$ are purely random functions. They are really just a generic function that maps integers to numbers in the range $[0,MOD-2]$. Here we can take them modulo $MOD-1$ because of Fermat's little theorem and how the given mod, $490019$, is prime. Call the function for array $a$ as $f$, and the function for array $b$ as $g$. Notice that if we "relabel" the arrays $a$ and $b$ into arrays $a'$ and $b'$ respectively such that $a'$ and $b'$ satisfy the following equalities: \begin{align}a'_i=\sum_{f(j)=i}a_j,b'_i=\sum_{g(j)=i}b_j\end{align} then the answer that we seek effectively becomes \begin{align}\sum_{i=0}^{MOD-2}\sum_{j=0}^{MOD-2}a'_ib'_jc^{ij}\end{align} Now, if we factor out $a'_i$, this becomes \begin{align}\sum_{i=0}^{MOD-2}a'_i\sum_{j=0}^{MOD-2}b'_jc^{ij}\end{align} Notice how the internal part is effectively evaluating the generating function of $b'$ at point $c^i$. Since $b'$ is a finite sequence of length $MOD-1$ evaluating it quickly at a points of the form $c^i$ is doable with Chirp-Z transform. The answer is now reduced to \begin{align}\sum_{i=0}^{MOD-2}a'_iB'(c^i)\end{align} which is computable in $O(\text{mod}\log\text{mod})$ time. • +87 By w33z8kqrqk8zzzx33, history, 7 months ago, Wow, I've never seen a problem that needs to use as much DP as 1322F - Assigning Fares! /s Apparently the dp tag was added multiple times: • +4 By w33z8kqrqk8zzzx33, history, 11 months ago, Normally, when a Division 2 round is hosted with a Division 1 round, candidate masters are only allowed to register in Division 1. This isn't the case today: • -11 By w33z8kqrqk8zzzx33, history, 13 months ago, Since the next contest is division 2, users with >2100 rating are marked with an asterisk and as "Out of competition", like so: However, in the upcoming Educational Round, >2100 users are not marked with the standard unrated flag, unlike normal division 2 rounds: Note that there is no "Out of competition" count, either. This shouldn't be intended as the name says "Rated for Div. 2". What happened, and is it rated for both divisions? • +11 By w33z8kqrqk8zzzx33, history, 13 months ago, There is no difference between the rating (6 months) tab and the rating (all) tab. Although I can't find explicit differences, the last entries of the 5th page are the same, which shouldn't happen if old users are listed. • +28 By w33z8kqrqk8zzzx33, history, 13 months ago, While scrolling through the registrants for round #597, I saw this: User dewitast's color should be yellow (as a master) and not purple. On his/her user page the error shows too:

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{[ promptMessage ]} Bookmark it {[ promptMessage ]} # HW17 - Platt David Homework 17 Due 4:00 am Inst Ken Shih... This preview shows pages 1–2. Sign up to view the full content. Platt, David – Homework 17 – Due: Oct 17 2005, 4:00 am – Inst: Ken Shih 1 This print-out should have 6 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. The due time is Central time. Please learn chapter 30, section 1 by your- self to solve some of these problems. This section will be included in Quiz2. 001 (part 1 of 2) 10 points Assume: The mobile charge carriers are ei- ther electrons or holes. The holes have the same magnitude of charge as the elec- trons. The number of mobile charge car- riers for this particular material is n = 8 . 49 × 10 28 electrons / m 3 . Note: In the figure, the point at the upper edge P 1 and at the lower edge P 2 have the same x coordinate. A constant magnetic field of magnitude points out of the paper. There is a steady flow of a horizontal current flowing from left to right in the x direction. 2.2 m 4 . 9 cm 6 cm 7 . 5 A P 1 P 2 V ~ B B = 1 . 2 T y x The charge on the electron is 1 . 6021 × 10 - 19 C. This preview has intentionally blurred sections. Sign up to view the full version. View Full Document This is the end of the preview. Sign up to access the rest of the document. {[ snackBarMessage ]}

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Slope intercept form coloring activity sheets Coloring activity Slope intercept form coloring activity sheets View print Finding Slope Worksheet With Answer Key pdf template , download form online. It is possible to convert equation in standard form to slope intercept form. This is an extension using the base of the lesson materials to explore parallel and perpendicular lines i. Vary the coefficients and explore how the graph changes in response. Slope- Intercept Form Answer Key. Tips for Using PhET. Compare the slope- intercept form of a linear equation to its graph. Point- slope Form Slope- intercept Form Two- point Form Equation of a Line The slope ( gradient) activity of a line is sheets a number that denotes the sheets ' steepness' of the line also commonly called ' rise over run'. Slope- intercept Form Of A Linear Equation Examples Worksheet - Johnny Wolfe Jay High School activity Education Linear Equations In " slope- Y- intercept" Form Worksheets With Answers - Fpc Math 10 Education. Materials: Students will each need the following materials:. This activity works well in groups or with students working in pairs at a coloring whiteboard ( have students draw an empty grid on the board for their answers). Standard coloring worksheet counterparts are available as well. Slope intercept form coloring activity sheets. 23 Finding Slope Worksheet Templates are collected for any of your needs. sheets adding subtracting integers color by number worksheets math color activity by number math coloring activities math coloring worksheets middle school math multiplying dividing integers. When completed, the correctly graphed lines will created a “ stained activity glass window” which can be colored activity for a fun art- math crossover project. Unlike other match- ups in this binder, this is a sheets double match- up. Knowledge of relevant formulae is a must for students of Grade 8 and above to solve some of these worksheets. Examples include lines with positive , zero, negative undefined slopes. Although algebra worksheets are not the primary activity in the classroom there is still value in practicing math skills with paper pencil. These algebra worksheets are designed to provide variation in work assigned to students beyond the standard worksheet. Where m = coloring the slope of the line, b = the y intercept It is generally easier to graph an equation in the slope- intercept form of an coloring equation. coloring Students will graph both standard form and slope- intercept. B W2R0 activity f1K21 fK Su activity gtpa y 1S zo QfRtlw ja jr Ee4 lLyLSC2. Students must match up the slope and the y- intercept for each box activity in the grid. c x QAPl 7ly Trpifg uh Tt3ss zr QeTsLe4r Xvle 6dq. Graphing equations Stained Glass: Activities: Only 8 equations ( more would coloring have been too cluttered). Study the steps in the example below where a standard equation is changed to slope- intercept form. 7) Slope of a Linear Equation Coloring Worksheet You can purchase my worksheets bundle by CLICKING HERE. c S PMZaAd Xe4 ywKiJt 5h o oI 7nWf0i ynri wtceO WP1r YeD- DA 4l Vg4e8bhr Zad. Students will practice graphing coloring lines in slope- intercept form. Five of the problems, the coloring student is given the slop. Slope intercept form coloring activity sheets. Teaching Resources. This product is coloring a coloring activity that allows the student to practice with point slope form. Student Activity: Match Up on Slope- Intercept Form. Language English: Keywords Algebra Lines, Linear Equation, Pre- Algebra, Graphing Lines, Slope- activity Intercept Form: Simulation( s) Graphing Lines ( HTML5), Slope Graphing Slope - Intercept ( HTML5. Slope- Intercept Lesson and Activity Sheet: Description Subject. ( more) n slope intercept form. Slope- Intercept Form. Search the PhET Website Simulations. Instructions: Write the equation of the line in slope- intercept form. Education Worksheets, Practice Sheets & Homework Sheets. Sheets form Students will practice working with slope intercept form including writing the equation of line given either A) slope and intercept B) slope and a point or C) two points. Also students will practice writing the slope intercept equation of a line from its graph. In addition, many students often struggle with remembering the difference between slope equal to zero and an undefined slope. I hope this slope activity will provide a helpful visual to aid in understanding and retention. Included in this download: I’ ve included color and black and white versions in this free download. ``slope intercept form coloring activity sheets`` Worksheets for slope and graphing linear equations With this generator, you can make worksheets for these pre- algebra and algebra topics ( grades 7- 9) : graphing linear equations, when the equation is given in the slope- intercept form ( y = mx + b ). Slope Intercept Form. Showing top 8 worksheets in the category - Slope Intercept Form.

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# Vector space of dim n and its subspaces Let $V$ be a vector space of dim $n$ over a finite field $F$ with $q$ elements. (a) Find the no.of dim 1 subspaces of $V$ (b) For each $1\leq k \leq n$, find the no.of dim $k$ subspaces of $V$ My Work: Let $V=<v_1,v_2,...,v_n>$. Since $v_1,v_2,...,v_n$ linearly independent, it has the following $n$ no. of dim 1 subspaces: $<v_1>,<v_2>,...,<v_n>$. So, I think answer for part (a) is $n$. Am I correct? Now, how can I do part (b). Is it $nC_k$? Please give me a hint. Fix a basis of $V.$ With respect to that basis, every element of $V$ can be uniquely expressed as an element of $F^n.$ Now a one dimensional subspace of $V$ is of the form $\alpha w_1,$ for some $w_1 \in V \setminus \{0\}.$ Let $w_1= (\alpha_1, \cdots ,\alpha_n)$ (w.r.t. the chosen basis). So at least one of the $\alpha_i$ is non-zero. Suppose $\alpha_1 \neq 0.$ After multiplying by $\alpha^{-1},$ we can assume that $w_1 = (1, \alpha_2, \alpha_3, \cdots , \alpha_n).$ Now note that, for every choice of $(\alpha_2, \cdots , \alpha_n) \in F^{n-1},$ we will get different one dimensional vector subspace of $V.$ So for $w_1$, the number of choice is $q^{n-1}.$ Similarly, if we fix $1$ at each of the $n$ co-ordinates, we will get $q^{n-1}$ different one dimensional vector subspaces of $V.$ Surely, there will be some common subspaces. So we need to count them also. Let $w_{1,2} \in V$ be of the form $(1, 1, \alpha_3, \cdots , \alpha_n).$ We have $q^{n-2}$ independent choices for such a vector. All of them will give different one dimensional subspaces of $V.$ Also, all these vectors were counted in both $w_1$ and $w_2.$ So we need to subtract them. Similarly for $w_{i,j}, i \neq j.$ Now consider $w_{1,2,3} \in V, w_{1,2,3} = (1,1,1,\alpha_4, \cdots , \alpha_n).$ We have $q^{n-3}$ different choices for this type of vectors and each of them will give different one dimensional subspaces of $V.$ But these were subtracted before. So we need to add them. And so on. This is a bit of messy. But this is an approach to solve this kind of problems. This is only for one dimensional subspaces. For $k$ dimensional subspaces, though the idea is essentially the same, but more caution is required.

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# String Graph of a Genome Regular readers are familiar with our explanation of de Bruijn graphs through the following steps - ii) We explained that, in the error-free world, de Bruijn graph constructed from short reads sampled from a genome looks identical to the de Bruijn graph of a genome. So, the genome assembly algorithm essentially consists of two steps - constructing de Bruijn graph from short reads (easy, but RAM consuming) and finding the genome sequence from the de Bruijn graph of a genome sequence (difficult, especially for repeat regions). We will present String Graph assemblers using similar steps. In this post, we will define string graph for a genome. Please study the following figure carefully. Top part of the above image shows a genome sequence. Yellow regions marked with 1-5 are unique segments, whereas red and purple regions are repetitive segments each appearing twice in the genome. The string graph for the genome is shown in the bottom figure. The graph has seven nodes consisting of five unique regions and two repetitive regions. Multiple appearances of the same repeat all collapse into the same node. The connectivity between the nodes (edges) follows the same order as the genome sequence. As an example, red repeat region comes after yellow segment 1 in the genome. Therefore, 3’ end of node ‘yellow segment 1’ is connected to 5’ end of red node. It is straightforward to derive the remaining edges based on the genome. If you remember how de Bruijn graph of a genome looked like, you will notice the following differences. i) The nodes of de Bruijn graph of a genome consisted of short k-mers of fixed size, whereas nodes of string graph are longer sequences with variable sizes. Therefore, the string graph needs far fewer nodes (and RAM) than de Bruijn graphs. ii) Typically, the k-mers of de Bruijn graph were shorter than reads. Therefore, de Bruijn graphs were constructed by spitting reads into short subunits. In contrast, nodes of string graph are likely to be longer than NGS read sizes, and thus string graphs are constructed by joining overlapping reads. Simple, huh? Not so fast. Think about this. When you are are determining overlap between reads to construct the string graph, you have to choose a minimum overlap size as an input parameter. If that minimum overlap size is 1, almost all reads will have some degree of overlap. At the other extreme, the minimum overlap size cannot be longer than the sizes of short reads. So, the overlap size parameter will have some impact on the quality of string graph, just like k-mer size has on de Bruijn graph. It is just that the string graph method shifts the burden on to computation for edges instead of storage for nodes. That is my simple understanding of trade-off between two approaches. (Note - Jared T. Simpson, who developed the SGA algorithm, graciously replied to my question about this issue at a reddit page. Readers are encouraged to take a look.) One final point - converting a genome into its corresponding string graph does lead to loss of information. If you check the figure presented above, you will find that the string graph is unique for the genome, but given the string graph, many possible genomes (including the original one) can be derived. However, the degree of loss of information is far lower than when a genome is converted into a de Bruijn graph of short k-mer size. Written by M. //

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book excerptise:   a book unexamined is wasting trees ## Martin Gardner's New Mathematical Diversions from Scientific American ### Martin Gardner Gardner, Martin; Martin Gardner's New Mathematical Diversions from Scientific American Simon and Schuster, 1966, 253 pages ISBN 0671209892, 9780671209896 topics: |  math | puzzle Some puzzles: 1. The binary system: Leibniz (1646- 1716) felt that binary digits represent 0=nonbeing or nothing; and 1 as being or substance. This is remarkably similar to much of the analysis in India, where shunya or kha can mean emptiness or the sky or ether. Leibniz was incidentally also a proponent of the Scythian theory of languages, which is a predecessor to the idea of Indo-European languages. He was also very interested in Chinese studies, and indeed, the idea for binary numbers came to him from an exposure to the Chinese "Yijing" diagram, which has similar metaphysical attributes, but is not used for computation a such. 2. Group theory and braids Game of "Tangloids" invented by Piet Hein (poet, friend of Bohr). Cut a plaque out of heavy paper in a coat-of-arms shape, punch three holes, and pass three sash cords through these, tying the other end at a chair. Now by rotating the plaque through the strings one can braid the rope in six ways. Doing it again creates further braids. Game involves untangling them by weaving, not rotating. Theorem: can always be done if there are an even number of rotations. Intuition: because even rotations sort of undo each other. 3. Eight problems problem 4: A group of cadets is marching in a 50m x 50m formation. Their pet dog starts from the middle of the back, runs to the front, turns back instantaneously, and runs back to the middle, at constant speed. In the meantime, the formation has moved 50m. How far did the dog run? DETAILED CONTENTS (listing all puzzles, journal references, and links) from http://www.mathematik.uni-bielefeld.de/~sillke/gardner/lit 1 The binary system 2 Group Theory and Braids - A Random Ladder Game: Permutaions, Eigenvalues, and Convergence of Markov Chains, [College Math J. 23:5 (1992) 373-385] - PSL(2,7) = PSL (3,2), MR 89f:05094 elegant proof 3 Eight Problems 3.1. Acute Dissection Triangle cut into seven acute ones (or eight acute isosceles) acute dissection of a square (8), pentagram (5), Greek cross (20) NU-Configurations in tiling the square, Math Comp 59 (1992)195-202 tiling a square with integer triangles 3.2 How Long is a "Lunar"? radius of the sphere, such that surface = volume 3.3 The Game of Googol (probability) 3.3. maximising the chance of picking the largest number 3.3. maximizing the value of the selected object (proposed be Cayley) 3.3.a On a Problem of Cayley, Scripta Mathematica (1956) 289-292 3.3.b An Optimal Maintenance Policy of a Discrete-Time Markovian 3.3.b Deterioration System, Comp. & Math. with Appl 24 (1992) 103-108 3.3.c A Secretary Problem with Restricted Offering Chances and Random 3.3.c Number of Applications, Comp. & Math. with Appl 24 (1992) 157-162 3.3.d On a simple optimal stopping problem, Disc. Math. 5 (1973) 297-312 3.3.e Stopping time techniques for analysts and probabilits (L. Egghe) 3.3.e LMS LNS 100 3.3.f Algebraic Approach to Stopping Variable Problems, JoCT 9 (1970) 3.3.f 148-161, distributive lattices <-> stopping variable problems 3.3.g secretary problem, Wurzel 27:12 (1993) 259-264 3.3.h Ferguson, Who solved the secretary problem? 3.3.h Statistical Science 4 (1989) 282-296 3.3.i Freeman, the secretary problem and its extensions: a review 3.3.i International Statistical Review 51 (1983) 189-206 3.4 Marching Cadets and a Trotting Dog 3.5 Barr's Belt 3.6 White, Black and Brown (logic) 3.7 The Plane in the Wind 3.8 What Price Pets? (linear Diophantine equation) 4 The Games and Puzzles of Lewis Carroll 5 Paper Cutting 5. theorem of Pythagoras, dissection proof, 6 Board Games 7 Packing Spheres 7.a figurative numbers, square, triangular, tetrahedral 8 The Transcendental Number Pi 9 Victor Eigen: Mathemagician 10 The Four-Color Map Theorem 11 Mr. Apollinax Visits New York 12 Nine Problems 12.1 The Game of Hip 12.1. two color the 6*6 square, s. t. there is no monochromatic square 12.1. the number of different squares in the n*n square is n²(n²-1)/12 12.1.a enumerating 3-, 4-, 6-gons with vertices at lattice points, 12.1.a Crux Math 19:9 (1993) 249-254 12.2 A Switching Puzzle: change two cars with a locomotive (circle and tunnel) 12.3 Beer Signs on the Highway (calculus, speed, time, distance) 12.4 The Sliced Cube and the Sliced Doughnut (geometry) cut the cube (regular hexagon), doughnut (two intersecting cirles) 12.5 Bisecting Yin and Yang (geometry) 12.5.a Bisection of Yin and of Yang, Math. Mag. 34 (1960) 107-108 12.6 The Blue-Eyed Sisters (probability) 12.7 How old is the Rose-Red City? (linear equations) 12.8 Tricky Track (logic, reconstruct a table) 12.9 Termite and 27 Cubes (hamiltonian circle, parity) 13 Polyominoes and Fault-Free Ractangles 13.a On folyominoes and feudominoes, Fib. Quart. 26 (1988) 205-218 13.b Rookomino (Kathy Jones) JoRM 23 (1991) 310-313 13.c Rookomino (K. Jones) JoRM 22 (1990) 309-316 (Problem 1756) 13.d Polysticks, JoRM 22 (1990) 165-175 13.e Fault-free Tilings of Rectangles (Graham) The Math. Gardner 120-126 14 Euler's Spoilers: The Discovery of an Order-10 Graeco-Latin Square Universal Algebra and Euler's Officer Problem, AMM 86 (1979)466-473 15 The Ellipse 15.a robust rendering of general ellipses and elliptic arcs, 15.a ACM Trans. on Graphics, 12:3 (1993) 251-276 16 The 24 Color Squares and the 30 Color Cubes (MacMahon) 12261 solutions of the 4*6 rectangle, 3*8 is impossible 17 H. S. M. Coxeter Coxeter's book Introduction to Geometry 1961 appl. of the M"obius band, contructions for 257, 65537 gon Morley's triangle, equal bisectors - Steiner-Lehmus Thm 17.a Angle Bisectors and the Steiner-Lehmus Thm, Math. Log 36:3 (1992)1&6 17.b equal external bisectors, not isoscele, M. Math. 47 (1974) 52-53 17.c A quick proof of a generalized Steiner-Lehmus Thm, 17.c Math Gaz. 81:492 (Nov. 1997) 450-451 17.h Morley's triangle (D.J.Newman's proof), M In 18:1 (1996) 31-32. kissing circles, Soddy's formular - Descartes' Circle Theorem 17.d Circles, Vectors, and Linear Algebra, Math. Mag. 66 (1993) 75-86 semiregular tilings of the plane, the 17 cristallographic groups tilings of Escher: Heaven-Hell, Verbum 17.e The metamorphosis of the butterfly problem (Bankoff) 17.e Math. Mag. 60 (1987) 195-210 (47 refs) 17.f A new proof of the double butterfly theorem, M. Mag. 63 (1990) 256-7 17.g Schaaf, Bibliography of Rec. Math. II.3.3 The butterfly problem 18 Bridg-it and Other Games winning Bridg-it, pairing stategy (Shannon switching game) Connections (ASS, 1992) = Bridg-it board: connect or circle 18.b Directed switching games on graphs and matroids, JoCT B60 (1986)237 18.c Shannon switching games without terminals, draft (I), see II, III 18.c Graphs and Combinatorics 5 (1989) 275-82 (II), 8 (1992) 291-7 (III) 19 Nine More Problems 19.1 Collating the Coins (coin moving xyxyx -> xxxyy) 19.2 Time the Toast (optimal shedule) 19.3 Two Pentomino Posers 19.3. 6*10 Rectangle with all pentominoes touch the border (unique) 19.4 A Fixed Point Theorem 19.5 A Pair of Digit Puzzles (cryptarithms) 19.6 How did Kant Set His Clock (calculus, time, speed) 19.7 Playing Twenty Questions when Probability Values are Known 19.7. Huffman coding, data compression 19.8 Don't Mate in One (chess) 19.9 Find the Hexahedrons 19.9. there are seven varieties of convex hexahedrons (six faces) 20 The Calculus of Finite Differences 20.d Symmetry Types of Periodic Sequences, Illionois J. of Math. 20.d 5:4 (Dec 1961) 657-665, appl. to music and switching theory 20.a generating two color necklaces, Disc. Math. 61 (1986) 181-188 20.b Generating Necklaces, J. of Algorithms 13:3 (1992) 414 Many of the chapters have many sub-problems; see the index at http://www.ms.uky.edu/~lee/ma502/gardner5/gardner5.html for a link of which problem appears in which text. ### Send your jottings to Book Excerptise to contribute some excerpts from your favourite book to book excerptise. send us a plain text file with page-numbered extracts from your favourite book. You can preface your extracts with a short review. email to (bookexcerptise [at] gmail [dot] com). bookexcerptise is maintained by a small group of editors. comments are always welcome at bookexcerptise [at] gmail.

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Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack It is currently 24 May 2017, 18:48 ### GMAT Club Daily Prep #### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email. Customized for You we will pick new questions that match your level based on your Timer History Track every week, we’ll send you an estimated GMAT score based on your performance Practice Pays we will pick new questions that match your level based on your Timer History # Events & Promotions ###### Events & Promotions in June Open Detailed Calendar # Unlike other forms of narrative art , a play, to be new topic post reply Question banks Downloads My Bookmarks Reviews Important topics Author Message TAGS: ### Hide Tags Manager Joined: 24 Aug 2012 Posts: 130 Followers: 2 Kudos [?]: 250 [0], given: 2 Unlike other forms of narrative art , a play, to be [#permalink] ### Show Tags 06 Oct 2012, 15:19 00:00 Difficulty: 25% (medium) Question Stats: 71% (02:26) correct 29% (01:35) wrong based on 196 sessions ### HideShow timer Statistics Unlike other forms of narrative art , a play, to be successful, must give pleasure to its immediate audience by reflecting the concerns and values of that audience. A novel can achieve success over months or even years, but a play must be a hit or perish, Successful drama of the Restoration period, therefore, in a good index to the typical tastes and attitudes of its time. The author of the above passage assumes that A) plays written for restoration audiences do not appeal to modern audiences. B) plays are superior to novels as a form of narrative art C) Restoration audiences were representative of the whole population of their time D) playgoers and novel readers are typically distinct and exclusive groups. E) Restoration drama achieved popular success at the expense of critical success. [Reveal] Spoiler: OA _________________ Push +1 kudos button please, if you like my post If you have any questions you can ask an expert New! Senior Manager Joined: 28 Jun 2009 Posts: 445 Location: United States (MA) Followers: 18 Kudos [?]: 176 [0], given: 46 Re: Unlike other forms of narrative art , a play [#permalink] ### Show Tags 06 Oct 2012, 17:34 C is correct. Premises: - a play must give pleasure to its immediate audience, unlike novels who have months/years to please readers. - a play must give pleasure to its immediate audience by reflecting the concerns and values of that audience Conclusion: - Successful drama of the Restoration period in(is??) a good index to the typical tastes and attitudes of its time. Assumption : Successful drama of the Restoration period agreed with tastes and attitudes of many people. i.e. Many people of the Restoration period enjoyed the drama. A) plays written for restoration audiences do not appeal to modern audiences. >> Argument doesn't say this. B) plays are superior to novels as a form of narrative art >> dramas and plays are compared, but author doesn't say which one is superior C) Restoration audiences were representative of the whole population of their time >> Correct. This is the assumption. Negating this (very few people enjoyed Restoration drama) we can shatter the conclusion. D) playgoers and novel readers are typically distinct and exclusive groups. >> Out of scope E) Restoration drama achieved popular success at the expense of critical success >> Argument doesn't say this. BSchool Forum Moderator Status: Flying over the cloud! Joined: 17 Aug 2011 Posts: 886 Location: Viet Nam Concentration: International Business, Marketing GMAT Date: 06-06-2014 GPA: 3.07 Followers: 74 Kudos [?]: 656 [0], given: 44 Re: Unlike other forms of narrative art , a play [#permalink] ### Show Tags 09 Oct 2012, 02:29 The restoration audience must represent of the whole population of at a time, then the conclusion will be accepted. Without that, the audience in the argument is not representative. Then the argument will be collapsed. _________________ Rules for posting in verbal gmat forum, read it before posting anything in verbal forum Giving me + 1 kudos if my post is valuable with you The more you like my post, the more you share to other's need CR: Focus of the Week: Must be True Question Re: Unlike other forms of narrative art , a play   [#permalink] 09 Oct 2012, 02:29 Similar topics Replies Last post Similar Topics: 4 Owners of any work of art 13 19 Feb 2017, 05:46 18 Commemorative plaques cast from brass are a characteristic art form of 14 28 Feb 2017, 04:52 Unlike other species of the same family, which travel 2 01 Jun 2014, 21:56 11 Photography is no longer an art form. Nowadays everyone has 8 25 Apr 2017, 05:34 3 CR: Art Theft 19 18 May 2015, 05:27 Display posts from previous: Sort by # Unlike other forms of narrative art , a play, to be new topic post reply Question banks Downloads My Bookmarks Reviews Important topics Powered by phpBB © phpBB Group and phpBB SEO Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.

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Category: How are Weekly Unemployment Benefits Determined? Article Details • Written By: I. Ong • Edited By: C. Wilborn 2003-2018 Conjecture Corporation India is building what will become the world’s biggest statue; it will be twice as tall as the Statue of Liberty.  more... June 20 ,  1877 :  The world's first commercial telephone was installed.  more... wiseGEEK Slideshows Unemployment benefits refer to a sum of money given by the government or any authorized agency to individuals registered as unemployed, usually on a weekly basis. Weekly unemployment benefits are calculated based on the individual's earnings in the preceding months, as well as the number of dependents he is supporting. The actual formula for computation may vary based on location. The base period usually refers to the first four quarters from the five quarters preceding the week in which the individual intends to apply for unemployment benefits. The income received is listed for each of the four quarters in the base period. The two highest wages of the four quarters, added together, will be the starting point for computation. Note that if only two quarters from the base period had earnings, just one highest-earning quarter's wage will be considered in most cases. The next step in calculating the weekly unemployment benefits is to divide the total of the individual's two highest-earning quarters by 26. This is the number of weeks in two quarters, and will determine his average earnings per week. When dealing with just one quarter's earnings, the figure must be divided by 13 instead, which is the number of weeks in one quarter. Once the average weekly earnings have been calculated, the figure should be divided in half and rounded down to the nearest whole unit of currency, such as a dollar. A small percentage is usually added to the amount for each dependent being supported by the individual. This will be the sum of his weekly unemployment benefits. The exact figures for factoring dependents into the formula varies, so anyone interested should search for his specific government or agency website and check the details. He may also consult an unemployment attorney, who can then provide answers for any queries and concerns he might have. Some other factors must be considered when claiming weekly unemployment benefits. There is a maximum number of weeks in a year for which an individual may claim unemployment benefits. For the United States, the limit is 26 weeks in a year, in most circumstances, and the weeks may or may not be consecutive. Note that governments and agencies have specific budgets allotted per individual and will rarely go below their minimum or above their maximum amount. There are certain requirements that should be met before an individual is eligible for claiming weekly unemployment benefits. He must be registered with the relevant government department or agency, be unemployed at the time he applies for benefits, and be physically and mentally capable of working. He should be continuing his job search, attending required meetings with the department or agency, and be regularly claiming his weekly benefits. There are monetary requirements that the individual must meet as well. Wages in the last six months of his base period must be equal to or more than eight times what his weekly unemployment benefit rate will be in most cases. He must also have earned a minimum sum during his base period, the required minimum of which will vary based on location. Only if an individual meets the above criteria will he be eligible for applying for unemployment benefits.

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https://universalzeropoint.com/2017/09/14/the-tetractys-432-rolls-up/

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# The Tetractys – 432 rolls up What is the ether ? The ether is said to be a medium for the propagation of light. It is a space-filling substance or field in which “All things” operate through. Without this medium, there is no life, a dance between light and shadows. Gematria is a useful tool to begin an approach with numbers. 432 is the gematria value for ‘All things’ (παντα) in Greek. Is 432 to do with the properties of this medium ? 432 is also the gematria value for All Nations, Jerusalem, Bethlehem.. The number 432 does show a numerical structure which has a base represented by four dots, then 3 dots and finally two dots. This is the sequence 4 3 2. ##### .     .     .     .           Four dots Contemplating on this geometric figure, it could come to our mind the completion of a pyramid represented by the single point at the top from which All things comes into existence. The completion of 10 dots lead to a geometric figure that the Pythagoreans called Tetractys. It represents the organization of space from a two dimensional view. The structure of the tetractys shows the famous platonic solids such as the Tetrahedron, the cube and the octahedron. Fundamental solids appear from the basic foundation of space. • First row : From a single original point everything is created and brought into existence from nothingness. Th is could be considered as a state of awareness to that which is about to manifest into creation. • Second row : From a single point two further points are generated defining the first dimension. The possibility of going from one point to another brings the idea of motion into consciousness. • Third row : A line drawn between these three dots defines the second dimension. Structure is formed into consciousness with the possibility of quantification and measurement. • Fourth row : A line drawn between these four dots defines the third dimension where geometry takes form. From this triangle all regular polygons can be generated, such as the square, the pentagon, the hexagon etc. The Tetractys brings the feeling of a unity within geometry and the number 432. When Music is tuned at this frequency 432 Hz, this feeling of unity can be shared through vibration/energy and resonates much more with the heart center. The numbers encoded in these solids are harmonic. The peculiar quality of these numbers is they all add up to 9. 7 + 2 + 0 = 9 1+ 4 + 4 + 0 = 9                                  2 + 1 + 6 + 0 = 9 The number 9 is an important pillar in the structure of space-time and acts uniquely in the system of numbers. Below is a table listing some musical notes. Notes are based on a D scale from 144 Hz. “Music is geometry in time.” Arthur Honegger The rhombic dodecahedron has 4,320 degrees and is made from 12 rhombus. The sum of the four angles of a rhombus is always 360 degrees. The rhombic dodecahedron appears in nature in thestructure of the honeycomb cells. At the top is a pyramid made from three blue rhombus closing the end of the cell. The opening is a red hexagon prism at the bottom joining to the top with six green trapezes. Each cell is called “half of a rhombic dodecahedron”. The sum of the angles is 3,240 degrees, again adding up to 9. © [14/09/2017] by Salah-Eddin Gherbi

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Thomas' Calculus 13th Edition $\dfrac{-4}{x^{1/4}}+C$ As we know $\int x^n dx=\dfrac{x^{n+1}}{n+1}+C$ Thus, $\int x^{-5/4}dx=(\dfrac{x^{-5/4+1}}{-5/4+1})+C=\dfrac{-4}{x^{1/4}}+C$

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# How to generate a video file using a series of plots on MATLAB? I'm trying to stitch together a bunch of plots I created within a loop into a single video file. I've been at this for several hours, but had no luck. Here is my minimum working example where I attempt to use the VideoWriter function to create a video. I always get an error saying my frame(s) can't be copied into the video objects. Grr. Here is my minimum working example: ``````n=(1:50)*2*pi; for t = 1:1000 Y = sin(n*50/t); plot(Y); %plot shows a sine wave with decreasing frequency F(t) = getframe; %I capture the plot here end writerObj = VideoWriter('test2.avi'); %Attempt to create an avi open(writerObj); for t= 1:time writeVideo(writerObj,F(t)) end close(writerObj); `````` You are missing a constant height of images. You can guarantee it by, e.g., `ylim`: ``````time = 100; for t = 1:time fplot(@(x) sin(x*50/t),[0,2*pi]); % plot ylim([-1,1]); % guarantee consistent height F(t) = getframe; % capture it end writerObj = VideoWriter('test2.avi'); open(writerObj); writeVideo(writerObj, F) close(writerObj); `````` I have further replaced your discrete plot by a "continuous" one (using `fplot`). • I actually forgot to add the the axis limits in my MWE, but turns out my code kept crashing because the window would get moved somehow (I'm plotting a more complicated system, that takes a lot more time, and hence I keep moving the window around because I'm fidgety). But thanks nevertheless! – user1992705 Jan 17 '15 at 1:57 Matheburg answer is correct and identified the part which was causing the error (at some point the scale of your axis was resized, which cause the frame size to change). His solution works fine and if the usage of `fplot` works for you then follow his way. In case you still want to use the traditional `plot` (2d `lineserie` object) method, then here's how I usually organize "animated" plots: The `plot` function is high level. It means when it runs it plots the data (obviously) but also does a lot of other things. In any case it generate a completely new plot (erasing previous plot if `hold on` wasn't specified), but also readjust the axes limits and many other settings (color, style etc ...). If in your animation you only want to update the plot data (the points/line position) but not change any other settings (axes limits, colors etc ...), it is better to define the plots and it's settings one time only, outside of the loop, then in the loop you only update the `YData` of the plot object (and/or the `XData` if relevant). This is done by retrieving the plot object handle when you create it, then use the `set` method (which unlike `plot` will only modify the parameters you specify explicitly, and won't modify anything else). In your case it looks like this: ``````n=(1:50)*2*pi ; Y = sin(n*50) ; hp = plot(Y) ; %// Generate the initial plot (and retrieve the handle of the graphic object) ylim([-1,1]) ; %// Set the Y axes limits (once and for all) writerObj = VideoWriter('test2.avi'); %// initialize the VideoWriter object open(writerObj) ; for t = 1:1000 Y = sin(n*50/t) ; %// calculate new Y values set(hp,'YData',Y) ; %// update the plot data (this does not generate a "new" plot), nor resize the axes F = getframe ; %// Capture the frame writeVideo(writerObj,F) %// add the frame to the movie end close(writerObj); `````` Also, this method will usually runs faster, and save a significant amount of time if your loop has a great number of iterations. Side note: As said above, Matheburg solution runs also fine. For such an application, the difference of speed will not be a major issue, but note that the plots (and movie) generated are slightly different (due to it's use of `fplot` instead of `plot`). So I encourage you to try both versions and choose which one suits you best. • This is really good. The actual code I am running is more complex and takes much more simulation time. I was going to look for a faster way to plot stuff on MATLAB, but your answer saved me a lot of trouble. – user1992705 Jan 17 '15 at 2:02

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I am lost Please give guidance #1 the editor says: "The following is missing or broken when we tried to use it: alice, lloyd, tyler, students, here is my code: def get_average(students): results = [ ] for students in students: results.append(get_average(students)) return average(results) students = [ lloyd,alice,tyler] print get_class_average(students) #2 May I ask you to post here your whole code with a proper formatting? There is a special icon </> to format the code in the top bar of the editor. #3 indent preformatted text by 4 spaces lloyd = { "name": "Lloyd", "homework": [90.0, 97.0, 75.0, 92.0], "quizzes": [88.0, 40.0, 94.0], "tests": [75.0, 90.0] } alice = { "name": "Alice", "homework": [100.0, 92.0, 98.0, 100.0], "quizzes": [82.0, 83.0, 91.0], "tests": [89.0, 97.0] } tyler = { "name": "Tyler", "homework": [0.0, 87.0, 75.0, 22.0], "quizzes": [0.0, 75.0, 78.0], "tests": [100.0, 100.0] } students = [lloyd, alice, tyler] def average(numbers): total = sum(numbers) total = float(total) total = total / len(numbers) def get_average(student): homework = average(student["homework"]) quizzes = average(student["quizzes"]) tests = average(student["tests"]) return 0.1 * homework + 0.3 * quizzes + 0.6 * tests if score >= 90: return "A" elif score >= 80: return "B" elif score >= 70: return "C" elif score >= 60: return "D" else: return "F"

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How a particle's spin is decided? • I • phoenix95 In summary, particle physicists can make theoretical predictions or directly measure the spin of particles. For stable or long-living charged particles, the spin can be measured by how they react to electromagnetic radiation. For shorter-lived particles, the spin can be determined by studying the angular and energy distributions of their decay products. The spin of the Higgs boson, for example, was measured using this method. The graviton, which has a spin of 2, has never been directly observed but its existence is inferred from the polarization type seen in gravitational waves. The theory of spin is based on how particles behave when rotated, with different particles having different rotation requirements due to their spins. More information on this topic can be found in particle physics and quantum phoenix95 Gold Member I'm taking a course in particle physics. One of the features different from particle to particle is the spin. For example Higgs boson has spin 0, muon and electron have spin 1/2, graviton has spin 2, and so on. How is this decided upon? Does it occur in the experiments or is it based on theoretical calculations? You can make theoretical predictions but you can also measure it. For stable or long-living charged particles you can directly measure how the particle react to electromagnetic radiation (e.g. for protons and electrons). For particles that live too short for this you can study the angular distributions and energy distributions of decay products as they depend on the particle spin. This is how the spin of the Higgs boson has been measured for example. The graviton has never been seen as individual particle, but particles that lead to the polarization type we see with gravitational waves have to have spin 2. phoenix95 mfb said: The graviton has never been seen as individual particle, but particles that lead to the polarization type we see with gravitational waves have to have spin 2. So I assume theoretical calculation of spin follows from the polarisation of the waves? How? If you rotate an electromagnetic wave around its propagation direction you have to rotate it by 360 degrees (2pi) until it matches the original wave. It has spin 1. If you rotate the wave function of an electron in an analog way you have to rotate it by 720 degrees (4pi) until it matches the original wave. It has spin 1/2. If you rotate a gravitational wave you have to rotate it by 180 degrees (pi) until it matches the original wave. It has spin 2. Every particle physics textbook and good textbooks on quantum mechanics should cover that. phoenix95 1. What is particle spin? Particle spin is a quantum mechanical property that describes the angular momentum of a particle. It is independent of its actual physical rotation and can have values of either +1/2 or -1/2. 2. How is a particle's spin determined? A particle's spin is determined by its intrinsic properties, such as its mass and charge. It is an inherent property of the particle and does not change over time. 3. What role does spin play in quantum mechanics? Spin plays a crucial role in quantum mechanics as it is one of the fundamental properties used to describe the behavior of particles. It is also used to explain various phenomena, such as the Pauli exclusion principle and the behavior of magnetic materials. 4. Can a particle's spin be changed or manipulated? No, a particle's spin cannot be changed or manipulated as it is an intrinsic property of the particle. However, its spin state can be measured and observed through certain experiments. 5. How is spin measured or observed in experiments? Spin can be measured or observed through various experiments, such as the Stern-Gerlach experiment or electron spin resonance. These experiments involve subjecting particles to external magnetic fields and observing the deflection or absorption of particles based on their spin states. • High Energy, Nuclear, Particle Physics Replies 49 Views 4K • High Energy, Nuclear, Particle Physics Replies 8 Views 1K • High Energy, Nuclear, Particle Physics Replies 11 Views 1K • High Energy, Nuclear, Particle Physics Replies 6 Views 2K • High Energy, Nuclear, Particle Physics Replies 3 Views 1K • High Energy, Nuclear, Particle Physics Replies 3 Views 4K • High Energy, Nuclear, Particle Physics Replies 4 Views 1K • High Energy, Nuclear, Particle Physics Replies 1 Views 2K • High Energy, Nuclear, Particle Physics Replies 7 Views 2K • Quantum Physics Replies 48 Views 3K

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A math-centered programming language library. 2018-09-13 23:57:33 -07:00 2018-03-24 17:17:06 -07:00 2018-09-13 23:57:33 -07:00 2018-09-13 23:57:33 -07:00 2018-04-21 14:09:01 -07:00 2018-02-03 23:47:05 -08:00 2018-02-04 15:58:21 -08:00 2018-08-11 01:40:30 -07:00 2018-08-20 00:00:02 -07:00 # libabacus A math-centered programming language library. libabacus is effectively a stripped down, embeddable programming language. It relies on the program it's embedded into to provide the standard library. In fact, it doesn't even provide an underlying implementation for numbers - the client code provides a means of convering a string into a number, and a way of freeing that value. libabacus takes care of the rest. The features of libabacus are geared towards calculators, so it does not provide higher-level abstractions like OOP. ## Syntax libabacus has fairly simple syntax. A simple number expression is ``````42 `````` If an operator `+` is registered with libabacus, then an expression using that operator looks like ``````21+21 `````` If two functions, `f` and `g` are registered with libabacus, where `f` takes one argument and `g` takes two, then the syntax for calling these functions is ``````f(42) g(21, 21) `````` Blocks are a way to combine a sequence of expressions into one. The value of a block is the result of the last expression in that block. Expressions are delimited by the `;` character. For example, ``````{ 3; 2; 1 } `````` evalutes to `1`. Blocks are the first bit of syntax we've seen that can evalute to a value that isn't a number. For instance, the empty block, `{}`, does not evaluate to a number. Instead, it evalutes to `()`. This is a value of the `unit` type, which only has one possible value, `()`. User-defined functions are supported by libabacus: ``````fun square(a: num): num { a*a } `````` Let's pick this apart. The first part of a function declaration is the `fun` keyword. The name of the function is next, followed by the list of parameters that this function accepts. Parameters are listed in the form `[name]:[type]`. The return type of the function must also be specified. Lastly, the block used to evaluate the function is needed. The block captures the scope in which the function was declared. For instance, in the following piece of code, ``````a = 0; fun test(): num { a = a + 1 } `````` `test` actually has access to `a`, and calling `test` many times will yield increasing values of a. Although all parameters must specify a type, this type can be arbitrary to allow for polymorphic functions. For instance, a function to apply another function to an argument twice can be written as: ``````fun apply_twice(func: ('T)->'T, a: 'T): 'T { func(a); func(a) } `````` ## Integration Everything in libabacus revolves around the `libab` struct. This struct is used to keep all the state related to the evaluation, and also contains the garbage collector. It needs to be instantiated using the `libab_init` function. ``````libab ab; libab_init(&ab, parse_function, free_function); `````` Please see `interactive.c` for an example of a simple yet complete implementation.

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1. ## Monotone Sequence Hi. I was wondering if someone could show me how to prove this statement, let P > 0, prove that (P^(1/n) is a monotone sequence and deduce by using a subsequence that the limit must be 1. I understand that if 0 < P < 1, then the sequence is increasing and if P > 1, the sequence is decreasing, but how do you show it? Also, how I do use the subsequence to prove its limit? 2. There are many ways to prove the proposition. I suspect that whoever set this for you to do has one particular way in mind. However, here is one way that I like. Given $p > 1\quad \Rightarrow \quad \ln (p) > 0$. Then $\begin{array}{rcl} 0 < a < b\quad & \Rightarrow & \quad a\ln (p) < b\ln (p) \\ \quad & \Rightarrow & \quad \ln \left( {p^a } \right) < \ln \left( {p^b } \right) \\ \end{array}$ . This shows that the sequence $p > 1,\quad \left( {p^{\frac{1}{n}} } \right)$ is decreasing; it is also bounded below by 1. I would use a subsequence converging to 1. 3. What's an appropriate subsequence? 4. I would just use the factor that (say $a\geq 1$) $1\leq a\leq n$ for sufficiently large $n$ it means $1\leq a^{1/n} \leq n^{1/n}$ now use the squeeze theorem. 5. Honestly though, what's an easy subsequence of this? We don't know what P is, so I'm not even sure what the terms in this sequence look like. Can you just pick a P and make that a subsequence? Somehow I don't think so. 6. Don't worry about it. I figured something out.

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# Allowable Signal Swing in BJT? 1. Aug 26, 2010 ### Peon666 I'm utterly confused about this concept and the text book quite efficiently confuses me further. I'll just try to explain it with an example: The circuit has a V(cc) = 10 V and V(ee) = -10 V. V(c) = 2 V, V(e) = -1.7 V, V(b) = -1 V, I(c) = 1 mA, I(e) = 1 mA. It says that allowable signal swing or B=100 is +8 V, -3.4 V. How's that? I can't figure. 2. Aug 26, 2010 ### skeptic2 If this is a homework problem, it should go there. What is the book asking for, the input peak to peak input voltage? The only thing I don't understand is what is the -3.4 V. B = 100 is probably referring to the beta or current gain of the transistor. The 8 V seems like a reasonable value for the output signal voltage swing. From the other data given it is possible to calculate the input peak to peak current and peak to peak voltage. What exactly is confusing you?

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 How do u find what a percentage of a number would b - AssignmentGrade.com How do u find what a percentage of a number would b QUESTION POSTED AT 16/04/2020 - 06:16 PM Multiply the number by the percent and do the decimal thing Related questions What is the least number that rounds up to 300 when rounding to the nearest hundred? QUESTION POSTED AT 02/06/2020 - 01:56 AM Antoine and Tess have a disagreement over how to compute a 15% gratuity on \$46.00. Tess says, “It is easy to find 10% of 46 by moving the decimal point one place to the left to get \$4.60. Do that twice. Then add the two amounts to get \$4.60 + \$4.60 = \$9.20 for the 15% gratuity.” How should Antoine respond to Tess’s method? QUESTION POSTED AT 02/06/2020 - 01:43 AM Is the data set “the number of leaves on a branch” quantitative or qualitative? If it is quantitative, is it discrete or continuous? QUESTION POSTED AT 02/06/2020 - 01:41 AM A painting is purchased for \$500. If the value of the painting doubles every 5 years, then its value is given by the function V(t) = 500 ⋅ 2t/5, where t is the number of years since it was purchased and V(t) is its value (in dollars) at that time. What is the value of the painting ten years after its purchase QUESTION POSTED AT 02/06/2020 - 01:37 AM Ivan finished 4/5 of his math homework problems and all 3 questions for his science homework before dinner. If he finished atotal of 43 problems before dinner, what is the total number of math homework problems he was assigned? QUESTION POSTED AT 02/06/2020 - 01:37 AM Find the six arithmetic means between 1 and 29. QUESTION POSTED AT 02/06/2020 - 01:36 AM Find an irrational number that is between 7.7 and 7.9. Explain why it is irrational. Include the decimal approximation of the irrational number to the nearest hundredth. (3 points) QUESTION POSTED AT 02/06/2020 - 01:29 AM Find the differential dy of y=1/x+1 Evaluate dy for x=1 , dx=−.01 QUESTION POSTED AT 02/06/2020 - 01:25 AM Let y=4x^2 find the differential dy when x=5 and dx=0.4 QUESTION POSTED AT 02/06/2020 - 01:22 AM A Pentagon has three angles that are congruent and two other angles that are supplementary to each other. Find the measure of each of the three congruent angles in the Pentagon QUESTION POSTED AT 02/06/2020 - 01:21 AM M is the midpoint of JK. the coordinates of J are (6,3) and the coordinates of M are negative (3,4) , find the coordinates of K. QUESTION POSTED AT 02/06/2020 - 01:21 AM In a triangle, the measure of the first angle is three times the measure of the second angle. The measure of the third angle is 55 more than the measure of the second angle. Use the fact that the sum of the measures of the three angles is 180 to find the measure of each angle to find the measure of each angle. QUESTION POSTED AT 02/06/2020 - 01:21 AM Find the derivative of the following functions f(x) = x^7 - 2x^3 - 9x QUESTION POSTED AT 02/06/2020 - 01:20 AM _____ 18. The scatter plot shows the study times and test scores for a number of students. How long did the person who scored 81 study? Type your answer in the blank to the left. A. 50 minutes B. 81 minutes C. 16 minutes D. 100 minutes QUESTION POSTED AT 01/06/2020 - 05:03 PM _____ 20. Brandon needs \$480 to buy a TV and stereo system for his room. He received \$60 in cash for birthday presents. He plans to save \$30 per week from his part-time job. To find how many weeks w it will take to have \$480, solve 60 + 30w = 480. Type your answer in the blank to the left. A. 16 weeks B. 13 weeks C. 15 weeks D. 14 weeks QUESTION POSTED AT 01/06/2020 - 04:55 PM Three-sevenths of a number is 21. Find the number QUESTION POSTED AT 01/06/2020 - 04:54 PM 14. Tell whether the sequence 1 3 , 0, 1, −2 … is arithmetic, geometric, or neither. Find the next three terms of the sequence. Type your answer in the blank to the left. A. neither; 7, -20, 61 B. geometric;7, -20, 61 C. arithmetic; − 1 3 , 1 1 3 , 3 D. geometric;−3 1 3 , −5 5 9 , −9 7 27 QUESTION POSTED AT 01/06/2020 - 04:49 PM Points B, D, and F are midpoints of the sides of ace EC = 44 and BF = 2x - 6. Find the value of x. QUESTION POSTED AT 01/06/2020 - 04:49 PM Use linear approximation to estimate the number sqrt(9.05) QUESTION POSTED AT 01/06/2020 - 04:48 PM Find the circumference of a circle that has a diameter of 2 ft. use 3.14 for pi QUESTION POSTED AT 01/06/2020 - 04:47 PM In a right triangle if one acute angle has a measure of 10 x + 3 and the other has a measure of 3x + 9 find the larger of these two angles QUESTION POSTED AT 01/06/2020 - 04:47 PM The soccer team collector \$800 at a carwash fundraiser they charge five dollars for small vehicles and \$10 for large vehicles the amount collected can be modeled by the equation 5X +10 Y equals 100 where X represents the number of smog equals a Y represents the number of large vehicles if the number of large vehicles washed was \$50 how many small vehicles were washed in total QUESTION POSTED AT 01/06/2020 - 04:46 PM QUESTION POSTED AT 01/06/2020 - 04:46 PM The function f(x) = –x2 + 24x – 80 models the hourly profit, in dollars, a shop makes for selling coffee, where x is the number of cups of coffee sold, and f(x) is the amount of profit. Part A: Determine the vertex. What does this calculation mean in the context of the problem? (5 points) Part B: Determine the x-intercepts. What do these values mean in the context of the problem? (5 points) I have the vertex and the x-intercepts but i need to know what they mean in the context of the problem. QUESTION POSTED AT 01/06/2020 - 04:46 PM Find the greatest common factor. 3x4y2 + 12x2y3 + 6x3y4 QUESTION POSTED AT 01/06/2020 - 04:45 PM Geometry help ASAP 15 points Need help to find A and B QUESTION POSTED AT 01/06/2020 - 04:45 PM Carlene is saving her money to buy a \$500 desk. She deposits \$400 into an account with an annual interest rate of 6% compounded continuously. The equation 400e^0.06t=500 represents the situation, where t is the number of years the money needs to remain in the account. About how long must Carlene wait to have enough money to buy the desk? Use a calculator and round your answer to the nearest whole number. QUESTION POSTED AT 01/06/2020 - 04:45 PM The population of a town grew from 20,000 to 28,000. The continuous growth rate is 15%. The equation mc024-1.jpg represents the situation, where t is the number of years the population has been growing. About how many years has the population of the town been growing? Use a calculator and round your answer to the nearest whole number. QUESTION POSTED AT 01/06/2020 - 04:44 PM What is a multiple, a prime number, and a composite number? QUESTION POSTED AT 01/06/2020 - 04:44 PM Find the greatest common factor. 2x3y + x2y2 + 4xy3 QUESTION POSTED AT 01/06/2020 - 04:44 PM

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CC-MAIN-2021-04

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https://www.kodytools.com/units/resistance/from/kohm/to/ohm

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# Kiloohm to Ohm Converter Convert → Ohm to Kiloohm 1 Kiloohm = 1000 Ohms ## One Kiloohm is Equal to How Many Ohms? The answer is one Kiloohm is equal to 1000 Ohms and that means we can also write it as 1 Kiloohm = 1000 Ohms. Feel free to use our online unit conversion calculator to convert the unit from Kiloohm to Ohm. Just simply enter value 1 in Kiloohm and see the result in Ohm. Manually converting Kiloohm to Ohm can be time-consuming,especially when you don’t have enough knowledge about Electrical Resistance units conversion. Since there is a lot of complexity and some sort of learning curve is involved, most of the users end up using an online Kiloohm to Ohm converter tool to get the job done as soon as possible. We have so many online tools available to convert Kiloohm to Ohm, but not every online tool gives an accurate result and that is why we have created this online Kiloohm to Ohm converter tool. It is a very simple and easy-to-use tool. Most important thing is that it is beginner-friendly. ## How to Convert Kiloohm to Ohm (kΩ to Ω) By using our Kiloohm to Ohm conversion tool, you know that one Kiloohm is equivalent to 1000 Ohm. Hence, to convert Kiloohm to Ohm, we just need to multiply the number by 1000. We are going to use very simple Kiloohm to Ohm conversion formula for that. Pleas see the calculation example given below. $$\text{1 Kiloohm} = 1 \times 1000 = \text{1000 Ohms}$$ ## What Unit of Measure is Kiloohm? Kiloohm is a unit of measurement for electrical resistance. Kiloohm is a multiple of electrical resistance unit ohm. One kiloohm is equal to 1000 ohms. ## What is the Symbol of Kiloohm? The symbol of Kiloohm is kΩ. This means you can also write one Kiloohm as 1 kΩ. ## What Unit of Measure is Ohm? Ohm is a unit of measurement for electrical resistance. By definition, electrical resistance of a conductor is equal to one ohm when a constant potential difference of one volt applied between its ends produces in this conductor a current of one ampere. ## What is the Symbol of Ohm? The symbol of Ohm is Ω. This means you can also write one Ohm as 1 Ω. ## How to Use Kiloohm to Ohm Converter Tool • As you can see, we have 2 input fields and 2 dropdowns. • From the first dropdown, select Kiloohm and in the first input field, enter a value. • From the second dropdown, select Ohm. • Instantly, the tool will convert the value from Kiloohm to Ohm and display the result in the second input field. Kiloohm 1 Ohm 1000 # Kiloohm to Ohm Conversion Table Kiloohm [kΩ]Ohm [Ω]Description 1 Kiloohm1000 Ohm1 Kiloohm = 1000 Ohm 2 Kiloohm2000 Ohm2 Kiloohm = 2000 Ohm 3 Kiloohm3000 Ohm3 Kiloohm = 3000 Ohm 4 Kiloohm4000 Ohm4 Kiloohm = 4000 Ohm 5 Kiloohm5000 Ohm5 Kiloohm = 5000 Ohm 6 Kiloohm6000 Ohm6 Kiloohm = 6000 Ohm 7 Kiloohm7000 Ohm7 Kiloohm = 7000 Ohm 8 Kiloohm8000 Ohm8 Kiloohm = 8000 Ohm 9 Kiloohm9000 Ohm9 Kiloohm = 9000 Ohm 10 Kiloohm10000 Ohm10 Kiloohm = 10000 Ohm 100 Kiloohm100000 Ohm100 Kiloohm = 100000 Ohm 1000 Kiloohm1000000 Ohm1000 Kiloohm = 1000000 Ohm # Kiloohm to Other Units Conversion Table ConversionDescription 1 Kiloohm = 1000 Ohm1 Kiloohm in Ohm is equal to 1000 1 Kiloohm = 1000000 Milliohm1 Kiloohm in Milliohm is equal to 1000000 1 Kiloohm = 0.001 Megaohm1 Kiloohm in Megaohm is equal to 0.001 1 Kiloohm = 1000000000 Microohm1 Kiloohm in Microohm is equal to 1000000000 1 Kiloohm = 1000000000000 Abohm1 Kiloohm in Abohm is equal to 1000000000000 1 Kiloohm = 1000000000000 EMU of Resistance1 Kiloohm in EMU of Resistance is equal to 1000000000000 1 Kiloohm = 1.11265002973e-9 Statohm1 Kiloohm in Statohm is equal to 1.11265002973e-9 1 Kiloohm = 1.11265002973e-9 ESU of Resistance1 Kiloohm in ESU of Resistance is equal to 1.11265002973e-9 1 Kiloohm = 1000 Volt/Ampere1 Kiloohm in Volt/Ampere is equal to 1000 1 Kiloohm = 0.000001 Gigaohm1 Kiloohm in Gigaohm is equal to 0.000001 1 Kiloohm = 1000000000000 Nanoohm1 Kiloohm in Nanoohm is equal to 1000000000000 1 Kiloohm = 1000 Reciprocal Siemens1 Kiloohm in Reciprocal Siemens is equal to 1000 1 Kiloohm = 0.038740461439806 Quantized Hall Resistance1 Kiloohm in Quantized Hall Resistance is equal to 0.038740461439806 1 Kiloohm = 33.36 Planck Impedance1 Kiloohm in Planck Impedance is equal to 33.36

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CC-MAIN-2024-38

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https://www.speedsolving.com/wiki/index.php?title=BigRoux&printable=yes

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# BigRoux BigRoux method [[Image:]] Information about the method Proposer(s): Ruud Pollé Proposed: 2020 Alt Names: none Variants: none No. Steps: 5 No. Algs: None Avg Moves: A lot Purpose(s): Speedsolving The BigRoux method is a 4x4 speedsolving method proposed by Ruud Pollé. It is largely based on Yau with the main difference being the first three edges and the fourth edge. In Yau, the first three edges form three quarters of the cross, while in BigRoux, these edges can be random, as long as they include the first edge used in first block in Roux. The fourth edge is consequently not the fourth cross edge but it can be any random edge that can be easily solved. BigRoux (as is implied in the name) can also be used for bigger cubes. ## Overview 1. Solve 2 opposite centers. 2. Solve 3 dedges. These can be any colour combination and can be done more quickly than when focusing only on cross dedges, because some dedges are already partially or completely paired up. 3. Solve the remaining 4 centers, maintaining the first three dedges by keeping them on the left side and using only Rw, 3Rw, 2L, and U moves. 4. Pair up the remaining dedges without messing up the first three, starting with the first edge that can be solved the quickest. 5. Solve First Block + Second Block + CMLL + L6E (3x3) and Parity. ## Pros • Easy edgepairing • Takes less time to pair up the first four edges than Yau, and doesn't focus on CFOP exclusively. • Can also be used for CFOP 3x3x3 stage. ## Cons • Centers are a little bit harder.

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CC-MAIN-2020-34

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1. Re: Sun flickering?! No. It is about the size of the shadow the moon throws onto the Earth's surface. As Bill's post above shows the moon's shadow, on the Earth's surface, is about 110km. 2. The Following 3 Users Say Thank You to Ernie Nemeth For This Post: AngelEyes (9th August 2017), Foxie Loxie (8th August 2017), jc71 (8th August 2017) ... 4. The Following 3 Users Say Thank You to Hervé For This Post: Bill Ryan (8th August 2017), Foxie Loxie (8th August 2017), jc71 (8th August 2017) 5. Re: Sun flickering?! Posted by Bill Ryan (here) Posted by jc71 (here) There is probably something big I am missing here... Yes, I think you are missing something quite big... the huge size of the sun. Well yes I can see it is quite huge, but also the distance to it is quite far as well. I'll have to draw some big diagram to satisfy myself that this works. When you try to draw it on say an A4 piece of paper, the sizes of the sun, moon and earth are too small to really understand the angles. Thanks for the input. I'll go back to the drawing board (literally) JC 6. The Following 2 Users Say Thank You to jc71 For This Post: Bill Ryan (8th August 2017), Foxie Loxie (8th August 2017) 7. Re: Sun flickering?! The incredible coincidence of this sun, earth, moon relationship: The moon is just the right distance from the Earth and just the right diameter to barely cover the surface of the sun as seen from Earth! This allows for a total solar eclipse (none of the suns disk can be seen, only the corona - the fire surrounding the sun) within the umbra thrown by the shadow of the moon. 8. The Following 4 Users Say Thank You to Ernie Nemeth For This Post: AngelEyes (9th August 2017), Bill Ryan (8th August 2017), Foxie Loxie (8th August 2017), jc71 (8th August 2017) 9. Re: Sun flickering?! Posted by Hervé (here) ... Thanks Hervé. It clearly works very well on this diagram, but it is misleading in that obviously the sun is much further away from the Earth, and much larger than it appears here. Clearly if the proportions have been scaled down correctly then it works fine. I am just trying to satisfy myself that it does work to scale rather than just accepting diagrams like this representation. It does seem that the answer is in the massive difference in diameter between the sun and the moon. I am going to go back to the drawing board JC 10. The Following 3 Users Say Thank You to jc71 For This Post: Bill Ryan (8th August 2017), Foxie Loxie (9th August 2017), Hervé (8th August 2017) 11. Re: Sun flickering?! ... Solar System – sizes but not distances are to scale. The Sun and the eight planets of the Solar System 12. The Following 4 Users Say Thank You to Hervé For This Post: AngelEyes (9th August 2017), Bill Ryan (8th August 2017), Foxie Loxie (9th August 2017), jc71 (8th August 2017) 13. Re: Sun flickering?! Posted by Hervé (here) ... Solar System – sizes but not distances are to scale. The Sun and the eight planets of the Solar System Thanks. Yes the sizes are massively different. It is just the distance between them that isn't easy to illustrate on diagrams like this whilst keeping the Earth and Moon at an easily visible size, but I can see how it is very likely to be correct when drawn out to scale (the angle of the cone). I just wanted to show it to myself to get my head round it fully. I will go and do that now JC 14. The Following 4 Users Say Thank You to jc71 For This Post: AngelEyes (9th August 2017), Bill Ryan (8th August 2017), Foxie Loxie (9th August 2017), Hervé (9th August 2017) 15. Re: Sun flickering?! I really appreciate all the replies. I am definitely going to study more and on history of our sun and solar system. All of this is a big interest to me and yes I will admit I do spend alot of time on youtube and I really need to steer away from it and do some digging. 16. The Following 3 Users Say Thank You to AngelEyes For This Post: Bill Ryan (9th August 2017), Foxie Loxie (9th August 2017), Hervé (9th August 2017) 17. Re: Sun flickering?! Posted by Bill Ryan (here) Posted by AngelEyes (here) 93 Million miles is local in astronomical terms...right next door. I keep hearing that term? "Local Sun". didnt know this! thank you! Well, the sun really is very local to us in galactic terms! Here's an analogy: If our sun was your neighboring house, say 100 yds away, right next door, and you could talk to your neighbors over the fence — then the next nearest star (Proxima Centauri) would be the next nearest house, 15,700 miles away. And that's the NEXT CLOSEST star to us. Well said Bill, that really puts it into a more comprehensible perspective. 18. The Following 4 Users Say Thank You to 7alon For This Post: AngelEyes (9th August 2017), Bill Ryan (9th August 2017), Foxie Loxie (9th August 2017), Noelle (9th August 2017) 19. Re: Sun flickering?! To understand the distance from the earth to the sun I like to use diameters, as that really illustrates the difference in sizes. An AU (astronomical unit) is defined as the distance from the earth to the sun... 92,960,000 miles The diameter of the sun is... 864,575.9 miles The distance from earth to sun is about 107 sun diameters. Only 107! Easily understood - and means that the sun is extremely large. In comparison, the earth's diameter is... 7,917.5 miles So 11,747 earths fit in the same distance, or 11, 640 more earths than suns. 20. The Following 3 Users Say Thank You to Ernie Nemeth For This Post: AngelEyes (9th August 2017), Foxie Loxie (9th August 2017), Noelle (9th August 2017) Posting Permissions • You may not post new threads • You may not post replies • You may not post attachments • You may not edit your posts

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http://www.exercise4weightloss.com/points-plus.html

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 # Weight Watchers Point Plus Weight Watchers introduces Points Plus. As of 01/2011, they have changed to the new plus system. So what is it and what does it mean for new and existing members? If you are like hundreds of other members trying to lose weight, you have transitioned  to the new and improved points system. Perhaps you are a new member and want to reach your weight loss goals but need to understand the system a bit better. So you may be wondering what it's all about, how it's calculated and why it's a better way of assigning foods a points value. This page will give you an overview of some of the major changes in the program and how points are calculated for the foods you eat. This article is broken down into a few pages. This first page gives you the overview. The next pages go into more detail on the food points calculation and the allowances. You can use the links below to read just portions of the plan. If you want to read the entire article, use the next/previous buttons on each page. Overview Freebies How It's Calculated Points Allowance ## Weight Watchers Points Changes-Overview Before diving into how the new points plus calculation works, let's review some of the changes. Calories are not Created Equal One of the major changes for the new points calculation is calories - or lack of calories in the calculation. The prior method put a heavy emphasis on calories in determining the final points value for a food item. Basically, on the old method a small bag of pretzels had the same points value as an apple. The problem was that there was no incentive to select the healthier and more nutritious apple over the bag of pretzels. With the new points plus method, calories are no longer in the calculation. Instead, other nutritional values, such as carbs and protein, are now considered in addition to fat and fiber. Calories are not used at all. ## Freebies On Points Plus With the old method, there were several food items that ended up calculating to a zero points value. However, some fruits and veggies still had a points value to them based on the old formula. Now with the new points plus system, most veggies and fruits are zero points - or freebies. Fruits, while on the old method usually calculated to a points value, on the new most of these are zero. I say most because there are exceptions. Fresh fruits are all zero points. In addition, frozen or canned fruits are also zero provided there are no additives. This means no added sugar. It must use only the fruits own juice to be considered a freebie. If you are not sure, then check with the Weight Watchers tools or your leader. If you are still unsure, always error on the conservative side and calculate the points as if it were not a freebie. While most veggies are zero points, there are a few that are not. Items like potatoes, lentils and beans, while in the veggie category, are not freebies. Other vegetables that have a points plus value include parsnips, chick peas, and corn just to name a few. Check with the Weight Watchers etools or your leader if you are unsure if a veggie is zero points or not. So why are many fruits and veggies now zero points on the new system? Well this is one area of concern and confusion for many. While I use the points plus system, I am not claiming to be an expert here. But I will attempt to explain why these items are totally free on the new method. #### Calculator Use this free online points plus calculator to find the values for your recipes. First, the zero points value does not count as zero in all cases. If you use fruits or vegetables in a recipe, say peppers in your sauce or grapes in a fruit salad, then you need to include these values into the overall points calculation for the recipe. The reason for this is you need to count the overall nutritional value for the full recipe. Fruits and veggies will add protein and fibers (and other nutrients) into the totals. Whew! not sure I explained that very clearly. Here's some comments on this subject from Weight Watchers forums that I found that may explain it better. "It has always been our policy at Weight Watchers to incorporate the nutrients of vegetables (and now fruit) into recipes. Why? A few reasons. 1) Vegetables and fruit add fiber and other nutrients, and without including them it can impact the Points value. 2) Our recipes are often featured in articles and magazines nationally and as a result we need to disclose this info to ensure the appropriate calories and nutrient content are displayed if evaluated by organizations outside of Weight Watchers. 3) Since many non-Weight Watchers recipes include nutritional information these days, we want our calculations to match those you may do for recipes you find in other places. We don’t want to unfairly advantage our own recipes. 4) Once you start combining vegetables and fruits with other foods, you change the experience of eating them. Few people “pig out” on carrots but might on carrot cake. To ignore them in recipes would place our member at risk for abuse potential. Secondly, another reason behind the freebies for fruits and veggies has to do with their nutrient composition as compared to other foods that may have the same calorie count. These types of foods are higher in fiber than say a piece of bread. Your body works harder to process foods higher in protein or fibers than it does foods higher in carbs. This means that you are burning away those calories faster. On the other hand, a piece of bread is higher in carbohydrates and fat, and your body does not work as hard to process these types of calories. That means they are more likely to be stored - and these stored calories can turn into fat. Lastly, it is assumed that we will be less likely to "pig out" on veggies and fruits versus chips and cookies. So even though the fruits and veggies have calories, etc., we probably won't eat more in a day than our body can process efficiently so that the calories are not stored as fat. If you are not following the points plus plan, then check out how to calculate the original points values. Weight Watchers Points Plus Restaurant List Eat out at your favorite restaurant knowing the points plus values for the menu items you order. Weight Loss Workouts

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# Take a derivative with respect to an expression in Symbolics The Symbolics documentation says (bold italic emphasis added) ``````struct Differential <: Symbolics.Operator `````` Represents a differential operator. Fields • `x` : The variable or expression to differentiate with respect to. This implies that one can take a derivative wrt an expression rather than a variable, although the documentation does not show such an example. For a simple expression this works as expected: Derivative wrt a simple expression rather than a variable ``````julia> using Symbolics julia> @variables x 1-element Vector{Num}: x julia> a = cos(x) cos(x) julia> b = cos(x) cos(x) julia> f = x*a x*cos(x) julia> a === b false julia> Da = Differential(a) (::Differential) (generic function with 2 methods) julia> Db = Differential(b) (::Differential) (generic function with 2 methods) julia> expand_derivatives(Da(f)) x julia> expand_derivatives(Db(f)) x `````` For a more complicated expression it doesn’t work as expected: Derivative wrt a more complex expression ``````julia> a1 = cos(x)sin(x) cos(x)*sin(x) julia> b1 = cos(x)sin(x) cos(x)*sin(x) julia> a1 === b1 false julia> a1 == b1 (cos(x)*sin(x)) == (cos(x)*sin(x)) julia> f1 = x*a1 x*cos(x)*sin(x) julia> Da1 = Differential(a1) (::Differential) (generic function with 2 methods) julia> Db1 = Differential(b1) (::Differential) (generic function with 2 methods) julia> expand_derivatives(Da1(f1)) 0 julia> expand_derivatives(Db1(f1)) 0 `````` Can you only take derivatives wrt simple expressions f(x) where f is one of the math functions defined in Base, and x is a variable? Or are you not supposed to take derivatives wrt expressions at all?

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# Simple Cryptography Logic Level 5 You are voyaging on a tour of the Pacific. On the last day of your travels, this message, wrapped up in a bottle, drifts up to your ship. Find the sum of all the numbers that occur in this sentence. As an explicit example, if the number three and twenty-six are present in the sentence, one would input $$3+26=29$$. Hint: If the picture does not immediately give you a hint, it probably will not give you one at all. All is revealed in the solution. ×

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### FIN 501 Module 5 Case Previewing 9 of 1 total pages. Money-back guarantee Regular Price: \$50.00 You Save: \$15.00 You have 0 credits. Earn credits #### Description FIN 501 Module 5 Case Net Present Value, Mergers, and Acquisitions One of financial goals of the financial managers is to maximize the shareholders wealth. Therefore, merger and acquisition decisions should be consistent with shareholder wealth maximization criteria and financial characteristics of the targets should be considered in the decision process. The NPV method is one of the useful methods that help financial managers to maximize shareholders wealth. Module 5 Case Assignment has two parts. Part I of this case assignment is related to capital budgeting decision and part II is about mergers and acquisitions. Please read both parts carefully before you start answering the questions. Part I: Net Present Value (NPV) method is one of the most important methods which is used to make capital budgeting decisions by almost every company. NPV method is important because it helps financial managers to maximize shareholders wealth by making better capital budgeting decisions. Suppose Google is considering a new project that will cost \$2,425,000 (initial cash outflow). The company has provided the following cash flow figures to you: YearCash Flow 0-\$2,425,000 1450,000 2639,000 3700,000 4550,000 51,850,000 PV of CF = CF1 / (1+r)1 + CF2 / (1+r)2 + CF3 / (1+r)3 + CF4 / (1+r)4 + CF5 / (1+r)5 2) Calculate NPV NPV = Total PV of CF Initial cash outflow or -Initial cash outflow + Total PV of CF r = Discount rate (9%) If you do not know how to use calculator, please use the present value tables. If Google's cost of capital (discount rate) is 11%, what is the project's net present value? Based on your analysis and findings, what would you recommend to the executives and the shareholders of Google? Should the project be accepted? The shareholders of Google would also like to know the meaning of NPV concept. You may use the following steps to calculate NPV: 1) Calculate present value (PV) of cash inflow (CF) Part II: Rumors that Google is Considering Acquiring Groupon Rumors about potential mergers and acquisitions are often a hot topic in the business press. There are rumors that Google is considering acquiring Groupon As you know from reading the material in the background materials, mergers and acquisitions can potentially bring about great rewards but also can potentially bring great risks and pitfalls. For this assignment, do some research concerning the arguments both for and against such an acquisition from a financial perspective. For this module we are not so concerned with how consumers may fair, as this is an issue for the government to consider if they have to approve this acquisition. Instead you are considering this from the point of view of whether or not such an acquisition would be a profitable undertaking that would add value to the shareholders of two corporations (Google and Groupon). The following article provides information on Google's potential acquisition of Groupon: Lachapelle, T. (2012). Buying groupon hard for anyone as growth slows: real m&a. Retrieved December, 2012 from But do not limit yourself to this article. Use Proquest, EbscoWeb, and other sources in the Cyberlibrary. Use various internet search engines such as news.google.com for the latest news on this acquisition. Then write a five to seven pages report for the shareholders of Google and Groupon by answering the following questions and the questions in part I: 1) Do you think Google's potential acquistion of Groupon would add value to the shareholders of both corporations? Why or why not? 2) Based on your analysis and findings (Part I and Part II), what would you recommend to the shareholders of Google and Groupon? Please explain your reasoning. The main focus of this assignment will be answering the questions above and the questions in part I. ?The impact on Groupon shareholders ?The financial conditions of both corporations (do not forget to consider the new project proposed by Google in part I) ?Why might one combined Google/Groupon company be more profitable than if they remained separate companies? In general, what makes an acquisition successful? ?Potential pitfalls - might the combined entity actually be less profitable than either company operating independently? What are the risk factors with this potential acquisition? In addition to making use of concepts from the background materials for this module, feel free to use concepts from Modules 1-4 as well. 3) What do you perceive you have learned in the Module 5 Case Assignment? Which of the following learning objectives do you feel you have mastered? ?Describe and apply net present value (NPV) method to make capital budgeting decisions ?Identify success factors in mergers and acquisitions ?Explain and discuss financing options for financing mergers and acquisitions ?Apply principles of risk and valuation analysis to mergers and acquisitions Please provide your evaluation of the Module 5 Case Assignment in brief. NOTE: Please note that your report/assignment will not be accepted without proper citations and references. You must use the sources from the background material together with the sources you find your own. It is also REQUIRED that you answer all the questions related to learning outcomes. @dgoodz 10866 830 Rating: Published On: 05/15/2013 Print Length: 1 page(s) Word Count: 2,336 File Name: FIN 501 Module 5 Case.docx File Size: 59.66 KB (0.06 MB) Sold By:

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I'm reviewing for a final and I'm having trouble recalling how to put equations into the proper form to make a straight-line graph. General guidance for when deal with these sorts of problems would be appreciated. For each equation, show how to rewrite the equation to make a straight-line graph of some function of y versus some function of x. Identify the slope and the vertical intercept. (1) y=[c+dx^(1/3)]^2 (2) y=ae^(kx) (3) y=kx^n (4) (y^2+b)^(1/2)=ax (5) y=a[1-bx^(3/4)] Thanks for the help!

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# How do you solve 2x+3y=6 and y=2x-6 using substitution? May 15, 2016 (x,y)=color(blue)(""(3,0)) (see below for solution by substitution) #### Explanation: Given [1]$\textcolor{w h i t e}{\text{XXX}} 2 x + 3 y = 6$ [2]$\textcolor{w h i t e}{\text{XXX}} y = 2 x - 6$ Since from [2] we have that $y = 2 x - 6$ we can replace $y$ with $\left(2 x - 6\right)$ in [1] to get [3]$\textcolor{w h i t e}{\text{XXX}} 2 x + 3 \left(2 x - 6\right) = 6$ Simplifying [4]$\textcolor{w h i t e}{\text{XXX}} 8 x - 18 = 6$ [5]$\textcolor{w h i t e}{\text{XXX}} \rightarrow 8 x = 24$ [6]$\textcolor{w h i t e}{\text{XXX}} \rightarrow x = 3$ Since from [6] $x = 3$ we can replace $x$ with $\left(3\right)$ in [2] to get [7]$\textcolor{w h i t e}{\text{XXX}} y = 2 \left(3\right) - 6$ and simplifying [8]$\textcolor{w h i t e}{\text{XXX}} y = 0$

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Geometry.. Given: A(3,-1), B(5,2), C(-2,0), P(-3,4), Q(-5,-3), R(-6,2). Prove: angles ABC and RPQ are congruent by completing the paragraph proof. AB=RP=13, BC=(?)=53, and CA=QR=26. So segment AB is congruent to (?), segments BC and PQ are congruent and segment CA is congruent to segment QR. Therefore triangle ABC is congruent to (?) by (?), and angles ABC and RPQ are congruent by (?). AB = �ã[(5-3)^2 + (2+1)^2] = �ã(4+9) = �ã13 RP = �ã([-3+6)^2 +(4-2)^2] = �ã(9+4) = �ã13 BC = �ã[(5+2)^2 + (2-0)^2] = �ã(49+4) = �ã53 PQ = �ã[-3+5)^2 + (4+3)^2] = �ã(4+49) = �ã53 AC = �ã[3+2)^2 + (-1-0)^2] = �ã(25+1) = �ã26 RQ = �ã[(-6+5)^2 + (2+3)^2] = �ã(1+25) = �ã26 clearly we have corresponding pairs of sides equal, so by SSS, ∆ABC≅∆RPQ I guess I don't understand how to write the answer. Angle ABC is congruent to RPQ by____? and angles ABC and RPQ are congruent by _____? 1. 👍 0 2. 👎 0 3. 👁 225 1. 👍 0 2. 👎 0 posted by Henry Similar Questions 1. Geometry Given: A(3,-1), B(5,2), C(-2,0), P(-3,4), Q(-5,-3), R(-6,2). Prove: angles ABC and RPQ are congruent by completing the paragraph proof. AB=RP=13, BC=(?)=53, and CA=QR=26. So segment AB is congruent to (?), segments BC and PQ are asked by Lisa on July 24, 2011 2. Geometry Given: A(3,-1), B(5,2), C(-2,0), P(-3,4), Q(-5,-3), R(-6,2). Prove: angles ABC and RPQ are congruent by completing the paragraph proof. AB=RP=13, BC=(?)=53, and CA=QR=26. So segment AB is congruent to (?), segments BC and PQ are asked by Wendell on July 26, 2011 3. Geometry Given: A(3,-1), B(5,2), C(-2,0), P(-3,4), Q(-5,-3), R(-6,2). Prove: angles ABC and RPQ are congruent by completing the paragraph proof. AB=RP=13, BC=(?)=53, and CA=QR=26. So segment AB is congruent to (?), segments BC and PQ are asked by Wendell on July 25, 2011 4. GEOMETRY Reflective sets of angles Given: asked by Happy Face on September 28, 2010 5. Geometry Reflective sets of angles Given: asked by Happy Face on September 28, 2010 6. Math Suppose line GH is congruent to line JK, line HE is congruent to line KL, and angle 1 is congruent to angle L. Can you prove that triangle GHI is congrunet to triangke JKL, abd if so, how? A. You can use SAS to prove the triangles asked by Bettey on October 8, 2018 7. geometry Complete the flow proof for a Hypotenuse-Angle Theorem. Given AC congruent DF, asked by chloe on April 10, 2015 8. Geometry I need help on these two. Consider tirangles ABC and DEF. Side A is congruent to side F. Angle A is congruent to angle F. Angle B is congruent to angle E. What postulate or theorem can be used to prove that the two triangles are asked by Amy on August 21, 2006 9. Geometry Given: ABCD is a parallelogram; asked by DANIELLE on June 13, 2007 10. geometry given angle amd and zdm are right angles given: segment AM and ZD are congruent prove: angle a is congruent to z (CPCTC) I know that reflexive prop is needed and all right angles are congruent, also sas Please help with 3 asked by sweet pea on November 9, 2015 More Similar Questions

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Can anyone help me make sense of the Princeton Review score? : General GMAT Questions and Strategies Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack It is currently 20 Jan 2017, 12:14 ### GMAT Club Daily Prep #### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email. Customized for You we will pick new questions that match your level based on your Timer History Track every week, we’ll send you an estimated GMAT score based on your performance Practice Pays we will pick new questions that match your level based on your Timer History # Events & Promotions ###### Events & Promotions in June Open Detailed Calendar # Can anyone help me make sense of the Princeton Review score? Author Message Intern Joined: 13 Nov 2010 Posts: 23 Followers: 1 Kudos [?]: 9 [0], given: 0 Can anyone help me make sense of the Princeton Review score? [#permalink] ### Show Tags 22 Nov 2010, 20:23 I took the free test at Princeton Review and got a score of 650. Can someone help me understand it? Here is the details: Verbal: 33 Math: 48 Total: 650 I missed eight questions in verbal. They are questions 1, 14,15, 18,19, 21,29,35. I guess I was given very easy questions. But I don't understand why that is the case? given I only missed one question in the first 13 questions? My other test score are 720 on TestPrep, 690 on MGMAT. Thanks! Retired Moderator Status: The last round Joined: 18 Jun 2009 Posts: 1310 Concentration: Strategy, General Management GMAT 1: 680 Q48 V34 Followers: 79 Kudos [?]: 1004 [0], given: 157 Re: Can anyone help me make sense of the Princeton Review score? [#permalink] ### Show Tags 22 Nov 2010, 21:12 princeton-review-cats-vs-gmat-prep-gmat-62608.html Let us know, if you need any help. _________________ Intern Joined: 13 Nov 2010 Posts: 23 Followers: 1 Kudos [?]: 9 [0], given: 0 Re: Can anyone help me make sense of the Princeton Review score? [#permalink] ### Show Tags 22 Nov 2010, 21:18 thanks! this is helpful. they are giving me super easy questions, i guess thats why.. Re: Can anyone help me make sense of the Princeton Review score?   [#permalink] 22 Nov 2010, 21:18 Similar topics Replies Last post Similar Topics: Please can anyone help me with these GMAT Test Prep Questions 4 01 Feb 2016, 06:11 Analysing my Verbal Score - Does it make sense? 4 15 Apr 2015, 18:38 1 Help understanding Princeton Review Diagnostic score 3 06 Jun 2012, 12:46 7 If the perimeter of a rectangular property is 46 meters, and the area 5 10 Jul 2010, 15:27 GMAT: Can anyone help clarify my score? 2 23 Nov 2009, 20:31 Display posts from previous: Sort by # Can anyone help me make sense of the Princeton Review score? Moderators: WaterFlowsUp, HiLine Powered by phpBB © phpBB Group and phpBB SEO Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.

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# Leetcode The Skyline problem solution In this Leetcode The Skyline problem solution A city's skyline is the outer contour of the silhouette formed by all the buildings in that city when viewed from a distance. Given the locations and heights of all the buildings, return the skyline formed by these buildings collectively. ## Problem solution in Python. ```class Solution: def getSkyline(self, buildings: List[List[int]]) -> List[List[int]]: if not buildings: return [] points = [] for left, right, height in buildings: points.append((left, -height)) points.append((right, height)) points = sorted(points, key=lambda x: (x[0], x[1])) # break ties when x coordiantes are equal from heapq import heappop, heappush, heapify res, pq = [], [float('inf')] prev_max_height = 0 for x, height in points: if height < 0: heappush(pq, height) else: pq.remove(-height) heapify(pq) cur_max_height = pq[0] if cur_max_height != prev_max_height: if cur_max_height == float('inf'): cur_max_height = 0 res.append([x, -cur_max_height]) prev_max_height = cur_max_height return res ``` ## Problem solution in Java. ```class cord{ int x,y; boolean isStart; cord(int x,int y,boolean f){ this.x=x;this.y=y;isStart=f; } } class Solution { public List<List<Integer>> getSkyline(int[][] buildings) { List<List<Integer>> ans=new ArrayList<>(); if(buildings.length==0) return ans; List<cord> l=new ArrayList<>(); for(int i[]:buildings){ cord c=new cord(i[0],i[2],true),c1=new cord(i[1],i[2],false); l.add(c);l.add(c1); } Collections.sort(l,new Comparator<cord>() { @Override public int compare(cord a,cord b){ if(a.x!=b.x) return a.x-b.x; else{ if(a.isStart && b.isStart) return b.y-a.y; else if(a.isStart!=b.isStart) return a.isStart?-1:1; else return a.y-b.y; } } }); TreeMap<Integer,Integer> m=new TreeMap<>(); m.put(0,1); int prevMax=0; for(cord i:l){ if(i.isStart) m.put(i.y,m.getOrDefault(i.y,0)+1); else{ int v=m.get(i.y)-1; if(v==0) m.remove(i.y); else m.put(i.y,v); } int max=m.lastKey(); if(max!=prevMax){ List<Integer> t=new ArrayList<>(); t.add(i.x);t.add(max); ans.add(t); prevMax=max; } } return ans; } } ``` ## Problem solution in C++. ```bool cmp(vector<int> &A, vector<int> &B){ if(A[0]!=B[0]) return A[0]<B[0]; else if(A[1]==B[1]) return B[2]==1; else if(A[2]==0 && B[2]==0) return A[1]>B[1]; else if(A[2]==1 && B[2]==1) return A[1]<B[1]; return true; } class Solution { public: vector<vector<int>> getSkyline(vector<vector<int>>& buildings) { int n=buildings.size(); vector< vector<int> > A; for(int i=0;i<buildings.size();i++){ A.push_back({buildings[i][0],buildings[i][2],0}); A.push_back({buildings[i][1],buildings[i][2],1}); } sort(A.begin(),A.end(),cmp); multiset<int> pq; vector< vector<int> > ans; int maxValue=0; pq.insert(0); for(int i=0;i<A.size();i++){ if(A[i][2]==0){ pq.insert(A[i][1]); } else{ pq.erase(pq.find(A[i][1])); } auto itr=pq.end(); itr--; if(maxValue!=*itr) ans.push_back({A[i][0],*itr}); maxValue=*itr; } return ans; } }; ```

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# How Many Gallons is 32 Cups? There are so many different ways to measure liquids – by the pint, quart, gallon, fluid ounce, tablespoon, teaspoon, and more. But how much is 32 cups in gallons? To answer this question, we need to know a little bit about the history of measurement. There are so many different measurements for liquids – it can be confusing! Here’s a quick guide to help you out the next time you’re trying to convert cups to gallons. 1 gallon = 16 cups Credit: 9jafoods.com ## How Many Cups Makes 1 Gallon? One gallon is equal to 16 cups. ## Does 16 Cups Equal 1 Gallon? No, a gallon is equivalent to 16 cups. ## Is 8 Cups a Gallon? There are a few different measurements for a gallon, but the most commonly used one in the US is the liquid gallon. This measurement is used for both dry and wet goods. One US liquid gallon is equal to 4 quarts, 8 pints, 16 cups or 128 fluid ounces. So yes, 8 cups is a gallon. ## Is 2 Gallons Greater Than 32 Cups? This is a bit of a tricky question, as it depends on what kind of cups we are talking about. If we are talking about 8 oz. cups, then 32 cups is equal to 4 gallons. However, if we are talking about smaller cups, such as 4 oz. cups, then 2 gallons is greater than 32 cups. ## 32 Cups = How Many Quarts If you’re wondering how many quarts are in 32 cups, the answer is 8 quarts. This is because there are 4 cups in 1 quart, so 32 divided by 4 equals 8. This means that if you have a recipe that calls for 8 quarts of ingredients, you’ll need 32 cups to make it. This can be helpful to know when you’re batch cooking or preparing food for a large group. Keep in mind that 1 cup is equal to 16 tablespoons, so if your recipe calls for 2 cups of liquid, you’ll need 32 tablespoons (or 2 quarts). Now that you know the answer to the question, “32 cups equals how many quarts,” put it to good use in your kitchen! ## How Many Cups in a Gallon A gallon is a unit of measurement that is most commonly associated with liquids. There are many different types of gallons, including the imperial gallon, which is used in the United Kingdom, and the US gallon, which is used in the United States. The imperial gallon has a capacity of 4.54609 liters while the US gallon has a capacity of 3.785411784 liters. One imperial gallon is equivalent to 1.2 US gallons. How Many Cups in a Gallon? There are 16 cups in a gallon. This means that there are 4 quarts in a gallon or 8 pints in a gallon. If you’re using measurements other than cups, it’s important to note that 1 cup = 0.125 gallons or 8 fluid ounces. ## 32 Cups to Liters Converting between cups and liters is a two step process. First convert the cups to fluid ounces and then convert the fluid ounces to liters. There are 8 fluid ounces in a cup so 32 cups is equal to 256 fluid ounces. There are 33.8140225 fluid ounces in a liter so divide 256 by 33.8140225 to get 7.527396195 L which rounds up to 7.53L . ## 16 Cups to Gallons There are all sorts of conversions we need to make in our daily lives. For example, how many quarts are in a gallon? How many teaspoons are in a tablespoon? What about converting cups to gallons? This is actually a pretty easy conversion to make, and it only requires a little bit of math. Here’s how you do it: 1 cup = 0.25 gallons ## Conclusion If you’re planning on hosting a party or making a big batch of something, it’s important to know how many gallons are in 32 cups. This can be handy when trying to determine how much food or drink to prepare. According to the blog post, there are 4 gallons in 32 cups. This means that if you have a recipe that calls for 8 cups of liquid, you would need 2 gallons. Similarly, if you’re making a dish that requires 16 cups of ingredients, you would need 4 gallons. How is Matt Stonie Not Fat?

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## JS Bach: WTC I, E Minor Fugue Hello all, It will help if you have read the post: Significance of the number nineteen We are looking for the dynamic symmetry in JS Bach's WTC I, E Minor Fugue. This is a two-voice fugue, which could have been named an invention, but qualifies as a fugue. The agent defining the symmetry is lengthy consecutive parallel intervals and the number 19. Counting measures, we have the first 19 meassures ending with a measure of consecutive parallel octaves. The second 19 measures also ends with a measure of consecutive parallel octaves. These 38 measures (2x19) lead to a four-measure coda yielding the total 42 measure fugue. Any odd number has a central number that divides two equal portions. Thus it behooves us to observe the midpoints of our two 19 measure leads. Measure 10 mediates the first 19 with consecutive parallel sixths. Measure 29 mediates the second 19 with consecutive parallel thirds. Sixths and thirds so highlighted might lead the contrapuntalist to suspect Double Counterpoint at the octave. A simpler understanding might be gained that the combination of a sixth to a third will span an octave. (C up to A = sixth [C,D,E,F,G,A]; continuing A up to C = third [A,B,C]; overall the resulting C up to C is an ocatve [C,D,E,F,G,A,B,C]. The parallelisms are distinguished by length of consecutiveness, minimally nine sixteenths, and the full measure of twelve sixteenths for measures 19 and 38. Thus the two midpoints of the 19 measure portions have combined meaning for the overall middle 38 measure lead to the coda. Indeed, measure 20 continues with four more sixteenths to perfect the middle of the 38 measure lead to the coda. Thus the fugue is organized by the number 19 with significant intervalic parallelisms yielding dynamic symmetry. Cheers, ## Proportions: The Number 19 The number nineteen is a favorite number used by Bach. I will be using analyses of the number 19 in Bach and Beethoven. So first, here are some sites on the number nineteen. http://www.vortexmaps.com/htmla/nineten.htm http://www.geocities.com/WestHollywood/Park/6443/Submitters/the_number_nineteen.htm http://www.vortexmaps.com/htmla/planets.htm The proportions for the number nineteen are: 3:2:5:7:12:19:31:50 etc. Beginning with the numbers 3 and 2, adding consecutive numbers yield the next number in the sequence. Maybe the most frequently and maybe least noticed proportions from the series are the seven days of the week, from which we separate two weekend days and five work days; and 12 is used twice to count the number of hours in a day, and 12 months divide a year. Less formally astrology is planned in 19 year cycles. Cheers, and happy counting ## Stravinsky/Schönberg Artur Schnabel: "You may find this hard to believe, but Igor Stravinsky has actually published in the papers the statement, 'Music, to be great, must be completely cold and unemotional'! And last Sunday, I was having breakfast with Arnold Schoenberg, and I said to him, 'Can you imagine that Stravinsky actually made the statement that music, to be great, must be cold and unemotional?' At this, Schoenberg got furious and said, 'I said that first!'" * * * ## Richard Strauss: Don Juan by Andrew Clements Friday January 12, 2001 The Guardian Don Juan was the work that made the 25-year-old Richard Strauss a star when it was first performed in Weimar in 1889 - and with good reason. An epoch-making score, it redefined the parameters of musical potential. No composer had previously used orchestral forces with such flamboyant audacity, and the history of sonority would never be quite the same again. In his picture of the famous womaniser, Strauss also placed a hitherto unimagined emphasis on erotic hedonism, which remains startling more than a century later. The result has always been a firm favourite with players and audiences alike, though Don Juan is much more than a virtuoso musical porn show, and the whole thing can come adrift if conductors fail to probe its deeper ambiguities. Strauss took as his source an unfinished play by the deranged poet Nikolaus Lenau, in which the Don is very much portrayed as the prototype of the Nietzschean figures to whom Strauss was later drawn - an amoral being "beyond good and evil" whose sexual exploits form a psychological defence against his own destructive nihilism. A sense of jittery, existential danger needs to be added to the glamorous sexiness of it all if the piece is to succeed. Several of Strauss's own performances survive, of which the finest - measured in speed but relentless in intensity - is his 1944 radio broadcast with the Vienna Philharmonic (Preiser). A similar spaciousness, rather than superficial glitter, pervades Wilhelm Furtwängler's majestic 1954 version with the same orchestra (EMI). The usually great Bruno Walter was never quite at his best in Strauss's music and his 1952 version with the New York Philharmonic (Sony) finds him occasionally ill at ease. Leopold Stokowski, ever the wizard when it comes to orchestral flamboyance, generates tremendous, visceral excitement. Among the next generation of interpreters we find versions by Karajan (DG), Solti (Decca), Boehm (DG) and Rudolf Kempe (EMI), all great, all radically different. Karajan's lushness contrasts sharply with Solti's nervous edginess. Boehm is all romantic radiance and warmth, while Kempe, with the Dresden Staatskapelle on glorious form, is deeply humane, portraying the Don very much as a man whose emotions, though transitory, are sincere. More recently we have Neeme Jarvi controversially and brilliantly turning the Don into a Sadean brute as part of his Chandos Strauss cycle with the Royal Scottish National Orchestra; Claudio Abbado, very fierce with the Vienna Philharmonic yet again (DG); and Herbert Blomstedt and the San Francisco Symphony, almost matchless when it comes to exposing Strauss's gorgeous palette of orchestral colour (Decca - the sound is astonishing). But there's one version that towers above the rest, namely the 1954 RCA recording with the Chicago Symphony and Fritz Reiner. The work has never sounded quite so electrifyingly raunchy or so dangerous as it does here, while the downbeat ending is shockingly, devastatingly sad. The playing is stupendous and the whole thing knocks you sideways. It ranks among the most stunning performances ever committed to disc - an absolutely unmissable achievement. Key recording: Fritz Reiner (RCA) Guardian Unlimited © Guardian Newspapers Limited 2004 ## Tchaikovsky: Instrumentation and nationalism Tchaikovsky wrote this: Letter to Mme von Meck, Clarens, March 5 (17), 1878 You ask how I manage my instrumentation. I never compose in the abstract; that is to say, the musical thought never appears otherwise than in a suitable external form. In this way I invent the musical idea and instrumentation simultaneously. Thus I thought out the scherzo of our symphony [Fourth Symphony] at the moment of its composition---exactly as you heard it. It is inconceivable except as pizzicato. Were it played with the bow, it would lose all its charm and be a mere body without a soul. As regards the Russian element in my works, I may tell you that not infrequently I begin a composition with the intention of introducing some folk melody into it. Sometimes it comes of its own accord, unbidden (as in the finale of our symphony). As to this national element in my work, its affinity with the folk songs in some melodies and harmonies comes from my having spent my childhood in the country, and, from my earliest years, having been impregnated with the characteristic beauty of our Russian folk music. I am passionately fond of the national element in all its varied expressions. In a word, I am Russian in the fullest sense of the word. * * * ## Rimski-Korsakov: Formal Study From a letter to Semyon Kruglikov, November 9, 1880 Nikolai Andreyevitch Rimski-Korsakov (1844-1908) wrote: One can learn by oneself; sometimes one needs advice, but one has also to learn, that is, one must not neglect harmony and counterpoint and the development of a good technique and a clean leading subject. All of us, myself and Borodin and Balakirev, but especially Cui and Moussorgsky, neglected this. I consider that I caught myself in time and made myself get down to work. Owing to such deficiencies in technique Balakirev writes little; Borodin, with difficulty; Cui sloppily; Moussorgsky, messily and often nonsensically; and all this constitutes the very regrettable specialty of the Russian school. Like his colleagues in the "Big Five," Rimski-Korsakov was a musician by avocation, at least at the inception of his composing career. By profession he was a naval officer, following in the tradition of his family. His first large scale work, a Symphony in E-flat minor (Opus 1), was composed under Balakirev's influence and guidance, while he was still ignorant of even the names of chords and the elementary rules of part writing. Unlike his colleagues, he devoted himself assiduously to the formal study of harmony, counterpoint and form, study which aroused cynicism in Moussorgsky (who dubbed it "routine, lifeless, and reactionary" and skepticism in Tchaikovsky (who spoke of "contrapuntal intricacies"). Nevertheless, it was this study which enabled him to revise and polish Moussorgsky's at times awkwardly written and often unfinished works after the latter's death, to orchestrate Dargomijsky's Stone Guest and with his pupil, Glazounov, to finish and orchestrate Borodin's Prince Igor. Numbered among his many gifted students were Glazounov, Ipolitov-Ivanov, and Stravinsky. Cheers, .. ## Nikolai Rimsky-Korsakov Nikolai Rimsky-Korsakov (1844-1908), an outstanding and leading figure in the music of Russia, an eminent master of orchestral expression, a fervent devotee of Beauty in music, and preponderantly true to the spirit and idiom of his nation. His whole active life was devoted to the promotion of the musical art of his native land. Though not the oldest nor the first Russian master, there is something patriarchal in Rimsky-Korsakov's position; he is cited as the father of Russian school of orchestration; and, as teacher of many later celebrities, his strong and beneficent influence was far reaching. In addition to his superb orchestral Suite Sheherazade (from the Arabian Nights), Op. 35, I would recommend his the Oriental Suite Antar ("Poet and beloved Hero of the Desert"), Op. 9 (1881). Both of these consist of four Movements, though the latter are not strictly analogous to those of the Symphony. In their character they show that, despite his devotion to Russian folk-lore and folk-song, he had a decided taste for the Oriental in music, and caught its idiom most successfully. Antar is generally listed as Rimsky-Korsakov's Second "Symphony," though the title Suite is more accurate. The story runs thus: Antar rescues the Fairy Gul-Nazar (as a gazelle) from the pursuit of a giant bird. As a reward, she promises him three great Delights of Life: Revenge, Power, and Love. These episodes form the basis of the four Movements, of which the Finale is the best---the exceeding skillful combination of the Fairy-theme and an Oriental Dance. The Symphonies of this master (not to mention the Suites) are three in number: the First, in E major (1865); the Second,in C, and a Symphonietta in A minor---all admirable, but not on a plane with the Suites. Cheers, ## Pioneers of the Romantic School Carl Maria von Weber (1786-1826) is generally regarded by historians as the founder of the Romantic school of musical expression; and he was undoubtedly the earliest distinguished forerunner of the great master minds: Schubert, Mendelssohn, Schumann, and Brahms. The most important and popular of Weber's Symphonies was the second, in C. But there were a number of other pioneers who did significant work, paved the way for coming achievements; they were not "Masters" in the broader historical sense, but they were Masters in their day and generation, as compared with a host of less renowned composers; and they richly merit honorable mention here. Nor were they the very first: the workings of a Romantic spirit may be recognized as far back as history reaches. There probably never was a human who, in trying to express something in tones, did not vaguely essay to express the self. Thus we conclude that there is no incompatibility between the Romantic and Classic spirits, nor is there any overt antagonism there; those with romantic incentives have always admitted and respected the necessity of law and order, and, conversely, the classical-minded surely always claimed the right to say, in tones, under surveillance of the law, what they felt. Schumann and his adherents called themselves Neo-Romanticists, and were a bit more clamorous in their call for freedom. And these were succeeded by the Futurists, Polytonalists, Atonalists, and by the mid twentieth century, by the Ultra-Futurists, Cacophanists, and Exoticists who simply go still farther in their disregard of the older conventions. Just where these will land us, Heaven no doubt knows, but no mortal can foretell what Music (?) will be, a thousand years hence. The present storm will clear up---as surely as the sun emerges after devastating turmoil of the elements; and the results will mean real Progress, to the joy and benefaction of humanity. It may be harking too far back to include G.J. (Abt) Vogler (1749-1814) in this list, but he was the author of at least one Symphony (in C) which was exceedingly popular; and he exerted a powerful influence as teacher---Weber and Meyerbeer were among his many pupils; furthermore, he outlived Haydn and Mozart. Then came Peter von Winter (1754-1825) author of nine Symphonies, one of which, The Battle (with Chorus) appeared in 1814. Ignaz J. Pleyel (1757-1831), who produced twenty-nine Symphonies, much admired for their grace. Next followed in chronological order: Luigi Cherubini (1760-1842), an illustrious master of dramatic music, in France, and celebrated also for his contrapuntal erudition. On a visit to London in 1815 he wrote a Symphony for the Philharmonic Society, his only work of that type, and one that has historic interest alone. Etienne Mehul (1763-1817), another outstanding representative of the dramatic side of musical art in France, author of many Operas, and four excellent Symphonies. Then the cousins, Andreas Romberg (1767-1821), the composer of ten Symphonies, the best of which is one in D; and Bernard Romberg (1767-1841), who wrote a least one noteworthy Symphony---a tribute "Upon the death of Queen Louise." Sigismund Neukomm (1778-1858), pupil of Haydn, an enormously prolific and popular composer, among whose works was a Heroic Symphony, written 1818---thirteen years after the creation of Beethoven's Eroica. George Onslow (1784_1852), composer of four Symphonies, one of which, in A major, possesses positive merit. Luwig Spohr (1784-1859), famous violinist, author of nine noteworthy Romantic Symphonies, the best known and admired, though not the most distinguished of which is the celebrated Fourth, in F (1834), The Consecration of Tone (or Tones); it is an example of straightforward program music, mirroring in succession: "Chaos, without Tone; Awakening; Cradle song; Dance; Serenade; Martial music; Funderal music; and Comfort in Tears"---a work of no little originality, and melodic and harmonic charm, but wholly wanting (in consequence of its descriptive purpose) in symphonic compactness and structural logic. In its day it was sure of a place on orchestral programs, and was everywhere heartily applauded; but, in company with many another meritorious production of the above-listed symphonists, it is now overshadowed and eclipsed by the preeminent creations of true, genuine Masters , from Haydn to Brahms---and of later time. Finally, Johann W. Kalliwoda (1801-1866), who produced seven Symphonies, the third of which, written in 1831, exhibits qualities of substantial worth, deserving of sincere recognition. Like the others, it is now forgotten. Cheers, ## The Enlightenment: The Salon Although the leading figures of the Enlightenment were all men, the social context was the highly-civilized "salon", usually presided over by a women with some independent wealth. On Julie de Lespinasse From Memoir of Baron de Grimm Her circle met daily from five o'clock until nine in the evening. There we were sure to find choice men of all orders in the State, the Church, the Court,-military men, foreigners, and the most distinguished men of letters. Every one agrees that though the name of M. d'Alembert may have drawn them thither, it was she alone who kept them there. Devoted wholly to the care of preserving that society, of which she was the soul and the charm, she subordinated to this purpose all her tastes and all her personal intimacies. She seldom went to the theatre or into the country, and when she did make an exception to this rule it was an event of which all Paris was notified in advance.... Politics, religion, philosophy, anecdotes, news, nothing was excluded from the conversation, and, thanks to her care, the most trivial little narrative gained, as naturally as possible, the place and notice it deserved. News of all kinds was gathered there in its first freshness. From Memoir of Marmontel The circle was formed of persons who were not bound together. She had taken them here and there in society, but so well assorted were they that once there they fell into harmony like the strings of an instrument touched by an able hand. Following out that comparison, I may say that she played the instrument with an art that came of genius; she seemed to know what tone each string would yield before she touched it; I mean to say that our minds and our natures were so well known to her that in order to bring them into play she had but to say a word. Nowhere was conversation more lively, more brilliant, or better regulated than at her house. It was a rare phenomenon indeed, the degree of tempered, equable heat which she knew so well how to maintain, sometimes by moderating it, sometimes by quickening it. The continual activity of her soul was communicated to our souls, but measurably; her imagination was the mainspring, her reason the regulator. Remark that the brains she stirred at will were neither feeble nor frivolous: the Coudillacs and Turgots were among them; d'Alembert was like a simple, docile child beside her. Her talent for casting out a thought and giving it for discussion to men of that class, her own talent in discussing it with precision, sometimes with eloquence, her talent for bringing forward new ideas and varying the topic-always with the facility and ease of a fairy, who, with one touch of her wand, can change the scene of her enchantment-these talents, I say, were not those of an ordinary woman. It was not with the follies of fashion and vanity that daily, during four hours of conversation, without languor and without vacuum, she knew how to make herself interesting to a wide circle of strong minds. From Letter of Julie de Lespinasse to the Comte de Guibert. I love you too well to impose the least restraint upon myself; I prefer to have to ask your pardon rather than commit no faults. I have no self­love with you; I do not comprehend those rules of conduct that make us so content with self and so cold to those we love. I detest prudence, I even hate (suffer me to say so) those "duties of friendship" which substitute propriety for interest, and circumspection for feeling. How shall I say it? I love the abandonment to impulse, I act from impulse only, and I love to madness that others do the same by me. Ah! mon Dieu! How far I am from being equal to you! I have not your virtues, I know no duties with my friend; I am closer to the state of nature; savages do not love with more simplicity and good faith. The world, misfortunes, evils, nothing has corrupted my heart. I shall never be on my guard against you; l shall never suspect you. You say that you have friendship for me; you are virtuous; what can l fear? I will let you see the trouble, the agitation of my soul, and I shall not blush to seem to you weak and inconsistent. I have already told that I do not seek to please you; I do not wish to usurp your esteem. I prefer to deserve your indulgence-in short, I want to love you with all my heart and to place in you a confidence without reserve.... From Letters of Julie de Lespinasse, Katherine P. Wormley, trans. (Boston: Hardy, Pratt and Co., 1903), p9,. 34-35, 75. Madame Geoffrin was married to a rich man. His money seems to have been the main benefit she found in the marriage. She used it to help her philosophe friends. From Memoir of d'Alembert Much has been said respecting Madame Geoffrin's goodness, to what a point it was active, restless, obstinate. But it has not­been added, and which reflects the greatest honour upon her, that, as she advanced in years, this habit constantly increased. For the misfortune of society, it too often happens that age and experience produce a directly contrary effect, even in very virtuous characters, if virtue be not in them a powerful sentiment indeed, and of no common stamp. The more disposed they have been at first to feel kindness towards their fellow creatures, the more, finding daily their ingratitude, do they repent of having served them, and even consider it almost as a reproach to themselves to have loved them. Madame Geoffrin had learnt, from a more reflected study of mankind, from taking a view of them more enlightened by reason and justice, that they are more weak and vain than wicked; that we ought to compassionate their weakness, and bear with their vanity, that they may bear with ours.... The passion of giving, which was an absolute necessity to her seemed born with her, and tormented her, if l may say so, even from her earliest years. While yet a child, if she saw from the window any poor creature asking alms, she would throw whatever she could lay her hands upon to them; her bread, her linen, and even her clothes. She was often scolded for this intemperance of charity, sometimes even punished, but nothing could alter the disposition, she would do the same the very next day.... Always occupied with those whom she loved, always anxious about them, she even anticipated every thing which might interrupt their happiness. A young man, [note: yhis young man was d'Alembert himself] for whom she interested herself very much, who had till that moment been wholly absorbed in his studies, was suddenly seized with an unfortunate passion, which rendered study, and even life itself insupportable to him. She succeeded in curing him. Some time after she observed that the same young man, mentioned to her, with great interest, an amiable woman with whom he had recently become acquainted. Madame Geoffrin, who knew the lady, went to her. "I am come," she said, "to intreat a favour of you. Do not evince too much friendship for * * * * or too much desire to see him, he will be soon in love with you, he will be unhappy, and I shall be no less so to see him suffer; nay, you yourself will be a sufferer, from consciousness, of the sufferings you occasion him." This woman, who was truly amiable, promised what Madame Geoffrin desired, and kept her word. As she had always among the circle of her society persons of the highest rank and birth, as she appeared even to seek an acquaintance with them, it was supposed that this flattered her vanity. But here a very erroneous opinion was formed of her; she was in no respect the dupe of such prejudices, but she thought that by managing the humours of these people, she could render them useful to her friends. "You think," said she, to one of the latter, for whom she had a particular regard, "that it is for my own sake I frequent ministers and great people. Undeceive yourself,-it is for the sake of you, and those like you who may have occasion for them...." From Memoir of Baron de Grimm Whether from malice or inattention, one who was in the habit of lending books to the husband of Madame Geoffrin, sent him several times in succession the first volume of the Travels of Father Labbat. M. Geoffrin with all the composure possible, always read the book over again without perceiving the mistake. "How do you like these Travels, Sir?"-"They are very interesting, but the author seems to me somewhat given to repetition."-He read Bayle's Dictionary with great attention, following the line with his finger along the two columns. "What an excellent work, he said, if it were only a little less abstruse."-"You were at the play this evening, M. Geoffrin, said one, pray what was the performance?"-"I really cannot say, I was in a great hurry to get in and had no time to look at the bill."- However deficient the poor man was, he was permitted to sit down to dinner, at the end of the table, upon condition that he never attempted to join in conversation. A foreigner who was very assiduous in his visits to Madame Geoffrin, one day, not seeing him as usual at table, enquired after him: "What have you done, Madam, with the poor man whom I always used to see here, and who never spoke a word?"-"Oh, that was my husband!-he is dead." From Baron de Grimm, Historical and Literary Memoirs and Anecdotes, (London: Henry Colburn, 1815), Vol. 3, pp. 400-405, 52­53. This text is part of the Internet Modern History Sourcebook. The Sourcebook is a collection of public domain and copy-permitted texts for introductory level classes in modern European and World history. Unless otherwise indicated the specific electronic form of the document is copyright. Permission is granted for electronic copying, distribution in print form for educational purposes and personal use. If you do reduplicate the document, indicate the source. No permission is granted for commercial use of the Sourcebook. (c)Paul Halsall Aug 1997 halsall@murray.fordham.edu ## Arnold Schönberg: Verklärte Nacht From Julian Ribke (translation: Mary Whittall) Schönberg found the inspiration for his string sextet in Richard Dehmel's poem 'Verklärte Nacht', which was first published in the collection 'Weib und Welt' and later incorporated in Dehmel's novel 'Zwei Menschen'. Although Schönberg expressly uses the term "programme music", in the note he wrote on the work in 1950 he makes a careful distinction: "My composition was, perhaps, somewhat different from other illustrative compositions, firstly, by not being for orchestra but for a chamber group and secondly, because it does not illustrate any action or drama, but was restricted to portray nature and express human feelings... in other words, it offers the possibility to be appreciated as 'pure' music." Richard Dehmel confirms the effect the sextet makes as autonomous music in a letter to Schönberg (12 December 1912): "Yesterday evening I heard Transfigured Night, and I would consider it a sin of omission if I did not say a word of thanks to you for your wonderful sextet. I had intended to follow the motives of my text in your composition, but I soon forgot to do so, I was so enraptured by the music." Schönberg wrote back (13 December 1912) that he was "reflecting in music" what Dehmel's poetry "stirred up" in him. Schönberg follows Dehmel's poem in the structure of the sextet: he divides the single-move-ment work into five sections of differing expressive character. Parts 1, 3 and 5, describing the two people and the atmosphere of their surroundings as they walk through the moonlit wood, frame two episodes, the woman's confession and the man's reply. But in spite of these divisions, the form can be understood in more ways than one. 'Transfigured night' prefigures a form of construction which Schönberg was to perfect in his succeeding instrumental works: 'Pelleas and Melisande' op.5, the D minor Quartet op.7 and the Chamber Symphony op.9. Each of these single-movement works can be regarded with equally good reason as an expanded first-movement sonata form, or as a complete symphony in which the movements are connected. In the sextet, too, the statement of themes is followed by complex developmental working, and in the fifth section the thematic complexes which have programmatic significance are brought together, so that this part of the work assumes the general character of a recapitulation. Again, the second section of the work, where the woman speaks and which itself falls into five parts, can be interpreted as the principal movement of a cyclic work; in turn the man's reply can be seen as performing the function of the slow movement in a symphony. It would be amiss, however, to interpret the form overall as a rondo with recurring refrains: although the theme from the introduction permeates all three of the "moonlit wood" sections, they are transformed in expression and function as they absorb and prolong the emotional atmosphere of the episodes. After the woman's excited outburst the theme from the introduction returns 'fortissimo' and marked "schwer betont" (with heavy emphasis), and rising quaver (eighth-note) figures make it more urgent, until the music gradually calms down and the third section dies away on sustained E flat minor chords. In the final section the theme floats radiantly in gentle 'pianissimo' above the arpeggios of the second violin: in the poem the surroundings have been transformed from a "bare, cold wood" to "high, bright night". There is an abundance of thematic material in part 2, the woman's confession. One group after another builds up to a climax of intensity: a virtuoso display by Schönberg of Brahms's technique of developing variation. This section ends with an expressive recitative-like passage which leads without a break into the "moonlit wood" theme and the third section. Although there are thematic links with what has gone before, the second episode, the man's answer, is also complete in itself. After the anxious E flat minor ending of the third section, the establishment of D major and the powerful, introductory cello cantilena have a liberating effect. A further change in mood is created by muted F sharp major harmonics, ornamented with rapid semiquaver (16th-note) figurations, which, Schönberg wrote, "express the beauty of the moonlight" which suffuses the man's comforting words. The significance given to thematic working and the interweaving of the sections is reminiscent of Wagnerian leitmotive technique. That, and the serious engagement with the Lisztian precedent of symphonic single-movement form, show the influence that the legacy of the New German movement had on Schönberg. In the article "My Evolution" (1949) he explained which where the Wagnerian and Brahmsian elements he had incorporated in his own style in 'Transfigured Night': "The thematic construction is based on Wagnerian 'model and sequence' above a roving harmony on the one hand, and on Brahms's technique of developing variation - as I call it - on the other. Also to Brahms must be ascribed the imparity of measures ... But the treatment of the instruments, the manner of composition, and much of the sonority were stricly Wagnerian. I think there were also some Schönbergian elements to be found in the breadth of the melodies...in contrapuntal and motivic combinations, and in the semi-contrapuntal movement of the harmony and its basses against the melody. Finally, there were already some passages of unfixed tonality which may be considered premonitions of the future". * * * ## Anton Bruckner Symphonies I have profound respect for Bruckner's work. Bruckner's deeply meditative music poses a challenge to listeners. The nine symphonies, most spanning an hour in length, gradually unfold over broad landscapes. Bruckner's symphonies begin quietly and take the shape of theme and variation; an opening theme is smoothly spun, which initiates a synthesis to take place over the entire work. The music is a reflection of Bruckner's Catholic faith, often taking on a medieval quality and reminiscent of church modes. Moments of high drama, quiet ponderousness, and absolute silence lie side by side, forming a coherent whole beyond the limits of earthly reality. A Bruckner symphony does not refer to concrete images, nor does it undergo a familiar style of "development"; it simply exists as a vast, autonomous body of sound. Bruckner's works were outlandish to the Viennese public, but helped propel European music into the era of Mahler, Strauss, and Debussy by further broadening the limits of symphonic time and space. Bruckner did enjoy increasing fame in his late years, as society became accustomed to the workings of Wagnerism; by the time of his final illness, he was a former professor of the Vienna Conservatory and the recipient of a government pension for his goodwill to the Austrian Empire. Bruckner's works have found performances worldwide, due to a steady growth in popularity since his death in 1896. A lack of interference by the Nazi government, who otherwise stunted the progress of Mahler, Kurt Weill, Boris Blacher, and others, was particularly helpful, as was the dedication of conductors such as Wilhelm Furtwängler, Daniel Barenboim, and Herbert von Karajan to performing Bruckner whenever the chance has presented itself. Still to be resolved, however, are questions about the scores themselves; they were sometimes revised through Bruckner's own decision, but also through the persuasion of friends who thought his music could be made "listener-friendly." One should note the different versions of some symphonies, with unwanted cuts and alterations still being weeded out by musicologists. Despite this controversy and the strife during his own lifetime, Bruckner's creative achievement endures. Whether written for church or concert hall, his music pulls audiences into a different realm, where ordinary thought is transcended. His first numbered symphonies (1, 2, 3) and his two earlier attempts (Number 0, or "Die Nullte," and the "Study" Symphony) are moving, but they are curiosities in comparison to the middle (4, 5, 6) and late (7, 8, 9). Symphony Number 4 ("Romantic") is his most medieval and most popular; Number 7 is noted for its sublimity, written in tribute to the recently-deceased Wagner; Number 8 is his farthest-reaching; while Number 9, left incomplete, assures us of Bruckner's peace in later life. The numerous masses, motets, and hymns are also unparalleled in both aesthetic and religious terms. As attention spans become narrower and values change from the spiritual to the material, musicians have feared Bruckner's music losing popularity. But it is this inherent spirituality, this certainty of faith, which makes it perhaps even more attractive in our time. Cheers, ## Dukas: The Sorcerer's Apprentice Andrew Clements Friday May 12, 2000 The Guardian Ever since Walt Disney's Fantasia in 1940, Paul Dukas's Symphonic Scherzo after Goethe has been inseparable from the image of Mickey Mouse trying to stem the battalions of buckets marching through the sorcerer's cellar. That sequence has been a mixed blessing for the reputation of The Sorcerer's Apprentice: the piece may have become a popular classic as a result, but such familiarity has bred, if not exactly contempt, then at least a taking for granted of the work's brilliance as a piece of orchestral writing, for Dukas (1865-1935) was one of the most gifted and self-critical of all the turn-of-the-century French composers. This intense self-scrutiny meant that, especially in the second half of his life, Dukas destroyed more music than he allowed to survive, and his reputation now rests on just 15 works, including a symphony, a ballet (La Péri), two major piano works and one unfairly neglected opera (Arianne et Barbe-Bleue, to a libretto by Maeterlinck). The Sorcerer's Apprentice was written in parallel with the symphony and first performed in the same year (1897); some of its themes share more than just a family likeness with that work, and it has been suggested that Dukas originally intended it as the symphony's scherzo. But the bigger work is entirely abstract and, as the subtitle indicates, The Sorcerer's Apprentice is explicitly programmatic. Based on Goethe's poem of the same name, it is self-contained in its own right. The construction is very rigorous; Dukas was essentially a conservative composer who idolised Beethoven, but tended to pursue his harmonic and rhythmic schemes to their logical conclusion. The way in which the main theme of the scherzo is remorselessly accumulated from tiny cells fascinated the modernists around him, and both Stravinsky's Fireworks and Debussy's Jeux are indebted to Dukas's method of construction. But the genius of the piece is that for all its formal rigour it seems natural and, in its dazzling orchestral colours, vividly pictorial. Conductors, then, need to balance the rigour of The Sorcerer's Apprentice with its sheer élan, and always remember that it is a scherzo. Toscanini certainly understood that - his version (Pearl) is lightning fast, while Leopold Stokowski, who recorded it for the Disney soundtrack, brings out all the orchestral splendour (Biddulph). Among the more recent versions, it's James Levine with the Berlin Philharmonic (Deutsche Grammophon) who, surprisingly perhaps, balances the athleticism and structural coherence best; Charles Dutoit (Decca) is fractionally too staid, though the Montreal Symphony's playing is superb. The only disadvantage of the Levine version is that it is coupled with Saint-Säens rather than with more Dukas, but David Zinman and the Rotterdam Philharmonic, who produce a fine-grained and intelligent performance, combine it with La Péri and Dukas's overture Polyeucte, as well as Vincent d'Indy's Symphony. A perfect introduction to a fascinating composer. Key recording: Zinman (Philips 454 127-2) Guardian Unlimited © Guardian Newspapers Limited 2004 ## Tchaikovsky: Sixth Symphony, B minor, Op.74 Tchaikovsky wrote his Sixth, and last, Symphony (Op.74 in B minor) in 1893, very shortly before his sudden death. He himself called it the Pathetic, and the impression became quite general that he had been laboring under the premonition of his approaching end. Nothing could be farther from the truth; moreover, only the brief final Movement is genuinely pathetic, and that but part of the time, this pathetic mood being brightened by contrasting episodes of decidedly hopeful and consoling quality. The first Movement is tragic rather than pathetic, yet here again frequent gleams of light and warmth fall across the background of passion---in this way, to be sure, accentuating the tragic pulses by their contrast. The first Movement is in regular, but broad sonata-allegro form. A brief Introduction (Adagio) precedes the principal Theme, based entirely upon the opening motive; and two Codettas follow the subordinate Theme. This first Movement contains a number of stirring climaxes, carried out with that logical force and sureness of aim in which Tchaikovsky was adept. There is no authentic slow Movement, or, more correctly stated, the slow Movement is shifted to the last place in the Symphony---as Finale. The second Movement has, however, the lyric tone due at this point; it is graceful, charmingly melodious song, or dance, in swaying 5/4 meter. Its complacent, happy countenance is slightly clouded with a veil of melancholy in the Trio. The third Movement represents the Scherzo, though it carries no title. It is anything but "pathetic," and it has a unique structural plan: an apparently unimportant motive, in striking rhythmic form, creeps in (in the ninth measure) quite incidentally---later turns out to be the index of the subordinate Theme---and then advances steadily into overpowering prominence; its ultimate complete supremacy is recorded in crashing blasts of the brass instruments, in a climax that is almost without parallel in legitimate symphonic literature. The design is sonatine-allegro (there is no Development). The Finale, contrary to all precedent, is a slow Movement, Adagio lamentoso, that is no doubt chiefly responsible for the designation of the Symphony as a whole. Its principal Theme is profoundly "pathetic;" but the subordinate Theme is a lyric melody (in Song-form) of rich, trustful quality, that breathes hope and solace: some music lovers may regret the return to deep sadness at the end. Cheers, ## BBC SO to present portrait of Argentine Composer Osvaldo Golijov The BBC Symphony Orchestra and Christopher Cook are presenting a portrait concert of Osvaldo Golijov which will feature four premieres of the composer's work. Golijov's music has become familiar to audiences in the US but is still relatively unknown in the UK. The concert, which will be broadcast by Radio 3 at 19.30 on 16th February, will feature Last Round (UK premiere); Tekyah (UK premiere); Ainadamar Arias and Ensembles (world premiere); Ayre (European premiere). ## Schumann Festival 2006 With Mozart celebrations bubbling up everywhere, we should pause to remember that Schumann died 150 years ago, 1856. Cheers, ### Friday, February 10, 2006 February 9, 2006 New York Times By DANIEL J. WAKIN The New York Philharmonic, not known for its quick-stepping ways, is entering the new world of digital downloading under a three-year recording deal with Deutsche Grammophon, the orchestra announced yesterday. Deutsche Grammophon, using live recordings by the orchestra, will release four concerts a year, probably through iTunes and perhaps through other Web sites, said Zarin Mehta, the orchestra's president. The first is due in about two months and will be priced at about \$8 to \$10, he said. It will consist of this weekend's program at Avery Fisher Hall, Mozart's Symphonies Nos. 39, 40 and 41, conducted by Lorin Maazel. Listeners will probably have the choice of downloading a movement, a symphony or the whole concert, Mr. Mehta said. The orchestra thus finds itself in the vanguard of purveying performances through the Internet. Few others have done so, although many are contemplating the move. Mr. Mehta also announced another recording deal, an arrangement with New World Records to release two CD's a year of new works commissioned and played by the Philharmonic in their world premieres. Those recordings, too, will be available by download, said the orchestra's spokesman, Eric Latzky. The Philharmonic, with one of the largest back catalogs of any major orchestra, has not been releasing recordings on a large scale since a series on the Teldec label in the 1990's, when Kurt Masur was the music director. In fact, few orchestras have been recording much in recent years, citing the expense under contracts with their musicians and a decline in the market. But an agreement with the Philharmonic players changed the fee structure, Mr. Mehta said, and allowed the moves. Instead of receiving flat fees and relinquishing rights, the musicians will share in any future revenues. It is by no means clear whether the deals will be profitable. The New World project is going forward only because of foundation support. As for the possibilities of making money from downloading, Mr. Mehta said: "There will be some money to be made. But in the heyday of the record industry, artists made money but orchestra institutions never made that much money. What it did was really provide income for the musicians. It made them feel worthwhile. It was a great calling card." In the rubble of the current classical recording landscape, all sorts of experiments are being tried. Opera houses are providing online streaming. The Sydney Symphony in Australia will provide 10 streamed and downloadable concerts. The London Symphony Orchestra produces its own CD's. The Philadelphia Orchestra has a three-year deal with the Ondine label, under which it will produce its own concerts and Ondine will distribute and market them. The Milwaukee Symphony this year began MSO Classics, which offers concerts for downloading on iTunes. "This is such a new world to all of us," Mr. Mehta said. "We don't know at this stage what the market is for it." In the Philharmonic's case, Deutsche Grammophon will market the recordings and pay the orchestra a percentage of revenues. Billboard magazine recently reported that the downloading of digital albums grew 94 percent in 2005, compared with a 15 percent decline in album sales. The Los Angeles Philharmonic is negotiating with Universal to make its concerts available for download. Its music director, Esa-Pekka Salonen, predicted the death of CD's in a recent interview, saying that his children did not go to stores for music but used their iPods. Mr. Mehta described the recording plans during a news conference to announce the orchestra's 2006-7 season, its 165th. Two major commissions will be played: a trombone concerto by Melinda Wagner, to be performed by the orchestra's principal trombonist, Joseph Alessi, and a piano concerto by Mr. Salonen, who will conduct. It will be his first appearance with the orchestra since his 1986 debut. Three previously announced long-term relationships will start next season, with Riccardo Muti conducting four weeks of concerts and David Robertson and Alan Gilbert two weeks each. Colin Davis will mark his 80th birthday with a Mozart program. The early-music specialists Harry Bicket and Bernard Labadie will make their first appearances with the orchestra. The Philharmonic will follow recent performances of "Candide" and "Sweeney Todd" with a semistaged performance of Stephen Sondheim's "Company." "The orchestra can swing," Mr. Mehta said. Mr. Maazel will conduct six programs of Brahms, the first time he will have done any of the symphonies since taking over the orchestra. His predecessor, Mr. Masur, did them often and well, he said. "I felt we should have a decent waiting period," he added. Next season will be Mr. Maazel's fifth as music director, with two more to go, and he implied that he would not be extending the contract. "By the end of my fifth season," he said, "I will start to gradually think how sad it will be to leave the orchestra after my seventh." Copyright 2006 The New York Times Company ## Inside the Orchestra By Philip Kennicott Washington Post Staff Writer Friday, February 3, 2006; C01 "It's not drudgery," says Dick, one of the large cast of Philadelphia Orchestra musicians identified only by first name in Daniel Anker's documentary "Music From the Inside Out." But what he really means is, it's not drudgery so long as you can still reconnect with what first made music meaningful to you. Good advice for anyone who is doing what they always wanted to do and finding it a bit routine. Anker's movie, which follows members of one of the country's greatest orchestras as it tours the world, skates around the drudgery question. We don't see lonely musicians closeted in practice rooms, and when they come together to play one of the great monuments of the repertoire -- Beethoven's "Eroica" Symphony or Brahms's First Symphony -- there's no reminder that each of them has played these same pieces perhaps hundreds of times before. Still, the musicians give enough unfiltered access to their lives to suggest the tensions and frustrations of making music as one cog in a very big, and often authoritarian, machine. For some, there is a struggle between submitting to the conductor's vision and maintaining some shred of independence or personality. There is the disappointment of those who aspired to solo careers and ended up in an orchestra. And there's a recurrent sense of loneliness and alienation that leads many musicians to take refuge in music as a bulwark against their own social isolation. The first of the film's three sections leaves one with a rather bleak view of the great core repertoire of the orchestra. Adam, a horn player, got a jazz degree. Jazz for him is "a looser way to play," in contrast to orchestral work, which, he says, is "artistically frustrating" at times. Zack finds the same release in bluegrass and fiddling. Nitzan, a trombone player, heads off to jam in a Latin music club after his regular Thursday night orchestra performance. The director's point, most likely, is the usual ideological one: Music is music is music, no matter what its style, purpose or supposed status in the world. But the darker message is that playing in an orchestra is so limiting that sane musicians need other outlets. As the film progresses, that unintended message takes on grander existential implications. Although no one can quite articulate it, being part of an orchestra puts the individual in constant contact with music so grand and utopian that it can either ennoble or wreck the soul. It demands from those who make it essentially the same bargain that the religious must make with God: You submit and serve, in return for a deeper sense of participation in the sublime. The problem is that music can't reward one in the same sense that many people believe God can. Ultimately, it is a human project, and the grandeur and sublimity it projects is simply the product of another human imagination. Submission to the divine is one thing; submission to the imagination of a deeply flawed man with a bad temper who lived two centuries ago and went by the name of Beethoven is another. The perversity of orchestral life is that it requires the yoking together of individual human beings to create music about independence, individual dignity and freedom. The most moving stories collected in this documentary hint, in one way or another, at the importance of selflessness among the players. We learn the full name of concertmaster David Kim when we see a clip of him, in 1986, competing in the prestigious Tchaikovsky Violin Competition. He took a medal and seemed to be on the verge of fulfilling his mother's ready-made dream for him before he was born: to be a concert soloist. "I got pretty close at some point," he says. But the gigs got smaller and further in between, and one day, after watching the movie "Jerry Maguire" -- about a man who reassesses his ambitions -- Kim gave up and joined an orchestra. It was, he says, a liberating but difficult epiphany. "Now I really feel like I'm the luckiest guy in the whole world," he says. The emotional challenges many of these musicians confront would make a lot more sense if the filmmaker made a better case for why the classical music written from the early years of the 18th century through the middle decades of the 20th century is, in fact, different from other music. For about 250 years, composers from Bach and Beethoven to Schoenberg constructed music with radically bigger ambitions than anything that had been made (in Western society) before them. Breaking free of preordained religious and political ideas about humanity, they offered a new sense, in sound, of what it meant to be and feel human. Their music suggested an unprecedented complexity and daring in the human project. It put the mortal individual at the center of the emotional and philosophical universe. Toiling in service to such grand visions is humbling, exhilarating and exhausting. The classical pianist who turns to jazz after a long day of playing Bach and Beethoven isn't necessarily making a case for the equivalence of these two different types of music; rather, like a guy who does theoretical physics by day and unwinds with pickup basketball in the evening, the musician takes a break, looks for other rewards (often social) and flexes different muscles. Orchestral musicians suffer the double indignity (or blessing) of living within the unreasonably grand visions of men such as Brahms and Mahler, and doing so as essentially anonymous worker bees. Their entire existence embodies a series of contradictions: vassals of utopian dreams, slaves to a fantasy of freedom, servants of an ideal of liberation. Federico Fellini probably got this basic absurdity of orchestral life best in his 1978 "Orchestra Rehearsal," in which open rebellion breaks out among the members of a tyrannized orchestra. His was a brutally comic vision of the basic contradictions of orchestral life. "Music From the Inside Out" has a softer touch, and some powerful moments, including a passage in which one of Brahms's most devastatingly beautiful melodies results from stitching together snatches of the tune from individual players. The filmmaker also got extraordinary access to the musicians, a rarity in a business perpetually hampered by paranoid public relations directors and their fatal inability to know what, in fact, is actually interesting about what orchestras do. Is it a great film? Not quite. It flits from idea to idea too promiscuously and relies too much on the visually deadening use of people talking on camera. For some incomprehensible reason, none of the music used is identified, except in the credits -- as if it doesn't really matter what we're hearing. But among the dull passages there are some moving stories, and a very loving sympathy for the people it profiles. Music From the Inside Out (97 minutes, at Landmark's E Street Cinema) is not rated but contains nothing objectionable even to the finest sensitivities. © 2006 The Washington Post Company ## Bach soothes animals at shelter An RSCPA rescue centre has installed a £2,000 sound system to play soothing classical music to stressed dogs. Staff at the kennels in West Hatch, near Taunton, Somerset, said they now hear Bach rather than barks. The animals are said to respond well to the strains of Beethoven and Mozart, but are not fans of pop or dance music. Deputy manager Anita Clarke said: "It's a very stressful environment for the dogs to be in here, so anything that can help is worth a go." 'Calming effect' The cost of the music system was met through fundraising by the Friends of West Hatch. Whale sounds and panpipes are also played and sometimes radio output so the animals get used to hearing people talking. Ms Clarke said: "Music is proven to have a calming effect on both animals and people. "It definitely works. It's quieter in the kennels now because if one dog barks when it's quiet they all start but if music's playing they don't." Story from BBC NEWS:http://news.bbc.co.uk/go/pr/fr/-/1/hi/england/somerset/4665252.stmPublished: 2006/01/31 11:06:43 GMT© BBC MMVI ## Classical website Andante shuts down The Classical Musician has just suffered another calamity. Andante.com, a web site whose stated goal was to be the leading classical music site on the internet has closed down, after it's French owners Naive told members of the site that it was no longer able to provide the resources to run the site. Andante offered digital downloads of classical music as well as a large range of news and reviews.

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# Functionals and their applications: Selected topics by Evans G.C. By Evans G.C. Best mathematics books Mathematik für Physiker 2: Basiswissen für das Grundstudium der Experimentalphysik Die für Studienanfanger geschriebene „Mathematik für Physiker'' wird in Zukunftvom Springer-Verlag betreut. Erhalten bleibt dabei die Verbindung einesakademischen Lehrbuches mit einer detaillierten Studienunterstützung. DieseKombination hat bereits vielen Studienanfangern geholfen, sich die Inhalte desLehrbuches selbständig zu erarbeiten. Additional info for Functionals and their applications: Selected topics including integral equations Sample text 36) It follows from simple computations that A0r r A0 + 2Aϕr r A0 = r B0r r B0 + 2Bϕr r B0 = 0. 37) r Let iλ be the integral constant, we have A0r + iλA0 = −2qϕr , B0r − iλB0 = 2Bϕr . 38) Define square characteristic functions as follows: A0 = iΨ21 , B0 = iΨ22 , ϕr = −iΨ1 Ψ2 . 40) Landau–Lifshitz Equations 50 where V1 = −iλr/2 q . 44) and the compatible condition is U1t − V1r + [U1 , V1 ] = 0. 34): λt = 2λ2 . 45) Introduce normal change: ˆ = g −1 Ψ, Ψ g(r, t) ∈ GL(2, C). 42) to give new eigenvalue equation ˆ r = Uˆr Ψ, ˆ Ψ where ˆ t = Vˆ1 Ψ, ˆ Ψ Uˆ1 = g −1 U1 g − g −1 gr , Vˆ1 = g −1 V1 g − g −1 gt , gr = U1 (λ = 0)g, gt = V1 (λ = 0)g. 79) for a uniaxial crystal. 38) n2j cos2 θk − µ(1 − n2j sin2 θk ) ρj = . 40) We note that and consequently (1) b1 (1) b2 (2) =− b2 (2) b1 = iρ1 . 36) that (j) h1 (j) h2 (j) = iρj , h3 (j) h2 = µ sin θk + (µ − 1) sin θk cos θk ) , µ sin2 θk + cos2 θk where as before the subscript j represents waves with refractive index nj . 37) for the refractive indices and find the values of ω for which the wave vector is zero. 42) it follows that k will be zero together with ω, and when ω k1 = ω µ(0) c , k2 = ω µ(0) c gM0 , 1 cos2 θk + µ(0) sin2 θk . J(x, t) = k τ = 16 4 2 And, we also have √ √ 3x 3x −1/2 tan h (λt + δ) (λt + δ)−1/2 4 4 √ √ 3x 3x (λt + δ)−1/2 − cos (λt + δ)−1/2 4 4 √ √ 3x 3x −1/2 y S = − sech tan h (λt + δ) (λt + δ)−1/2  4 4    √ √     3x 3x  −1/2  − sin cos (λt + δ) (λt + δ)−1/2    4 4    √    3x   2 z  (λt + δ)−1/2 . 25) Inhomogeneous Heisenberg Chain Inhomogeneous Ferromagnetic Equations Consider the nonhomogeneous ferromagnetic chain equation St (x, t) = f (x)S × Sxx + fx (x)(S × Sx ). 1) Let e1 (x, t), e2 (x, t), e3 (x, t) be the tangential vector, normal vector and co-normal vector of a moving space curve and form a natural coordinate system.

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Partner with ConvertIt.com New Online Book! Handbook of Mathematical Functions (AMS55) Conversion & Calculation Home >> Measurement Conversion Measurement Converter Convert From: (required) Click here to Convert To: (optional) Examples: 5 kilometers, 12 feet/sec^2, 1/5 gallon, 9.5 Joules, or 0 dF. Help, Frequently Asked Questions, Use Currencies in Conversions, Measurements & Currencies Recognized Examples: miles, meters/s^2, liters, kilowatt*hours, or dC. Conversion Result: ```typography pica = 4.23333333333333E-03 length (length) ``` Related Measurements: Try converting from "pica" to arpentcan, bolt (of cloth), bottom measure, chain (surveyors chain), ell, en (typography en), engineers chain, foot, football field, French, furlong (surveyors furlong), Greek cubit, ken (Japanese ken), line, m (meter), palm, parasang, ri (Japanese ri), soccer field, sun (Japanese sun), or any combination of units which equate to "length" and represent depth, fl head, height, length, wavelength, or width. Sample Conversions: pica = 42,333,333.33 angstrom, .00595238 archin (Russian archin), .00925926 Biblical cubit, .00011574 bolt (of cloth), .2283105 digitus (Roman digitus), 1.10E-11 earth to moon (mean distance earth to moon), .00013889 engineers chain, .00231481 fathom, .19047619 finger, .01388889 foot, 12.7 French, .00228686 Greek fathom, .05488474 Greek palm, 8.77E-07 league, 2 line, .00015432 naval shot, .00000108 ri (Japanese ri), .00000286 Roman mile, .00069444 rope, .00002287 stadia (Greek stadia). Feedback, suggestions, or additional measurement definitions? Please read our Help Page and FAQ Page then post a message or send e-mail. Thanks!

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## Mathematics Faculty Articles Article 1-1-1995 #### Publication Title SIAM Journal on Matrix Analysis and Applications 0895-4798 16 4 1173 1183 #### Abstract Let Aand Bbe $n \times n$ positive semidefinite Hermitian matrices, let $\alpha$ and $\beta$ be real numbers, let $\circ$ denote the Hadamard product of matrices, and let $A_k$ denote any $k \times k$ principal submatrix of A. The following trace and eigenvalue inequalities are shown: $\operatorname{tr}(A \circ B)^\alpha \leq \operatorname{tr}(A^\alpha \circ B^\alpha ),\quad\alpha \leq 0\,{\text{ or }}\,\alpha \geq 1,$$\operatorname{tr}(A \circ B)^\alpha \geq \operatorname{tr}(A^\alpha \circ B^\alpha ),\quad 0 \leq \alpha \leq 1,$$\lambda^{1/ \alpha } (A^\alpha \circ B^\alpha ) \leq \lambda ^{1/\beta } (A^\beta \circ B^\beta ),\quad\alpha \leq \beta ,\alpha \beta \ne 0,$$\lambda ^{1/\alpha } [(A^\alpha )_k ] \leq \lambda ^{1/\beta } [(A^\beta )_k ],\quad\alpha \leq \beta ,\alpha \beta \ne 0.$The equalities corresponding to the inequalities above and the known inequalities $\operatorname{tr}(AB)^\alpha \leq \operatorname{tr}(A^\alpha B^\alpha ),\quad | \alpha | \geq 1,$ and $\operatorname{tr}(AB)^\alpha \geq \operatorname{tr}(A^\alpha B^\alpha ),\quad | \alpha | \leq 1$ are thoroughly discussed. Some applications are given. #### DOI 10.1137/S0895479893253616 COinS

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# Maths  K-1 + & - 30 plus Name: __________________ 15 + 5 = _____ 16 - 4 = _____ 12 - 9 = _____ 16 + 13 = _____ 16 + 4 = _____ 12 - 11 = _____ 23 - 13 = _____ 22 + 14 = _____ 30 + 4 = _____ 36 - 12 = _____ 29 - 12 = _____ 27 + 16 = _____ -------------------------------------------- back---------------------------------------------

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Application # The Main Principle of Satellite Navigation Satellite navigation is divided into systems such as angle measurement, time ranging, Doppler velocity measurement and combination method according to the geometric positioning principle of measurement navigation parameters. The angle measurement method and combination method have no practical application due to low precision. 1 Doppler speed positioning: “Mid Meridian” satellite navigation system adopts this method. The user positioning device measures the Doppler shift curve based on the Doppler shift between the frequency of the signal received from the navigation satellite and the frequency of the signal transmitted on the satellite, and the position of the user can be calculated from the curve and the satellite orbit parameter. 2 time ranging navigation positioning: “Navigation Star” global positioning system uses this system. The user receiving device accurately measures the propagation time of the signals sent by the four satellites in the system that are not in the same plane (to ensure the unique result, the four satellites cannot be in the same plane), and then complete a set of mathematical operations including four equations. The three-dimensional coordinates of the user’s position and the error between the user’s clock and the system time can be calculated. The difference between the geographic location coordinates measured by the navigation satellite and its true geographical location coordinates is called the positioning error. It is the most important performance indicator of the satellite navigation system. The positioning accuracy is mainly determined by the accuracy of the orbit prediction, the measurement accuracy of the navigation parameters, the geometric amplification factor and the measurement accuracy of the user dynamic characteristics. The accuracy of orbit prediction is mainly affected by the gravitational field model of the Earth and other orbital perturbations. The accuracy of navigation parameters is mainly affected by satellite and user equipment performance, signal error factors such as ionosphere, tropospheric refraction and multipath. Its geometric amplification factor is determined by The geometric relationship between the satellite and the user’s position during the positioning is graphically determined; the user’s dynamic characteristic measurement accuracy refers to the accuracy of the heading, speed and antenna height measurement of the user during positioning. Menu

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UK USIndia Every Question Helps You Learn TA stands for Territorial Army. # Letter Connections 3 Letter connections involve being able to count backwards, so get your Maths hat on and give these a go! In these 11-plus verbal reasoning quizzes you will be given three pairs of letters. You have to find the relationship between the first two pairs to work out the fourth pair. The first letters of both pairs are related, and the second letters of both pairs are related. No other relationship will be in the question. The alphabet has been around for a very long time, and the Greeks were the first people to use an alphabet. Ours is based on theirs, where the first letter was Alpha, and the last was Omega. Today these words mean the beginning and the end. Get your thinking cap on and give this quiz your best shot. Make sure you get all answers correct before moving on to our final quiz in the series. Example: The alphabet is given below to help you. Find the pair of letters that will complete the sentence in the most sensible way. When you have found the most appropriate pair of letters, choose the correct answer from the four choices available. A B C D E F G H I J K L M N O P Q R S T U V W X Y Z BC is to DE as GH is to ? To get from B to D we moved forward 2 letters, and to get from C to E we also moved forward 2 letters. Only IJ works. 1. The alphabet is given below to help you. Find the pair of letters that will complete the sentence in the most sensible way. When you have found the most appropriate pair of letters, choose the correct answer from the four choices available. A B C D E F G H I J K L M N O P Q R S T U V W X Y Z KO is to UF as CR is to ? UI MI KI II To get from K to U we moved forward 10 letters, and to get from O to F we moved backwards 9 letters. Only MI works. 'KO' was one of the original letters in the question. Do you know what sport uses KO as an abbreviation, and what it means? Read below to find out 2. The alphabet is given below to help you. Find the pair of letters that will complete the sentence in the most sensible way. When you have found the most appropriate pair of letters, choose the correct answer from the four choices available. A B C D E F G H I J K L M N O P Q R S T U V W X Y Z HP is to AQ as SJ is to ? JS KL LI LK To get from H to A we moved backwards 7 letters, and to get from P to Q we moved forward 1 letter. Only LK works 3. The alphabet is given below to help you. Find the pair of letters that will complete the sentence in the most sensible way. When you have found the most appropriate pair of letters, choose the correct answer from the four choices available. A B C D E F G H I J K L M N O P Q R S T U V W X Y Z ET is to VG as BV is to ? SI IS SJ SK To get from E to V we moved forward 17 letters, and to get from T to G we moved backwards 13 letters. Only SI works. The puzzle in question 1? The sport that uses 'KO' as an abbreviation is boxing, and it means 'Knock Out' 4. The alphabet is given below to help you. Find the pair of letters that will complete the sentence in the most sensible way. When you have found the most appropriate pair of letters, choose the correct answer from the four choices available. A B C D E F G H I J K L M N O P Q R S T U V W X Y Z HU is to FD as RX is to ? PP PG PL GP To get from H to F we moved backwards 2 letters, and to get from U to D we moved backwards 17 letters. Only PG works. 17 is a very interesting number, being a prime number and the smallest number that can be written in French as a compound word (dix-sept). It is also the number of syllables in a haiku, which is a short poem from Japan which has only three lines. You will encounter haiku in Secondary School, if you haven't already 5. The alphabet is given below to help you. Find the pair of letters that will complete the sentence in the most sensible way. When you have found the most appropriate pair of letters, choose the correct answer from the four choices available. A B C D E F G H I J K L M N O P Q R S T U V W X Y Z DK is to TA as FS is to ? UK UI VI VJ To get from D to T we moved forward 16 letters, and to get from K to A we moved backwards 10 letters. Only VI works 6. The alphabet is given below to help you. Find the pair of letters that will complete the sentence in the most sensible way. When you have found the most appropriate pair of letters, choose the correct answer from the four choices available. A B C D E F G H I J K L M N O P Q R S T U V W X Y Z GO is to BP as QG is to ? GI MH LI LH To get from G to B we moved backwards 5 letters, and to get from O to P we moved forward 1 letter. Only LH works. One of the possible answers was GB. Can you think of things that GB is short for? Read below for the answer 7. The alphabet is given below to help you. Find the pair of letters that will complete the sentence in the most sensible way. When you have found the most appropriate pair of letters, choose the correct answer from the four choices available. A B C D E F G H I J K L M N O P Q R S T U V W X Y Z BJ is to PQ as LS is to ? ZX ZZ XZ XY To get from B to P we moved forward 14 letters, and to get from J to Q we moved forward 7 letters. Only ZZ works 8. The alphabet is given below to help you. Find the pair of letters that will complete the sentence in the most sensible way. When you have found the most appropriate pair of letters, choose the correct answer from the four choices available. A B C D E F G H I J K L M N O P Q R S T U V W X Y Z SW is to BM as YP is to ? HF HG FG HI To get from S to B we moved backwards 17 letters, and to get from W to M we moved backwards 10 letters. Only HF works. The puzzle in question 6? GB stands for Great Britain, and also for Girls' Brigade, an organisation set up in Ireland in 1893 and in July 1965 merged with The Girls’ Guildry (founded in Scotland in 1900) and The Girls’ Life Brigade (founded in England in 1902) to form The Girls’ Brigade 9. The alphabet is given below to help you. Find the pair of letters that will complete the sentence in the most sensible way. When you have found the most appropriate pair of letters, choose the correct answer from the four choices available. A B C D E F G H I J K L M N O P Q R S T U V W X Y Z KP is to SH as QN is to ? FY YG YF EF To get from K to S we moved forward 8 letters, and to get from P to H we moved backwards 8 letters. Only YF works 10. The alphabet is given below to help you. Find the pair of letters that will complete the sentence in the most sensible way. When you have found the most appropriate pair of letters, choose the correct answer from the four choices available. A B C D E F G H I J K L M N O P Q R S T U V W X Y Z BM is to OG as FV is to ? SS SP ST PR To get from B to O we moved forward 13 letters, and to get from M to G we moved backwards 6 letters. Only SP works. Well done! You have completed the third of our four Letter Connections quizzes, which means you have only one more to do to become an expert. You will be seeing the alphabet in your sleep after the last one! But, think of the practice you are getting for your 11+ Author:  Stephen O'Hara

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Informatique / R Do you still have time to sleep ? June 11, 2012 | Last week, @3wen (Ewen) helped me to write nice R functions to extract tweets in R and build datasets containing a lot of information. I've tried a couple of time on my own. Once on tweet contents, but it was not convincing and once on the activit... [Read more...] French dataset: population and GPS coordinates May 24, 2012 | A short post today based on recent work by @3wen (Ewen Galic, graduate Student in Rennes, spending a year in Montreal). Since we were working on a detailed French dataset (per commune), we needed a dataset containing a list all communes, with popu... [Read more...] Maps with R, and polygon boundaries December 21, 2011 | With R, it is extremely easy to draw maps. Let us start with something simple, like French regions. Baptiste mentioned on his blog that shapefiles can be downloaded from http://ign.fr/ website. Hence, if you extract the zip file, it is possible to ... [Read more...] Playing with robots May 3, 2011 | My son would be extremely proud if I tell him I can spend hours building robots. Well, my robots are not as fancy as Dr Tenma's, but they usually do what I ask them to do. For instance, it is extremely simple to build a robot with R, to extract ... [Read more...] Maps with R, part… n+1 January 11, 2011 | Following the idea posted on James Cheshire's blog (here), I have tried to play a little bit with R and Google. And it works ! Consider for instance life expectancy at birth (that can be found - and downloaded - here). Using the following code, it ... Generating a quasi Poisson distribution, version 2 November 10, 2010 | Here and there, I mentioned two codes to generated quasiPoisson random variables. And in both of them, the negative binomial approximation seems to be wrong. Recall that the negative binomial distribution is where and in R, a negative binomial di... [Read more...] Pretty R code in the blog November 5, 2010 | David Smith (alias @revodavid, see also on the Revolutions blog, here) pointed out that my R code was not easy to read (not only due to my computing skills, but mainly because of the typography I use). He suggested that I use the Pretty R tool (her... [Read more...]

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Cody # Problem 290. Make one big string out of two smaller strings Solution 695247 Submitted on 2 Jul 2015 by Lim This solution is locked. To view this solution, you need to provide a solution of the same size or smaller. ### Test Suite Test Status Code Input and Output 1   Pass %% x = 'a'; y = 'b'; y_correct = 'ab'; assert(isequal(your_fcn_name(x, y),y_correct)) ans = ab 2   Pass %% x = 'a'; y = 'a'; y_correct = 'ab'; assert(~isequal(your_fcn_name(x, y),y_correct)) ans = aa

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# Inequalities: Body Mass Index and Compound Inequality Topics: Body mass index, Mass, Body shape Pages: 3 (778 words) Published: April 13, 2013 Inequalities Deborah White Ashford University MAT221: Introduction to Algebra (AFN1312A) Instructor:  Tracy Abram April 1, 2013 On page 151 of Elementary and Intermediate Algebra, the Body Mass Index (BMI) is given as: BMI= 703W/H2 W = one’s weight in pounds H = one’s height in inches. By calculating four intervals based on your height can be possible by using the Body Mass Index formula. However, in this situation I am going to use inequalities to calculate Body Mass Index(BMI) which is meant to use my height to calculate if I’m overweight , having a longer life span than average, or to calculate if I’m obese. In the real world it is significant to have knowledge about being overweight because this could come into the use of attention of medical assistance. By using inequalities and solving them could serve a far more severe importance than just a mathematical problem. The first interval for this problem is the solvation for a longer life span than average. 17< BMI <22The compound inequality. 17< 703W/H2 <22Use the BMI formula in replace of the original compound inequality so we now have an equivalent inequality. 17< 703W/62.002 <22 I replaced H2 for my height in inches. 17< 703W/3844 <22Then, I multiplied the three numbers by the denominator to rid the exponent that was on the bottom associated with my height. 17(3844)< 703W(3844)/3844 < 22(3844) In the fraction bar, the cancelling is made. 65348< 703W< 84568 The multiplications were carried out when I multiplied all of the numbers by 32844. 65348/703 < 703W/703 < 84568/703 I divide all three of the fractions by 703 to get W by itself. 93< W< 120.3 People who have the height of 62 inches will have a longer life span between the weight of 93 and 120.3 pounds. For my second interval, there are two ways of solving it. Without solving for W at the end, I’m going to separate W by itself before I go about solving it. 23<...

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My Math Forum Arithmetic Progression and Geometric Progression Algebra Pre-Algebra and Basic Algebra Math Forum May 1st, 2014, 12:03 AM #1 Senior Member   Joined: Sep 2013 From: Earth Posts: 827 Thanks: 36 Arithmetic Progression and Geometric Progression How to proof those formula in these two progressions? May 1st, 2014, 03:40 AM #2 Senior Member     Joined: Apr 2014 From: Greater London, England, UK Posts: 320 Thanks: 155 Math Focus: Abstract algebra (1) Arithmetic progression with first term $a$ and common difference $d$. The $n$th term is $T_n=a+(n-1)d$. Thus $$\sum_{k=1}^n\,T_k$$ $\displaystyle =\ \sum_{k=1}^n\,[a+(k-1)d]$ $\displaystyle =\ \sum_{k=1}^n\,a \, + \, d\sum_{k=1}^n\,(k-1)$ $\displaystyle =\ na+d\frac{(n-1)n}2$ $\displaystyle =\ \frac n2\left[2a+(n-1)d\right]$ (2) Geometric progression with first term $a$ and common difference $r$. Case 1: $r=1$ In this case the progression is a constant sequence consisting of $a$ in every term so the sum to $n$th term is $na$. Case 2: $r\ne1$ The $n$th term is $T_n=ar^{n-1}$. Thus $(r-1)T_n=a(r^n-r^{n-1})$ and $$\sum_{k=1}^n\,(r-1)T_k$$ $\displaystyle =\ a\sum_{k=1}^n\,(r^k-r^{k-1})$ $\displaystyle =\ a(r^n-r^0)$ by the method of telescoping $\displaystyle =\ a(r^n-1)$ $\displaystyle \therefore\ \sum_{k=1}^n\,T_k\ =\ \frac{a(r^n-1)}{r-1}$ Thread Tools Display Modes Linear Mode Similar Threads Thread Thread Starter Forum Replies Last Post jiasyuen Algebra 5 April 23rd, 2014 12:42 PM rnck Real Analysis 3 November 18th, 2013 08:19 PM jareck Algebra 3 July 6th, 2012 06:38 AM Algebra 2 April 5th, 2012 09:46 PM Francis410 Algebra 1 March 22nd, 2011 07:02 AM Contact - Home - Forums - Cryptocurrency Forum - Top

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# GATE | GATE IT 2006 | Question 64 Suppose that it takes 1 unit of time to transmit a packet (of fixed size) on a communication link. The link layer uses a window flow control protocol with a window size of N packets. Each packet causes an ack or a nak to be generated by the receiver, and ack/nak transmission times are negligible. Further, the round trip time on the link is equal to N units. Consider time i > N. If only acks have been received till time i(no naks), then the goodput evaluated at the transmitter at time i(in packets per unit time) is (A) 1 – N/i (B) i/(N + i) (C) 1 (D) 1 – e(i/N) Explanation: successfully delivered packets = (i-N) {transmission time of a packet =1 unit, so in i time i packets can be transmitted. And RTT = N, so only N packets are ACKed} So, for time i, i-N packets are transmitted Goodput = Successfully delivered data/ Time = (i-N)/i = 1- N/i Quiz of this Question Please comment below if you find anything wrong in the above post My Personal Notes arrow_drop_up Article Tags : Be the First to upvote. Please write to us at contribute@geeksforgeeks.org to report any issue with the above content.

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## Eggbot eggs 2015 : genetic algorithm This year’s addition to my eggbot programs is a genetic algorithm that evolves complex sine waves. Each of the eggs in the photo above was printed from the same program with waves evolved from random seeds. ## The individual designs Each design is a sine wave with eight different parameters: 1. Amplitude 2. Length 3. The number of waves to be strung together 4. Amplitude of the first modulation applied to the amplitude 5. Length of the first modulation applied to the amplitude 6. Amplitude of the second modulation applied to the amplitude 7. Length of the second modulation  applied to the amplitude 8. The modulations to be used (either 1 or both 1 & 2) The video above shows how the 8 parameters modulate the wave and how patterns build up over time. ## How the genetic algorithm works Each time the program is run, an initial population is created with 50 individual designs — each with random values assigned to the eight parameters. You then rate each individual design before evolving the next generation. The algorithm chooses individuals to carry on to the next generations (highly rated designs are more likely to be carried forward, but low rated designs may still be used). Designs that are carried forward are likely to be bred with other designs chosen for the next generation. Breeding involves picking a random integer N between 1 and 8 and taking the first N parameters of one individual and swapping them with the first N parameters of the other. This cross-over of the parameters creates new variations of the designs with qualities of both individuals (the parents). There is also a slim chance that one or more of the child’s parameters will change (mutate) between generations. The evolution process makes it relatively easy to search through a very wide range of possible combinations of parameter values by simply choosing designs with aspects that you like and seeing what different combinations of these qualities look like. I found that populations of 50 individuals are broad enough to get very interesting results in fewer than 10 generations while not having to rate too many design with each evolution. ## The output Below is a collection of 10 different designs generated in the same session. Each column in the image above shows the lineage of the design in the top row. This top row is the 5th generation. The next row down is the highest rated parent from the 4th generation. Coincidentally, neither of these designs were changed between the 3rd and 4th generation. ## The code The program is written in processing and the source is available on github. The algorithm is not limited to sine waves. To implement your own design, modify the Indivdual.pde file with any number of parameters. All my parameters are floats between 0 and 1, but this is not a requirement so long as you adjust your this class’ mutate function to fit your variable types. The other classes in the repository set up the UI and manage the evolution or individuals over multiple generations. You may choose to manipulate the following three variables in GA_eggbot.pde to work with different population sizes and different probabilities for crossovers and mutations. If you do make a design of your own, let me know in the comments below. ## Eggs 2014 Sine waves were a popular choice for this year’s eggs. And the Minecraft pigs were in demand as always. All the eggs pictures except the pigs were plotted directly from Processing, the pigs were drawn using Inkscape. I’ll post the files to Github within  a couple weeks. update: code and svg files are now available on Github.

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× Get Full Access to Math - Textbook Survival Guide Get Full Access to Math - Textbook Survival Guide × # New answer: Solve each equation by factoring ISBN: 9780078778568 361 ## Solution for problem 80 Chapter 8.1 California Algebra 2: Concepts, Skills, and Problem Solving | 1st Edition • Textbook Solutions • 2901 Step-by-step solutions solved by professors and subject experts • Get 24/7 help from StudySoup virtual teaching assistants California Algebra 2: Concepts, Skills, and Problem Solving | 1st Edition 4 5 1 270 Reviews 13 3 Problem 80 Solve each equation by factoring. Step-by-Step Solution: Step 1 of 3 ttl ')) lq,4T ) i :15r,^dn' V/u/re ) , OuerureU -) H/ !rl,,ur,'J*"h^"t -,J ..1 1. De.,&- b,Ai tb :1"1, *,J sL,k U- ) uf : Llo nt l1u / fl ) '2 N'tccrtpr-t... Step 2 of 3 Step 3 of 3 #### Related chapters Unlock Textbook Solution Enter your email below to unlock your verified solution to: New answer: Solve each equation by factoring ×

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