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https://pure.pucv.cl/es/publications/prospective-mathematics-teachers-learning-complex-numbers-using-t | math | In this paper we studied the personal mathematical work of 14 students in initial teacher training, in their first year of studies at a public university in Chile, based on two tasks on complex numbers. These tasks were set in a Computer Aided Assessment System (CAA) based on Moodle and Wiris and it was proposed to solve them using different Computer Algebra Systems (CAS), such as GeoGebra, Symbolab, Photomath and Wolfram Alpha among others. Difficulties and potentialities were observed in the mathematical work of the students. In the difficulties, it was observed that the students had problems interpreting the information from the CAS and the CAA feedback because their previous mathematical knowledge was not solid enough to do so. In the potentialities, it was observed that different characteristics of the task, together with the articulation of two or more artifacts allowed students to give meaning to the mathematical objects involved.
|International Journal of Mathematical Education in Science and Technology
|Aceptada/en prensa - 2022 | s3://commoncrawl/crawl-data/CC-MAIN-2024-10/segments/1707947476397.24/warc/CC-MAIN-20240303174631-20240303204631-00747.warc.gz | CC-MAIN-2024-10 | 1,053 | 3 |
http://www.angelfire.com/geek/alphabeta/zero_gravity.htm | math | Weightlessness is the experience (by people and objects) during free-fall, of
having no apparent weight. Although the term 'zero gravity' is often used as a
synonym, weightlessness in orbit is not the result of gravity itself being
eliminated or even reduced significantly (in fact, the acceleration due to
gravity at an altitude of 100 km is only 3% less than at the earth's surface — a
person at rest at that altitude would accelerate to earth at a familiar rate).
Weightlessness (roughly speaking) occurs when a body (e.g. a person) is: falling
freely; in orbit; in outer space (far from a planet, star, or other massive
body); in an airplane following a particular parabolic flight path (e.g. the
"Vomit Comet"); or one of several other (even more unusual) frames of reference.
More generally, weightlessness occurs when a person (or object) is subject (at most) to the single force of gravity (or is not acted upon by any accelerating force), vs. the far more typical (in human experience) cases in which an equal/opposite force is acting — such as:
1. standing on the ground, sitting in a chair on the ground, etc. (gravity is countered by the reaction force of the ground);
2. flying in a plane (gravity is countered by the lift the wings provide)
3. atmospheric reentry, use of a parachute: atmospheric drag decelerates the vehicle;
4. during an orbital maneuver in a spacecraft, or during the launch phase: the rocket provides thrust.
(The principal difference is that gravity acts directly on a person and/or other bodies, just like on the vehicle's mass — whereas forces like atmospheric drag and thrust act only on the vehicle body itself (and thus only secondarily, through the vehicle, on the person). In the first case the person and the vehicle floor are not 'pushed' towards one another; in the other cases, the force is transmitted through the vehicle's structure to the person and/or contents.)
What humans perceive as "weight" is not actually the force of gravity pulling us towards the ground (actually, towards the center of the Earth — although this is the technical definition of "weight"). What we feel as "weight", is actually the normal reaction force of the ground (or whatever surface we are supported by) "pushing" upwards against us to counteract gravity's downward pull — that is: the "apparent weight". (In the remainder of this article, the term 'weight', without 'apparent', is used in this sense.) While this is not always intuitive, imagine the floor dropping out from under you: without it, you'd be falling — and experiencing weightlessness. It's the floor (or ground — whatever), supporting you against gravity's pull — and which keeps you from falling to the center of the Earth — that creates the sensation of "weight".
example: a wood block in a container in free-fall "experiences" weightlessness.
This is because there is no force from the container's bottom on the block,
against the pull of gravity, as both the container and the block are being
pulled down with the same acceleration. When the container is at rest on the
ground, however, the force of gravity pulling downwards on the block is exactly
matched (in the opposite direction, and by the same amount) by the support of
the bottom of the container.
Because the block is a solid, each horizontal cross section of the block experiences not only the force due to gravity on it, but also the weight of whatever portion of the block is above it. (In the case of an object, or portion thereof, which is not supported from below, but suspended from above, a 'negative pressure', or tension gradient exists. It occurs because each cross section of a hanging object, a rope for instance, must support the weight of every piece below it.) Part of feeling "weight", then, is actually experiencing such a pressure/tension gradient within one's own body parts (e.g.: while standing on one foot, the foot on the ground would feel the pressure of the entire body's weight, whereas the other leg and both arms would feel/be subjected to the tension gradients of their own weight being pulled down against their sockets).
In free-fall, a person or object experiences no measurable (or apparent) weight because all parts of the object are accelerating uniformly (any variations in acceleration due to tidal forces being imperceptible)..
Ours sponsors are Cruise and Stay, Cruise and Stay, | s3://commoncrawl/crawl-data/CC-MAIN-2017-17/segments/1492917123318.85/warc/CC-MAIN-20170423031203-00414-ip-10-145-167-34.ec2.internal.warc.gz | CC-MAIN-2017-17 | 4,396 | 27 |
https://mcq.jobsandhan.com/who-invented-dynamite/ | math | Who invented Dynamite? December 16, 2019 by mcq A) Graham Bell B) Nikola Tesla C) Alfred Nobel D) Louis Pateur View AnswerOption – C. More QuestionsIn the following question, various terms of an alphanumerical series are given with one or more terms missing as shown by (?). Choose the missing terms out of the given alternatives. P3C, R5F, T8I, V12L, ?The average age of 80 boys in a class is 15. The average age of group of 15 boys in the class is 16 and the average of another 25 boys in the class is 14. What is the average age of the remaining boys in the class ?Can character data be stored in computer memory?Which one of the following rivers has a cuspate delta?Which politician in British India had opposed to a Pakistan that would mean “Muslim Raj here and Hindu Raj elsewhere”?Where is the headquaters of world health organisationThe Sunga ruler Bhaga erected a monolithic ‘Garuda’ atPlant cell walls consist mainly ofThe reflex angle between the hands of a clock at 11:35 is ?The cost price of a college bag is 240% more than the profit obtained on it selling at Rs. 1540. What is the cost price of that college bag? | s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764494936.89/warc/CC-MAIN-20230127033656-20230127063656-00106.warc.gz | CC-MAIN-2023-06 | 1,138 | 1 |
https://informationtransfereconomics.blogspot.com/2013/12/plucking-rgdp-growth.html | math | I mentioned in this post that I had hypothesized earlier that the RGDP growth was operating like a bound; I decided to re-do some of the graphs from the second link as well as this link using a "plucking" framework. So first is the the implementation -- instead of showing S(y) as a path (where y is the time variable) through NGDP-MB space fit to a line, I instead fit to a linear bound. The result is below (the bound S is shown as a line tangent to the black empirical path):
The expected RGDP along S(y) is shown in black on this graph (the empirical RGDP is shown in green and the model calculation along the path is shown in blue):
Already you can see some hint of an upper bound (the recessions all appear to be sharp downward falls with overcompensating rises afterwards). We'll take out the trend and look at the deviations from it to make this a little clearer (the recessions are shown in red):
If we excise the recessions, it becomes even clearer (and the distribution looks more like random fluctuations around a mean):
Here is the original distribution of fluctuations (black line) and with the recessions excised (purple):
The distribution becomes noticeably more symmetric without the recessions (with a mean just below the trend, lending support to the plucking model). It is still not a normal distribution as it is much narrower than would be expected; it is not as narrow as e.g. a Cauchy distribution.
We can also look at deviations from inflation in this plucking framework:
Inflation it seems deviates systematically in both directions, in particular being unexpectedly low during the 1960s and rising during the oil shocks of the 1970s. The deviation from the expected inflation accounts for most of the deviation from NGDP growth:
In the posts linked above, I pointed to the lack of inflation in the 1960s being a mystery (which shows up as lower NGDP growth than expected). The plucking model translated into an ideal information transfer bound (IS ≤ ID, with IS being the information received by the supply and ID being the information transmitted by the demand) could give a potential explanation. The US economy increased information transfer efficiency from IS ~ say 10% of ID to IS ~ say 50% of ID in the immediate post-war period (the numbers 10% and 50% are for concreteness; I don't know what the exact values are or even if they can be determined). While this didn't affect real growth very strongly if at all, it manifested as low inflation (and hence low NGDP growth). After about 1980 we reached the bound given by S(y). (Per the fit above, is the fit a bound at IS = ID? or is it just IS ~ ID? Again, I can't answer that.) From that point on we had the "Great Moderation" where inflation and NGDP followed the expected path given by the bound S(y) until the "Great Recession", a major fall in information transfer efficiency.
One final note is that all the graphs here are only slight changes from the graphs in the posts linked above. | s3://commoncrawl/crawl-data/CC-MAIN-2023-40/segments/1695233511053.67/warc/CC-MAIN-20231003024646-20231003054646-00114.warc.gz | CC-MAIN-2023-40 | 2,976 | 10 |
https://senseis.xmp.net/?SLDiagramsWithDrago | math | SL Diagrams with Drago
SL enables to include diagrams with simple text conventions presented in any Edit page and fully described in HowDiagramsWork. To make the creation of diagrams even easier, Drago features a dialog to export what you see in the goban, or part of the goban, into a diagram formatted with SL conventions.
The Export position... dialog enables to:
- select a rectangular zone on the goban
- define dimensions
- choose a graphic or text format
- set some options
- and export the content of the rectangle in the goban to the clipboard or a file with the selected format.
Take a look at the preview: http://www.geocities.com/wwwdrago/Images/ExportPosPreview.jpg (page is gone)
- WMF, GIF, PNG, BMP, JPEG, ASCII for rec.games.go and Sensei'Library
Done through the File>Export position... menu.
Drag the cursor from one corner to the opposite corner of the rectangular zone on the goban. The selected area is displayed as a thumbnail in the dialog.
Select the ASCII format and push the "+" button to open the format option box to set the ASCII mode on SL. To get the diagram, press the "Clipboard" button and copy the content of clipboard in your SL page.
The example of HowDiagramsWork page
If you see and select the following position in Drago:
After copying in clipboard, you will get the following text diagram:
$$ $$ . . . . . . . . . $$ . 0 . . . . . a . $$ 1 2 . X . O . b . $$ . . . . . . . c . $$ . C . B . W . . . $$ . . . . . . . x . $$ . S . # . @ . y . $$ . . . . . . . z .
...giving the next figure:
You should get in SL the content of Drago thumbnail with some limitations:
- SL admits only the following marks: letter a-z, circle and square.
- SL displays only move numbers from 1 to 10.
Herman Hiddema: The latest version of SL supports larger numbers (up to 99).
SL enables to create diagrams with moves numbered from 1 to 10. To export SL diagrams with numbered moves using Drago, the rule is simple: "what you see is what you get". More clearly, if you see a stone numbered between 1 and 10 on Drago goban, you will get the number in the SL diagram. Keep in mind they are a lot of possibilities to see a number on a stone with Drago:
- To see all move numbers, set the "Show last move" option to "All" in the Options>Moves dialog.
- If you use the "As books" option, you can insert figure (FG property) and move renumbering (MN property) with the Edit>Insert>Others dialog.
- If you use the "As board" option, you can use only the MoveNumber property.
- You can put a string label on a stone. If the label is a number between 1 and 10, it will be seen in the SL diagram.
- At last, the "Number" markup enables to input directly on a stone a label equal to the stone number.
As a validation test for the export to SL function, here are the diagrams generated with Drago from the first section of unkx80 tutorial. Could be completed with the comments... (hello unkx80!)
- Unlucky: SL doesn't handle TRiangle property. I replaced them with CiRcles.
- Could be fine to insert as title the content of NodeName property.
How to deal with coordinates?
You can cause a diagram to show coordinate markers by putting "c" after the dollar signs on the first line: "$$c". The "c" must follow the color indicator ("B" or "W"), if present: "$$Bc".
This is missing in the current version and will be fixed in the next one (3.00, should come soon now). | s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882571909.51/warc/CC-MAIN-20220813051311-20220813081311-00264.warc.gz | CC-MAIN-2022-33 | 3,372 | 34 |
http://instruktsiya.info/business/engineering-mathematics-formula-pdf-16756.php | math | ENGINEERING MATHEMATICS FORMULA PDF
document issued by the Department of Engineering, but obviously reflects the particular Speigel, M.R., Mathematical Handbook of Formulas and Tables. math to math for advanced undergraduates in engineering, economics, physical sciences, and mathematics. The ebook contains hundreds of formulas, tables. Third edition as the Newnes Engineering Mathematics Pocket Book Fourth edition . formulae, definitions, tables and general information needed during.
|Language:||English, Spanish, Japanese|
|Genre:||Academic & Education|
|ePub File Size:||21.73 MB|
|PDF File Size:||8.44 MB|
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Use differentiation and integration tables to supplement differentiation and integration techniques. Differentiation Formulas. 1. 2. 3. 4. 5. 6. 7. 8. 9. Solution of quadratic equations by formula . Basic Engineering Mathematics, 4th Edition introduces and then consolidates basic mathematical principles. Jan 19, Formula. Handbook including. Engineering. Formulae,. Mathematics,. Statistics and. Computer Algebra instruktsiya.info - pdf.
Apart from describing the properties of the equation itself, these classes of differential equations can help inform the choice of approach to a solution. This list is far from exhaustive; there are many other properties and subclasses of differential equations which can be very useful in specific contexts.
Ordinary differential equations[ edit ] Main articles: Ordinary differential equation and Linear differential equation An ordinary differential equation ODE is an equation containing an unknown function of one real or complex variable x, its derivatives, and some given functions of x.
The unknown function is generally represented by a variable often denoted y , which, therefore, depends on x.
Integration Formula Sheet - Chapter 7 Class 12 Formulas
Thus x is often called the independent variable of the equation. The term "ordinary" is used in contrast with the term partial differential equation , which may be with respect to more than one independent variable.
Linear differential equations are the differential equations that are linear in the unknown function and its derivatives. Their theory is well developed, and, in many cases, one may express their solutions in terms of integrals. Most ODEs that are encountered in physics are linear, and, therefore, most special functions may be defined as solutions of linear differential equations see Holonomic function.
As, in general, the solutions of a differential equation cannot be expressed by a closed-form expression , numerical methods are commonly used for solving differential equations on a computer. Partial differential equations[ edit ] Main article: Partial differential equation A partial differential equation PDE is a differential equation that contains unknown multivariable functions and their partial derivatives. This is in contrast to ordinary differential equations , which deal with functions of a single variable and their derivatives.
PDEs are used to formulate problems involving functions of several variables, and are either solved in closed form, or used to create a relevant computer model.
PDEs can be used to describe a wide variety of phenomena in nature such as sound , heat , electrostatics , electrodynamics , fluid flow , elasticity , or quantum mechanics. These seemingly distinct physical phenomena can be formalised similarly in terms of PDEs. Just as ordinary differential equations often model one-dimensional dynamical systems , partial differential equations often model multidimensional systems.
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PDEs find their generalisation in stochastic partial differential equations. Non-linear differential equations[ edit ] Main article: Non-linear differential equations A non-linear differential equation is a differential equation that is not a linear equation in the unknown function and its derivatives the linearity or non-linearity in the arguments of the function are not considered here. There are very few methods of solving nonlinear differential equations exactly; those that are known typically depend on the equation having particular symmetries.
Nonlinear differential equations can exhibit very complicated behavior over extended time intervals, characteristic of chaos.
Even the fundamental questions of existence, uniqueness, and extendability of solutions for nonlinear differential equations, and well-posedness of initial and boundary value problems for nonlinear PDEs are hard problems and their resolution in special cases is considered to be a significant advance in the mathematical theory cf. Cancel reply. Please enter your comment!
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Engineering Mathematics Formula Sheet
Today Updates. Statics and Dynamics By R.
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Numerical Methods: This can also be used as a review guide. The x- and y-intercepts of a graph.
This means that the ball's acceleration, which is a derivative of its velocity, depends on the velocity and the velocity depends on time. Exponential Functions.
You should have learned the relevant theory before you apply these formulas. About the Author. | s3://commoncrawl/crawl-data/CC-MAIN-2020-05/segments/1579250615407.46/warc/CC-MAIN-20200124040939-20200124065939-00159.warc.gz | CC-MAIN-2020-05 | 5,620 | 30 |
http://nrich.maths.org/1934 | math | Two trees 20 metres and 30 metres long, lean across a passageway between two vertical walls. They cross at a point 8 metres above the ground. What is the distance between the foot of the trees?
Three triangles ABC, CBD and ABD (where D is a point on AC) are all
isosceles. Find all the angles. Prove that the ratio of AB to BC is
equal to the golden ratio.
ABCD is a rectangle and P, Q, R and S are moveable points on the
edges dividing the edges in certain ratios. Strangely PQRS is
always a cyclic quadrilateral and you can find the angles.
Three circles all of radius 2 cm touch as shown in the
A straight line $AG$ is tangential to the third circle, meeting
the middle circle at $H$ and $I$.
How long is $HI$?
What if there are four or more circles? | s3://commoncrawl/crawl-data/CC-MAIN-2017-17/segments/1492917121752.57/warc/CC-MAIN-20170423031201-00593-ip-10-145-167-34.ec2.internal.warc.gz | CC-MAIN-2017-17 | 753 | 12 |
https://apps.dtic.mil/sti/citations/ADA011007 | math | Kuratowski's and Wagner's Theorems for Matroids.
Technical summary rept.,
WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER
Pagination or Media Count:
In an earlier paper the author proved the following theorem which provides a strengthening of Tuttes well-known characterization of regular totally unimodular matroids A binary matroid is regular if it does not have the Fano matroid or its dual as a series-minor parellel-minor. In this paper the author proves two theorems which provide the same kind of strengthening for Tuttes characterization of the graphic matroids i.e., bond-matroids. These two theorems are called Kuratowskis and Wagners Theorems for Matroids in view of the graph theoretic results which they generalize.
- Theoretical Mathematics | s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178356456.56/warc/CC-MAIN-20210226085543-20210226115543-00580.warc.gz | CC-MAIN-2021-10 | 757 | 6 |
http://spanish.stackexchange.com/questions/tagged/vocales+deletreo | math | Spanish Language Meta
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cc by-sa 3.0 | s3://commoncrawl/crawl-data/CC-MAIN-2014-15/segments/1397609521512.15/warc/CC-MAIN-20140416005201-00007-ip-10-147-4-33.ec2.internal.warc.gz | CC-MAIN-2014-15 | 2,288 | 53 |
https://dtholidays.com/jobs-in-mathematics-field-2/ | math | There are various jobs in the mathematics field.
Inside the Usa, a large quantity of students get enthusiastic about mathematics as an undergraduate degree program. The graduate programs of mathematics are even more popular as they give students a possibility to study lots of regions of mathematics for example linear algebra, calculus, probability, discrete mathematics, complex analysis, analysis of functions, and others.
Mathematics best essay writing services offers many opportunities for those that are willing to study. Lots of graduates pursue careers in mathematics as they take pleasure in functioning with countless consumers and solving concerns. To start a career in mathematics, one particular can earn a Master’s degree in applied mathematics, or Doctoral degree in applied mathematics, or Ph.D applied mathematics.
A PhD in applied mathematics is obtained by carrying out analysis on mathematics, science, and related fields. Such fields include things like actuarial science, cosmology, general statistics, economics, and other individuals.
Although a PhD degree is acquired right after a Master’s degree, it tends to make it feasible to obtain jobs inside the mathematics field. college book report A PhD applied mathematician is then in a position to investigation topics that relate to the subjects covered within the Master’s degree courses.
A PhD in applied mathematics delivers the opportunity to study a wide selection of subjects that relate to several different regions of mathematics. These incorporate application of mathematics to different domains such as info technologies, economics, and medicine.
A Ph.D applied mathematician is generally in a position to select a topic in which they’re interested. professional writer service They’re able to then do study on this topic to discover the expected know-how to accomplish their operate. 1 may also get employment in a investigation institute if they’ve a doctorate in applied mathematics.
Students have to have to complete Master’s degrees in applied mathematics ahead of they may have the ability to apply for jobs within the mathematics field. Countless of these students have certain places of interest in specific areas of mathematics. These can involve locations just like geometry, functions, statistics, linear algebra, and other people.
A Ph.D applied mathematician can then write a dissertation that relates to their subject of interest academic assignment help as well as the study that they’ve carried out. A few of these dissertations then grow to be the basis for analysis projects that offer the Ph.D applied mathematician the chance to operate with mathematicians in the field of mathematics.
Many Masters in applied mathematics students who are organizing to accomplish research do not possess a selection of topic. Within this case, they’re able to function with other mathematicians within the location which might be associated with their location of interest. These people could then write dissertations that relate to the study that they’ve accomplished.
The quantity of time that a Ph.D applied mathematician can operate with mathematicians inside the field varies. They could devote up to three years working with mathematicians in the field. This typically is determined by the interests of your applicant and their practical experience in the field.
Those that are interested in Masters in applied mathematics could wish to decide on an additional topic soon after receiving their Masters in applied mathematics. In this case, they will need to contemplate getting a doctoral degree in some other area of mathematics. Such a Masters can assist to improve their operating expertise in mathematics as well as raise their understanding of other subjects.
People who choose to get jobs in mathematics field really should pursue their Master’s degree initially. Just after they full their Master’s degree, they will then apply for jobs in the mathematics field. Graduates are often well-paid professionals. | s3://commoncrawl/crawl-data/CC-MAIN-2020-24/segments/1590347385193.5/warc/CC-MAIN-20200524210325-20200525000325-00297.warc.gz | CC-MAIN-2020-24 | 4,033 | 13 |
http://www.slideshare.net/dantares/chapter-7-presentation-skills-11982394 | math | ME3101 / ME3102Mechanical Systems DesignChapter 7Presentation Skills
Presentation Skills•Anyone can present,but not everyone can doa good presentation.•For a goodpresentation to happen,it takes: •Preparation •Practiceand more Preparation.
Preparations – Before the PresentationAsk these questions:•What is the purpose of this presentation?•Who is my audience?•Where/When is my presentation?•What is the point I want to make?•Does the location have the equipments I need?•What attire is appropriate?
Preparations – Before the Presentation•Rehearse!•Try to keep to yourtimings duringpractice!•Avoid reading fromscripts if possible. Ifnot, cue cards wouldbe a better choice.•If time permits, dothe rehearsal on thepresentation groundsitself to getfamiliarized
During the PresentationRemember to do the following1. Greet the audience2. Introduce yourself3. Brief introduction about your presentation4. Use visual aids5. Practice good body language6. Clear verbal delivery
Tips for using visual aidsMicrosoft Powerpoint Prezi Google Docs Presentation
Tips for using visual aids•Limit the number of slides. If in doubt, 1 slide forevery 2 minutes is a good number to stick to.•Visuals are meant to enhance your presentation.Not take over it. Keep the slides uncluttered withjust enough text to illustrate your point.•Limit transitions and animations. Stayprofessional.•Make sure the slides can be seen clearly from theaudience’s point of view
Tips for using visual aids•Use diagrams to help the audience visualize your ideas.•Use a video simulator to help the audience see how exactly how youridea works! (An example of this is under the “Videos” tab on thewebsite•Or you could opt to perform an actual simulation with the audiencefor them to get an actual feel of it.
Tips for using visual aids 3D AutocadGoogle Sketchup
Body LanguageEye Contact:•Make eye contact with audience to engagetheir attention•Maintain eye contact for a few seconds atdifferent attention zones to prevent “fleetingeyes”•Be familiarized with content to preventconstant reference to notes
Body LanguagePosture•Stand straight with your shoulderspulled back.•Maintain an open body posture.•Face the audience•Use gestures to emphasize your point•Occasionally move about to establishpresence•Do not fidget.
Clear Verbal DeliveryVoice:•Project your voice to make sure thatyou can be heard.•Deliver your message slowly andclearly, this might be the first timethe audience heard about yourproject. Try to let them understandon the first delivery.•Use appropriate pauses.•Stay calm and be confident aboutyour content!
In ConclusionThe entirety of the project starts from the idea conception to the finalpresentation.No matter how good an idea is, it cannot be actualized if it cannot be sold toother people. | s3://commoncrawl/crawl-data/CC-MAIN-2016-40/segments/1474738660242.52/warc/CC-MAIN-20160924173740-00104-ip-10-143-35-109.ec2.internal.warc.gz | CC-MAIN-2016-40 | 2,850 | 13 |
http://wps.prenhall.com/wps/media/objects/3312/3392119/blb1607.html | math | Many substances behave as weak bases in water. Such substances react with water, removing protons from H2O, thereby forming the conjugate acid of the base and OH– ions:
The most commonly encountered weak base is ammonia:
The equilibrium-constant expression for this reaction can be written as
Because the concentration of water is essentially constant, the [H2O] term is incorporated into the equilibrium constant, giving
The constant Kb is called the base-dissociation constant, by analogy with the acid-dissociation constant, Ka, for weak acids. The constant Kb always refers to the equilibrium in which a base reacts with H2O to form the conjugate acid and OH–. Table 16.4 lists the names, formulas, Lewis structures, equilibrium reactions, and values of Kb for several weak bases in water. Appendix D of the textbook includes a more extensive list. Notice that these bases contain one or more lone pairs of electrons. A lone pair is necessary to form the bond with H+. Notice also that in the neutral molecules the lone pairs are on nitrogen atoms and that the other bases are anions derived from weak acids.
Calculate the concentration of OH– in a 0.15 M solution of NH3.
SOLUTION We use essentially the same procedure here as used in solving problems involving the ionization of weak acids. The first step is to write the ionization reaction and the corresponding equilibrium-constant (Kb) expression:
We then tabulate the equilibrium concentrations involved in the equilibrium:
(Notice that we ignore the concentration of H2O because it is not involved in the equilibrium-constant expression.) Inserting these quantities into the equilibrium-constant expression gives the following:
Because Kb is small, we can neglect the small amount of NH3 that reacts with water, as compared to the total NH3 concentration; that is, we can neglect x in comparison to 0.15 M. Then we have
Notice that the value obtained for x is only about 1 percent of the NH3 concentration, 0.15 M. Therefore, our neglect of x in comparison with 0.15 is justified.
Which of the following compounds should produce the highest pH as a 0.05 M solution: pyridine, methylamine, or nitrous acid? Answer: methylamine
How can we recognize from a chemical formula whether a molecule or ion is able to behave as a weak base? Weak bases fall into two general categories. The first category contains neutral substances that have an atom with a nonbonding pair of electrons that can serve as a proton acceptor. Most of these bases, including all the uncharged bases listed in Table 16.4, contain a nitrogen atom. These substances include ammonia and a related class of compounds called amines. In organic amines, one or more of the N H bonds in NH3 is replaced with a bond between N and C. Thus, the replacement of one N H bond in NH3 with a N CH3 bond gives methylamine, NH2CH3 (usually written CH3NH2). Like NH3, amines can extract a proton from a water molecule by forming an additional N H bond, as shown here for methylamine:
The chemical formula for the conjugate acid of methylamine is usually written CH3NH3+.
The second general category of weak bases is composed of the anions of weak acids. Consider, for example, an aqueous solution of sodium hypochlorite, NaClO. This salt dissolves in water to give Na+ and ClO– ions. The Na+ ion is always a spectator ion in acid-base reactions. However, the ClO– ion is the conjugate base of a weak acid, hypochlorous acid. Consequently, the ClO– ion acts as a weak base in water:
A solution is made by adding solid sodium hypochlorite, NaClO, to enough water to make 2.00 L of solution. If the solution has a pH of 10.50, how many moles of NaClO were added to the water?
SOLUTION NaClO is an ionic compound consisting of Na+ and ClO– ions. As such, it is a strong electrolyte that completely dissociates in solution into Na+, which is a spectator ion, and ClO– ion, which is a weak base with Kb = 3.3 10–7 (Equation 16.35). We wish to determine the concentration of ClO– in solution that would generate enough OH– ion to raise the pH to 10.50.
We first calculate the concentration of OH–(aq) at equilibrium. We can calculate [OH–] by using either Equation 16.14 or Equation 16.17; we will use the latter method here:
This concentration is high enough that we can assume that Equation 16.35 is the only source of OH–; that is, we can neglect any OH– produced by the autoionization of H2O. We now assume a value of x for the initial concentration of ClO– and solve the equilibrium problem in the usual way:
We now use the expression for the base-dissociation constant to solve for x:
We say that the solution is 0.31 M in NaClO, even though some of the ClO– ions have reacted with water. Because the solution is 0.31 M in NaClO and the total volume of solution is 2.00 L, 0.62 mol of NaClO is the amount of the salt that was added to the water.
A solution of NH3 in water has a pH of 10.50. What is the molarity of the solution? Answer: 0.0058 M | s3://commoncrawl/crawl-data/CC-MAIN-2018-26/segments/1529267860089.13/warc/CC-MAIN-20180618070542-20180618090542-00292.warc.gz | CC-MAIN-2018-26 | 4,991 | 22 |
http://mrwaynesclass.com/Kinemat/reading/questions/index.html | math | Identify the following quantities as being either a time, displacement, velocity, or acceleration measurement based on its units.
List the variables that are given in the following statements. Follow the format that is described in the reading.
A runner moves at 10 m/s while slowing down at 2 m/s2 for 3 seconds
Example Answer for this problem
vo= 10 m/s
a = -2 m/s2
t = 3 s
A car is moving at 22.5 m/s when it begins to speed up at 5 m/s2 for the next 11 seconds.
by Tony Wayne ...(If you are a teacher, please feel free to use these resources in your teaching.) | s3://commoncrawl/crawl-data/CC-MAIN-2019-22/segments/1558232259015.92/warc/CC-MAIN-20190526085156-20190526111156-00215.warc.gz | CC-MAIN-2019-22 | 564 | 9 |
http://www.wyzant.com/South_Boston_Boston_MA_algebra_1_tutors.aspx | math | Jamaica Plain, MA 02130
170/170 GRE. Success in Math and English
...I have several years part-time experience holding office hours and working in a tutorial office. I have a BA and an MA in mathematics. In both degrees the focus was on discrete math, logic, and algebra. I also taught a course in discrete math, held office hours,...
including algebra 1 | s3://commoncrawl/crawl-data/CC-MAIN-2014-15/segments/1397609537186.46/warc/CC-MAIN-20140416005217-00386-ip-10-147-4-33.ec2.internal.warc.gz | CC-MAIN-2014-15 | 353 | 4 |
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Der Genitiv von “Paket”: “des Pakets” oder “des Paketes”?
Ich suche den korrekten Genitiv des Worts Paket (des Wortes Paket?) Mir kommt "des Paketes" wie eine veraltete aber legale Form vor. Ist das 'e' vor dem Genitiv-s eine aussterbende Gattung?
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https://docserver.carma.newcastle.edu.au/view/subjects/28-XX.html | math | Items where Subject is "28-xx Measure and integration"
Group by: Creators | Item Type
Number of items at this level: 5.
Bailey, David H. and Borwein, Jonathan M. and Broadhurst, David J. and Zudilin, Wadim Experimental Mathematics and Mathematical Physics. Unpublished . (Unpublished)
Borwein, Jonathan M. and Bailey, David H. (2009) Highly Parallel, High-Precision Numerical Integration. International Journal of Computational Science and Engineering, 4 .
Borwein, Jonathan M. and Rose, Michael Expectations over Attractors of Iterated Function Systems. Applied Mathematics and Computation . (Submitted)
Borwein, Jonathan M. and Yao, Liangjin (2014) Legendre-type integrands and convex integral functions. Journal of Convex Analysis, 21 (1). pp. 264-288. ISSN 0944-6532
Rose, Michael G. (2015) Expectations over Deterministic Fractal Sets. PhD thesis, The University of Newcastle. | s3://commoncrawl/crawl-data/CC-MAIN-2017-17/segments/1492917122886.86/warc/CC-MAIN-20170423031202-00463-ip-10-145-167-34.ec2.internal.warc.gz | CC-MAIN-2017-17 | 881 | 8 |
https://skinner.ops.org/MAGNETTHEMES/AcceleratedMath/AmyKlinker/tabid/274/Default.aspx | math | Pi is a one of the most commonly known irrational numbers. It represents the ratio between the circumference of a circle (the distance around) to its diameter (the distance across). Because Pi is an irrational number, it is impossible to calculate exactly, but in any circle the circumference is approximately 3.14 times its diameter.
Pi Day is celebrated annually on March 14 and especifically at 1:59. This is to commenorate the first few digits of pi which 3.14159. | s3://commoncrawl/crawl-data/CC-MAIN-2018-09/segments/1518891816841.86/warc/CC-MAIN-20180225170106-20180225190106-00668.warc.gz | CC-MAIN-2018-09 | 468 | 2 |
https://wilbert.kobv.de/simpleSearch.do?fq=schlagwort_exakt%3A81R50&sortCrit=score&sortOrder=desc&hitsPerPage=10&fq=schlagwort_exakt%3A83E30&index=internal&query=journal%3A%7BCommunications+in+mathematical+physics%7D&plv=2 | math | Springer Online Journal Archives 1860-2000
Abstract An attempt is made to understand the root spaces of Kac Moody algebras of hyperbolic type, and in particularE 10, in terms of a DDF construction appropriate to a subcritical compactified bosonic string. While the level-one root spaces can be completely characterized in terms of transversal DDF states (the level-zero elements just span the affine subalgebra), longitudinal DDF states are shown to appear beyond level one. In contrast to previous treatments of such algebras, we find it necessary to make use of a rational extension of the self-dual root lattice as an auxiliary device, and to admit non-summable operators (in the sense of the vertex algebra formalism). We demonstrate the utility of the method by completely analyzing a non-trivial level-two root space, obtaining an explicit and comparatively simple representation for it. We also emphasize the occurrence of several Virasoro algebras, whose interrelation is expected to be crucial for a better understanding of the complete structure of the Kac Moody algebra.
Type of Medium: | s3://commoncrawl/crawl-data/CC-MAIN-2020-24/segments/1590347441088.63/warc/CC-MAIN-20200604125947-20200604155947-00297.warc.gz | CC-MAIN-2020-24 | 1,097 | 3 |
https://en.academic.ru/dic.nsf/enwiki/151471 | math | - Poisson's ratio
Poisson's ratio ("ν"), named after
Simeon Poisson, is the ratio of the relative contraction strain, or transverse strain (normal to the applied load), divided by the relative extension strain, or axial strain (in the direction of the applied load).
When a sample of material is stretched in one direction, it tends to contract (or rarely, expand) in the other two directions. Conversely, when a sample of material is compressed in one direction, it tends to expand (or rarely, contract) in the other two directions. Poisson's ratio (ν) is a measure of this tendency.
The Poisson's ratio of a stable material cannot be less than −1.0 nor greater than 0.5 due to the requirement that the
shear modulusand bulk modulushave positive values. Most materials have between 0.0 and 0.5. Cork is close to 0.0, showing almost no Poisson contraction, most steels are around 0.3, and rubber is nearly incompressible and so has a Poisson ratio of nearly 0.5. A perfectly incompressible material deformed elastically at small strains would have a Poisson's ratio of exactly 0.5. Some materials, mostly polymer foams, have a negative Poisson's ratio; if these auxetic materials are stretched in one direction, they become thicker in perpendicular directions.
Assuming that the material is compressed along the axial direction:
where: is the resulting Poisson's ratio,: is transverse strain (negative for axial tension, positive for axial compression): is axial strain (positive for axial tension, negative for axial compression).
Cause of Poisson’s effect
On the molecular level, Poisson’s effect is caused by slight movements between molecules and the stretching of molecular bonds within the material lattice to accommodate the stress. When the bonds elongate in the stress direction, they shorten in the other directions. This behavior multiplied millions of times throughout the material lattice is what drives the phenomenon.
Generalized Hooke's law
For an isotropic material, the deformation of a material in the direction of one axis will produce a deformation of the material along the other axes in three dimensions. Thus it is possible to generalize
Hooke's Lawinto three dimensions::
:where:, and are strain in the direction of , and axis: , and are stress in the direction of , and axis: is
Young's modulus(the same in all directions: , and for isotropic materials): is Poisson's ratio (the same in all directions: , and for isotropic materials)
The relative change of volume "ΔV"/"V" due to the stretch of the material can be calculated using a simplified formula (only for small deformations):
where: is material volume: is material volume change: is original length, before stretch: is the change of length:
If a rod with diameter (or width, or thickness) "d" and length "L" is subject to tension so that its length will change by "ΔL" then its diameter "d" will change by (the value is negative, because the diameter will decrease with increasing length):
The above formula is true only in the case of small deformations; if deformations are large then the following (more precise) formula can be used:
where: is original diameter: is rod diameter change: is Poisson's ratio: is original length, before stretch: is the change of length.
Orthotropic material, such as wood in which Poisson's ratio is different in each direction (x, y and z axis) the relation between Young's modulus and Poisson's ratio is described as follows:
where: is a
Young's modulusalong axis i: is a Poisson's ratio in plane jk
Poisson's ratio values for different materials
glasscomponent additions on Poisson's ratio of a specific base glass. [ [http://www.glassproperties.com/poisson_ratio/ Poisson's ratio calculation of glasses] ] ]
Negative Poisson's ratio materials
Some materials known as
auxeticmaterials display a negative Poisson’s ratio. When subjected to strain in a longitudinal axis, the transverse strain in the material will actually be positive (i.e. it would increase in cross sectional area). For these materials, it is usually due to uniquely oriented, hinged molecular bonds. In order for these bonds to stretch in the longitudinal direction, the hinges must ‘open’ in the transverse direction, effectively exhibiting a positive strain. [ [http://silver.neep.wisc.edu/~lakes/Poisson.html Negative Poisson's ratio ] ]
Applications of Poisson's effect
One area in which Poisson's effect has a considerable influence is in pressurized pipe flow. When the air or liquid inside a pipe is highly pressurized it exerts a uniform force on the inside of the pipe, resulting in a radial stress within the pipe material. Due to Poisson's effect, this radial stress will cause the pipe to slightly increase in diameter and decrease in length. The decrease in length, in particular, can have a noticeable effect upon the pipe joints, as the effect will accumulate for each section of pipe joined in series. A restrained joint may be pulled apart or otherwise prone to failure. [http://www.cpchem.com/hb/getdocanon.asp?doc=135&lib=CPC-Portal]
Another area of application for Poisson's effect is in the realm of
structural geology. Rocks, just as most materials, are subject to Poisson's effect while under stress and strain. In a geological timescale, excessive erosion or sedimentation of Earth's crust can either create or remove large vertical stresses upon the underlying rock. This rock will expand or contract in the vertical direction as a direct result of the applied stress, and it will also deform in the horizontal direction as a result of Poisson's effect. This change in strain in the horizontal direction can affect or form joints and dormant stresses in the rock. [http://www.geosc.psu.edu/~engelder/geosc465/lect18.rtf]
Impulse excitation technique
Coefficient of thermal expansion
* [http://silver.neep.wisc.edu/~lakes/PoissonIntro.html Meaning of Poisson's ratio]
* [http://silver.neep.wisc.edu/~lakes/Poisson.html Negative Poisson's ratio materials]
* [http://home.um.edu.mt/auxetic More on negative Poisson's ratio materials (auxetic)]
* [http://www.webelements.com/webelements/properties/text/definitions/poissons-ratio.html Poisson's ratio]
Wikimedia Foundation. 2010.
Look at other dictionaries:
Poisson's ratio — n. [see POISSON DISTRIBUTION] Physics an elastic constant of a material equal to the ratio of contraction sideways to expansion lengthwise when the material is stretched … English World dictionary
Poisson's ratio — Poisson s ratio. См. Коэффициент Пуассона. (Источник: «Металлы и сплавы. Справочник.» Под редакцией Ю.П. Солнцева; НПО Профессионал , НПО Мир и семья ; Санкт Петербург, 2003 г.) … Словарь металлургических терминов
Poisson’s ratio — Puasono santykis statusas T sritis fizika atitikmenys: angl. Poisson number; Poisson’s ratio vok. Poisson Konstante, f; Poissonsche Konstante, f; Poissonsche Zahl, f rus. коэффициент поперечного сжатия, m; коэффициент Пуассона, m pranc.… … Fizikos terminų žodynas
Poisson’s ratio — Puasono santykis statusas T sritis Standartizacija ir metrologija apibrėžtis Tempiamo arba gniuždomo bandinio skersinės ir išilginės santykinių deformacijų dalmens absoliučioji vertė. atitikmenys: angl. Poisson number; Poisson’s ratio vok.… … Penkiakalbis aiškinamasis metrologijos terminų žodynas
Poisson’s ratio — Puasono koeficientas statusas T sritis fizika atitikmenys: angl. Poisson’s ratio vok. Poisson Konstante, f; Poissonscher Koeffizient, m rus. коэффициент Пуассона, m pranc. coefficient de Poisson, m; rapport de Poisson, m … Fizikos terminų žodynas
poisson's ratio — noun also poisson ratio Usage: usually capitalized P Etymology: after S. Poisson : the ratio of transverse to longitudinal strain in a material under tension … Useful english dictionary
Poisson’s ratio — Puasono koeficientas statusas T sritis Standartizacija ir metrologija apibrėžtis Tempiamų arba gniuždomų kūno sluoksnių skersinės ir išilginės deformacijų dalmens absoliučioji vertė. atitikmenys: angl. Poisson’s ratio vok. Poisson Konstante, f;… … Penkiakalbis aiškinamasis metrologijos terminų žodynas
Poisson's ratio — Physics. the ratio, in an elastic body under longitudinal stress, of the transverse strain to the longitudinal strain. Also, Poisson ratio. [1925 30; see POISSON DISTRIBUTION] * * * … Universalium
Poisson's ratio — noun Etymology: S. Poisson Date: 1886 the ratio of transverse to longitudinal strain in a material under tension … New Collegiate Dictionary
Poisson's ratio — noun Of a material in tension or compression, the ratio of the strain in the direction of the applied load to the strain normal to the load. Abbreviated ν … Wiktionary | s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575540500637.40/warc/CC-MAIN-20191207160050-20191207184050-00543.warc.gz | CC-MAIN-2019-51 | 8,941 | 50 |
https://josmfs.net/tag/putnam-exam/ | math | This is a nifty problem from Presh Talwakar.
“This is adapted from the 1994 Putnam, A2. Thanks to Nirman for the suggestion!
Let R be the region in the first quadrant bounded by the x-axis, the line y = x/2, and the ellipse x2/9 + y2 = 1. Let R‘ be the region in the first quadrant bounded by the y-axis, the line y = mx and the ellipse. Find the value of m such that R and R‘ have the same area.”
See the Putnam Ellipse Areas Problem
Here is a problem from the famous (infamous?) Putnam exam, presented by Presh Talwalkar. Needless to say, I did not solve it in 30 minutes—but at least I solved it (after making a blizzard of arithmetic and trigonometric errors).
“Today’s problem is from the 1978 test, problem B1 (the easiest of the second set of problems). A convex octagon inscribed in a circle has four consecutive sides of length 3 and four consecutive sides of length 2. Find the area of the octagon.”
My solution is horribly pedestrian and fraught with numerous chances for arithmetic mistakes to derail it, which happened in spades. As I suspected, there was an elegant, “easy” solution (as demonstrated by Talwalkar)—once you thought of it! Again, this is like a Coffin Problem. See the Putnam Octagon Problem. | s3://commoncrawl/crawl-data/CC-MAIN-2023-50/segments/1700679100529.8/warc/CC-MAIN-20231204115419-20231204145419-00823.warc.gz | CC-MAIN-2023-50 | 1,243 | 7 |
https://www.myofficetricks.com/5-practical-excel-functions-to-improve-your-working-efficiency/ | math | Microsoft Excel is a widely used office software which you must have tried or at least heard in life. It’s convenient, powerful and also complicated for some newbies since there seems to be too much to learn. They may end up doing repetitive work manually without knowing how to use Excel formulas to complete their tasks. It’s undoubtedly a huge waste of time and effort.
In fact, you don’t need to spend much time on learning all the things about it. There are some useful Excel functions can greatly improve your working efficiency, and best of all, they are all easy to master.
1. SUM Fuction
Comparing to calculate the total amount of a lot of data manually, Excel itself can do a better and quicker job to calculate the summation. It’s called SUM function. To make use of it:
① Select the cell you want to output the result of calculation, then click the icon of Insert Function above the table.
② Choose SUM in the popping out window and hit OK.
③ The formula will be filled in the cell and a window called Function Arguments will pop out. You can click the up arrow to select the range of data to calculate or type it manually. In my case I want to sum the data from B2 to D2 (including C2), so the complete formula should be “=SUM(B2:D2)”.
④ If you want to sum the data of B2 and D2, you should set the value of Number 1 and Number 2 as B2 and D2 separately, or input complete the formula as “=SUM(B2, D2)” directly.
⑤ Hit OK, Excel will work the total amount out immediately.
⑥ There’s one more small trick I want to share. If you want to apply the same formula in a range of cells, put your cursor at the right lower corner of the cell till it turns into a small black cross. Drag it to contain all the cells you want to apply the same formula.
2. Calculate Percentages
It’s frequent at work to make sheets involving percentages of different departments in a whole company. Calculating percentages with a calculator surely won’t take a lot of your time. But if there’re piles of data to deal with in a short time, Excel functions can definitely do a quicker job.
① To calculate the percentage, you must know the total amount in advance. Like the table below, the first thing I should do is to sum the profits from F2 to F5 with the method of using SUM function.
② Then click G2, and input the formula “=F2/$F$6“. F6 refers to the value in the B22, which is also the total amount of profits. And the symbol “$” makes it a fixed value. It won’t change even when we apply this formula to other cells.
③ Press Enter key to work it out. Then with the trick I shared before, apply this formula to other cells in “Percentage” column.
④ If you want them to show as percentages instead of decimal fractions, just select all these cells and click the “％” icon in Home tab. The results will change into percentages immediately.
3. Evaluate the Average Value
Evaluating the average value is also a common need while doing calculations in Excel.
① Select a cell as the place to work the average value out, Click the icon of Insert Function – Averages, and then make your choice the poping out window of Function Arguments.
② Or you can input the formula “=AVERAGE(number1:number2)” directly. Here I want to evaluate the average value of the data from B2 to B5. So the complete formula is “=AVERAGE(B2:B5)”. Press Enter key and you can see the result.
4. Merge the Content in Different Cells
Sometimes you may need to merge the content from different cells in an existing table. If there’s a large amount of data for us to process in the table, Excel function can help you to save a lot of time and effort as well.
Like this table below, I’m required to merge the content of Column A and Column B in the new created “Merge” column.
① The first step is to merge the content of the first row in Column A and Column B. Input the formula “=CONCATENATE(A2,B2)” in F2 and then press Enter key. The text in A2 and B2 will be combined and filled in the F2 right away.
② Put the cursor at the lower-right corner of F2, it will turn to a small black cross. Then press and hold the left mouse, drag it to select all the cells in “Merge” column. Thus you can apply the same formula to a whole column, and the content from two columns will be merged successfully in a moment.
5. VLOOKUP Function
VLOOKUP can easily search through a column and find the corresponding data. For example, you can search for the score of a student in class quickly according to his or her name. It’s a very practical Excel function which can be massively used in work.
The basic formula for VLOOKUP is:
① Assuming there’s a long list of record in the table below. Now I want to find the score of someone, the first step should be inserting the formula correctly. So I click the cell I want to output the search result, which is F2 in my case, and hit the small icon of Insert Function.
② Type “VLOOKUP” in the textbox of Search for a function and hit Go. Click VLOOKUP in the section of Select a function and click OK to insert the formula (you can directly type it in the cell, of course).
③ Then you can input the value of each factor of the formula. For example, I want find the score of student F in the table, so the Lookup_value should be “F“. And the values of score are listed in the third column, so the Col_index_num should be “3“. Then set the Range_lookup as “0” for an accurate result.
④ As for the Table_array, a convenient way is clicking the small arrow on the right of the textbox, then hold and drag the left mouse to select all the cells in the table. The range of table will be inserted to the textbox accordingly.
⑤ Click that small arrow again to get back to Function Arguments window. Now all the textboxes have been filled up. Click OK to close the window. VLOOKUP function has already found the data I’m looking for in F2.
This is what I want to share for today, hope it can be a little inspiration to your work. In fact, except for the 5 useful Excel functions I mentioned above, there are many other practical functions and formulas can improve your efficiency of processing text and data. You can also give them a try in the future.
Left the repetitive tasks to machine, invest your energy in some more creative work! | s3://commoncrawl/crawl-data/CC-MAIN-2023-40/segments/1695233510676.40/warc/CC-MAIN-20230930113949-20230930143949-00630.warc.gz | CC-MAIN-2023-40 | 6,338 | 35 |
https://tgv.lamiacasaelanatura.it/molar-mass-calculator-using-ideal-gas-law.html | math | The calculated molar mass gives a reasonable formula for dinitrogen monoxide. Calculating Density of a Gas. The ideal gas law can be used to find the density of a gas at conditions that are not standard.
Internal Energy of an Ideal Gas. The internal energy is the total of all the energy associated with the motion of the atoms or molecules in the system. Microscopic forms of energy include those due to the rotation, vibration, translation, and interactions among the molecules of a substance. the molar volume of an ideal gas is: 22.41 L/mol, i.e., exactly one mole of any ideal gas at 273.15 K and 101.3 kPa pressure will occupy a volume of 22.41 L. This volume is called the . molar volume. In this experiment, you will confirm that the molar volume of hydrogen gas at STP is indeed 22.41 L/mol.
Hence, for a given temperature and pressure, the molar volume is the same for all ideal gases and is based on the gas constant: R = 8.314 462 618 153 24 m 3 ⋅Pa⋅K −1 ⋅mol −1, or about 8.205 736 608 095 96 × 10 −5 m 3 ⋅atm⋅K −1 ⋅mol −1. molar gas constant: T: absolute temperature (K) M: molar mass of the gas. The mean molar mass for dry air is about 0.0289645 kg/mol (kg/mol)
Ideal Gas Law is an equation of state of a hypothetical Gas, namely the ideal Gas. An ideal gas is an assembly of volume-less hard atoms which do not attract or repel each other but can collide with each other elastically. This equation can be applied for real gases at high temperature or at low pressure. Oct 10, 2016 · Molar volume: 22.414 L/mol. molar mass of N2: 28.01344 g/mol. density: (28.01344 g/mol) / (22.414 L/mol) = 1.2498 g/L N2 | s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038089289.45/warc/CC-MAIN-20210416191341-20210416221341-00194.warc.gz | CC-MAIN-2021-17 | 1,644 | 4 |
https://www.coursehero.com/sitemap/schools/413-Colorado-State/courses/6000382-CIVE502/ | math | Problem #1: Consider a square gate of side h that can rotate about a
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gate will open if h p = h .
For the square vertical part of the gate, the centroid, area and moment
1. kinematic eddy viscosity, v t , can be used to describe many relatively simple
turbulent flows. One empirical model for the eddy viscosity assumes it is a
function of the specific turbulence kinetic energy, k (dimensions L2 /T 2 ). And
the rate of diss
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3. Briefly describe a controversy surrounding the velocity-squared law.
4. Describe contributions of Daniel Bernoulli to the development of the Bernoulli | s3://commoncrawl/crawl-data/CC-MAIN-2017-26/segments/1498128320130.7/warc/CC-MAIN-20170623184505-20170623204505-00623.warc.gz | CC-MAIN-2017-26 | 723 | 11 |
https://www.oreilly.com/library/view/using-thematic-thinking/9780133448108/ch09.html | math | • What are the key messages of Thematic Thinking?
• Why do we get an incomplete picture of business reality if we do not heed Thematic Thinking?
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In the preceding chapters you have learned a lot about Thematic Thinking. Now that we have come so far it is time for wrapping it all together. The key message of the present book can be boiled down to a simple recommendation: Think thematic, and thus make better use of your possibilities! By now, you are equipped with all you need to know about when and how to apply Thematic Thinking and most importantly ... | s3://commoncrawl/crawl-data/CC-MAIN-2018-43/segments/1539583512592.60/warc/CC-MAIN-20181020055317-20181020080817-00463.warc.gz | CC-MAIN-2018-43 | 711 | 5 |
https://brainmass.com/business/business-math/pg21 | math | Calculate the tax disadvantage to organizing a U. S. business today, after passage of the Jobs and Growth Tax Relief Reconciliation Act of 2003, as a corporation versus a partnership under the following conditions. Assume that all earnings will be paid out as cash dividends. Operating income ( operating profit before taxes) will
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How can organizations determine if they are structured in the most effective and efficient manner? What are some advantages and disadvantages of each: (a) team-based, (b) network-based, and (c) boundaryless organizations?
You are working for an investment firm and have been asked to analyze and explain investments to your boss and clients who do not understand the various aspects of your job. You are working with the analysis of stocks, bonds and mutual funds. The following questions are examples of some of the analysis type problems that your bo
1. Find the median of the following set of numbers. 45, 21, 54, 22, 65, 61 Solution, explanation: 2. The following scores were recorded on a 100-point examination: 95, 75, 76, 86, 96, 71, 68, 81, 95, 76, 69, 82, 93, 88, 94 Find the mean and median final examination scores. Solution, explanation:
II. Create an income statement that finds the gross profit and net income for ABC Computers for the year ending August 31, 2007 if the company had net sales of $28,625; cost of goods sold of $13,247; and operating expenses of $2,752. III. Complete a vertical analysis of the income statement in part two. IV. In 2
Cully furniture buys 2 products for resale: big shelves (B) and medium shelves (M). Each big shelf costs $500 and requires 100 cubic feet of storage space, and each medium shelf costs $300 and requires 90 cubic feet of storage space. The company has $75000 to invest in shelves this week, and the warehouse has 18000 cubic feet av
A local church is studying the amount of offerings in an envelope from their early Sunday mornings services. The church studied 500 envelopes and found the following: Less than $5 200 $5 to $9.99 100 $10 to $19.99 75 $20 to $49.99 75 $50 or more 50 What is the probabi
Please see attached document. Sharifi Hospital basis its budgets on patient-visits. The hospital's static budget for October appears below: Budgeted number of patient visits 8,500 Budgeted variable overhead costs: Supplies (@$4.70 per patient-visit) $39,950 Laundry (@$7.80 per patient-visit) 66,300 Total v
The following costs appear in Malgorzata Company's flexible budget at an activity level of 15,000 machine hours: Total Cost Indirect materials: $7,800 Factory rent: $18,000 What would be the flexible budget amounts at an activity level of 12,000 machine hours if indirect materials is a variable cost a
Question 1 Jordan Company produced 150,000 floor lamps during the past calendar year. Jordan had 2,500 floor lamps in finished goods inventory at the beginning of the year. At the end of the year, there were 11,500 floor lamps in finished goods inventory. The lamps sell for $50 each. Jordan's accounting records provide the fol
Pitkins Company collects 20% of a month's sales in the month of sale, 70% in the month following the sale, and 6% in the second month following sale. The remainder is uncollectible. Budgeted sales for the next four months are: January February March April Budgeted Sales $200,000 $300,000 $350,000 $250,000
The following information relates to Minorca Manufacturing Corporation for next quarter: January February March Expected sales (in units) 440,000 390,000 400,000 Desired ending finished goods inventory (in units) 28,000 30,000 35,000 How many units should Minorca plan on producing for the month of February?
II. You are asked to make a depreciation schedule for a business asset. A depreciation schedule shows the remaining value of the asset at the end of each time period. Create a depreciation schedule for each of the following 1. A copy machine that costs $1,800, shipping $50 and installed for $125 depreciated using the stra
Which of the following should not influence a firm's dividend policy decision? The firm's ability to accelerate or delay investment projects, A strong preference by most shareholders in the economy for current cash income versus capital gains, constraints imposed by the firm's bond indenture, the fact that much of the firm's
Rooney Inc. recently completed a 3-for-2 stock split. Prior to the split, its stock price was $90 per share. The firm's total market value was unchanged by the split. What was the price of the company's stock following the stock split?
The firm's target structure is consistent with which of the following? Maximum earnings per share (EPS), Minimum cost of debt (rd), Highest bond rating, Minimum cost of equity (rs), or Minimum weight average cost of capital (WACC).
Millman Electronics will produce 60,000 stereos next year. Variable costs will equal 50% of sales, while fixed costs will total $120,000. At what price must each stereo be sold for the company to achieve an EBIT of $95,000?
1. The issuance price of a bond does not depend on the a. face value of the bond. b. riskiness of the bond. c. method used to amortize the bond discount or premium. d. effective interest rate. 2. Which of the following is true of a premium on bonds payable? a. It is a contra-stockholders' equity account. b. It
Consider the following contingency table: Under 20 21-30 31-40 Male 12 12 17 Female 13 16 21 a. If one person is selected at random, what is the probability that person is Female? ______ b. If one person is selected at random, what is the probability that person is ei
Swanson Inc. purchased $400,000 of Malone Corp. ten-year bonds with a stated interest rate of 8 percent payable quarterly. At the time the bonds were purchased, the market interest rate was 12 percent. Determine the amount of premium or discount on the purchase of the bonds.
Swanson Inc. purchased $400,000 of Malone Corp. ten-year bonds with a stated interest rate of 8 percent payable quarterly. At the time the bonds were purchased, the market interest rate was 12 percent. Determine the amount of premium or discount on the purchase of the bonds. a. $92,442 premium b. $92,442 discount c. $81,1
On January 1, 2006, an investor paid $291,000 for bonds with a face amount of $300,000. The contract rate of interest is 8% while the current market rate of interest is 10%. Using the effective interest method, how much interest income is recognized by the investor in 2006 (assume annual interest payments and amortization)?
Thirty flasks, 10 full, 10 half empty and 10 entirely empty, are to be divided among 3 sons so that flasks and content should be shared equally. How may this be done without pouring from one flask to another?
You must evaluate a proposal to buy a new milling machine. The base price is $108,000, and shipping and installation costs would add another $12,500.
You must evaluate a proposal to buy a new milling machine. The base price is $108,000, and shipping and installation costs would add another $12,500. The machine falls into the MACRS 3-year class, and it would be sold after 3 years for $65,000. The applicable depreciation rates are 33, 45, 15 and 7 percent. The machine would
1. Passenger comfort is influenced by the amount of pressurization in the airline cabin. Higher pressurization permits a closer-to-normal environment and a more relaxed flight. A study by an airline user group recorded the corresponding air pressure on 30 randomly chosen flights. The study revealed a mean equivalent pressure of
Match the letter of the term to the definition of that term. Definitions 1. The average of the squared deviation scores from a distribution mean. ____ 2. Midpoint in the distribution of numbers. ____ 3. It has to do with the accuracy and precision of a measurement procedure. ____ 4. Examines if an observed causal rela
Symbols Definitions 1. S (Uppercase Sigma) ____ a. Null hypothesis 2. m (Mu) ____ b. Summation 3. s (Lowercase Sigma) ____ c. Factorial 4. p (Pi) ____ d. Nonparametric hypothesis test 5. e (Epsilon) ____ e. Population standar
Burger and more business is worth 250,000. it is expected to grow at 12% per year compounded annually for the next 5 years. Find the expected future value. If funds from the sale of the business today would be placed in an account yielding 6% compounded semiannually, what would be the minimum acceptable price for Burger and
The earnings, dividends, and common stock price of Carpetto Technologies Inc. are expected to grow at 7 percent per year in the future. Carpetto's common stock sells for $23 per share, its last dividend was $2.00, and it will pay a dividend of $2.14 at the end of the current year. Assuming you have equal confidence in the outp
The earnings, dividends, and common stock price of Carpetto Technologies Inc. are expected to grow at 7 percent per year in the future.
The earnings, dividends, and common stock price of Carpetto Technologies Inc. are expected to grow at 7 percent per year in the future. Carpetto's common stock sells for $23 per share, its last dividend was $2.00, and it will pay a dividend of $2.14 at the end of the current year. Using the DCF approach, what is the cost of co
Percy Motors has a target capital structure of 40 percent debt and 60 percent common equity, with no preferred stock. The yield to maturity on the company's outstanding bonds is 9 percent, and its tax rate is 40 percent. Percy's CFO estimates that the company's WACC is 9.96 percent. What is Percy's cost of common equity? | s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600402093104.90/warc/CC-MAIN-20200929221433-20200930011433-00797.warc.gz | CC-MAIN-2020-40 | 9,556 | 34 |
https://homework.cpm.org/category/CON_FOUND/textbook/mc1/chapter/3/lesson/3.4.2/problem/3-109 | math | . Four friends worked together to wash all of the cars that the Kish family owns. They received $42.00 for doing the work and agreed to divide the earnings evenly. How much money will each friend earn? Show how you know. Homework Help ✎
Since we know there were four friends working, can we use division to find how much of the $42.00 each friend will get? | s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575540527205.81/warc/CC-MAIN-20191210095118-20191210123118-00302.warc.gz | CC-MAIN-2019-51 | 358 | 2 |
https://www.topperlearning.com/forums/home-work-help-19/please-can-i-get-a-complete-detailed-explanation-of-langmuir-chemistry-surface-chemistry-51175/reply | math | Please can i get a complete detailed explanation of Langmuir Adsorption Isotherm with its derivation?
In 1916, Irving Langmuir proposed an Adsorption Isotherm which explained the variation of Adsorption with pressure. Based on his theory, he derived Langmuir Equation which depicted a relationship between the number of active sites of the surface undergoing adsorption and pressure.
Assumptions of Langmuir Isotherm
Langmuir proposed his theory by making following assumptions.
1. Fixed number of vacant or adsorption sites are available on the surface of solid.
2. All the vacant sites are of equal size and shape on the surface of adsorbent.
3. Each site can hold maximum of one gaseous molecule and a constant amount of heat energy is released during this process.
4. Dynamic equilibrium exists between adsorbed gaseous molecules and the free gaseous molecules.
Where A (g) is unadsorbed gaseous molecule, B(s) is unoccupied metal surface and AB is Adsorbed gaseous molecule.
5. Adsorption is monolayer or unilayer.
Derivations of the Langmuir Adsorption Equation
Calculation of Equilibrium Constant
Langmuir proposed that dynamic equilibrium exists between adsorbed gaseous molecules and the free gaseous molecules. Using the equilibrium equation, equilibrium constant can be calculated.
Where Ka represents equilibrium constant for forward reaction and Kd represents equilibrium constant for backward direction.
According to Kinetic theory,
Rate of forward reaction = Ka [A] [B]
Rate of backward reaction = Kd [AB]
At equilibrium, Rate of forward reaction is equal to Rate of backward reaction
The above equation represents the equilibrium constant for distribution of adsorbate between the surface and the gas phase.
Langmuir Equation which depicts a relationship between the number of active sites of the surface undergoing adsorption (i.e. extent of adsorption) and pressure.
To derive Langmuir Equation and new parameter ? is introduced. Let ? the number of sites of the surface which are covered with gaseous molecules. Therefore, the fraction of surface which are unoccupied by gaseous molecules will be (1 ?).
Now, Rate of forward direction depends upon two factors: Number of sited available on the surface of adsorbent, (1 ?) and Pressure, P. Therefore rate of forward reaction is directly proportional to both mentioned factors.
Similarly, Rate of backward reaction or Rate of Desorption depends upon number of sites occupied by the gaseous molecules on the surface of adsorbent.
At equilibrium, rate of adsorption is equal to rate of desorption.
Ka P (1 ?) = Kd ?
We can solve the above equation to write it in terms of ?.
KaP KaP ? = Kd ?
KaP = KaP ? + Kd ?
KaP = (Kd + KaP) ?
Divide numerator and denominator on RHS by Kd, we get
in above equation we get
Langmuir Adsorption Equation
This is known as Langmuir Adsorption Equation. | s3://commoncrawl/crawl-data/CC-MAIN-2017-47/segments/1510934807146.16/warc/CC-MAIN-20171124070019-20171124090019-00535.warc.gz | CC-MAIN-2017-47 | 2,849 | 33 |
https://justlearning.in/tag/geometry/ | math | What is Geometry? Geometry is one of the most important subjects in mathematics. When you take geometry in school, you are developing spatial reasoning and problem-solving skills. Geometry is linked to many other topics in math, specifically measurement. The subject of geometry helps us study the concept of space, mainly its properties and concepts such … Continue reading “Geometry Kit for Special Students… Find Out!”
Mathematicians and Statisticians: Set Up Your Career As A Mathematician And Statistician…Find Out How!
Mathematics, rightly viewed, possesses not only truth but supreme beauty- a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting and music. Yet sublimely pure and capable of a stern perfection such as only the greatest art can show What … Continue reading “Mathematicians and Statisticians: Set Up Your Career As A Mathematician And Statistician…Find Out How!”
Are you interested in learning more about a career in geography? Geography is the science of place and space. Geographers are scientists who specialize in studying the earth, including its physical features, organisms, and natural phenomena. The chief types of geographers include physical geographers, who examine the processes that contribute to the rise of the … Continue reading “Thinking like a Geographer? Check These Signs to Find Out.”
Euclidian geometry is a mathematical system attributed to Alexandrian Greek Mathematician Euclid Introduction of Euclidian geometry The Greek mathematicians of Euclid’s time thought of geometry as an abstract model of the world in which they lived. The notions of point, line, plane (or surface) and so on were derived from what was seen around them. … Continue reading “Geometry In Everyday Life: Using Euclidian Principles… Find Out!”
The Pythagoras Theorem was named after the ancient Greek mathematician Pythagoras, supposedly the first to offer a proof of the theorem. Mathematics is a fascinating subject. Delve deeper into its nuances and intricacies, and you’re likely to fall in love with it. Vast, confounding and yet, mesmerizing, Maths holds its followers in thrall. An important … Continue reading “Did You Know? Mathematics Can Be A Lot More Interesting? Here Is Some Interesting Information!!”
These students have created some incredible model of geometrical insight that can make tricky maths easy. Trust us! This video witnesses the breaking of a common notion of maths. The word ‘geometry’ comes from the Greek words ‘geo,’ meaning the ‘earth,’ and ‘metrein,’ meaning ‘to measure.’ With the vision of ‘I hear, I forget, I … Continue reading “Geometrical insight | Maths Sessions are Easy-Peasy”
Did you know Euclid is the Father of Geometry? If no, you will learn about it in our video. These young wizards have created a model that can rescue difficult maths learning into easy learning. The word ‘geometry’ comes from the Greek words ‘geo,’ meaning the ‘earth,’ and ‘metrein,’ meaning ‘to measure.’ You must check … Continue reading “Euclid Model for geometrical shapes and their properties”
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Let O be the origin, and let OX, OY and OZ be three mutually perpendicular lines taken as the x-axis, y-axis and z-axis respectively in such a way that they form a right handed system. | s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141750841.83/warc/CC-MAIN-20201205211729-20201206001729-00690.warc.gz | CC-MAIN-2020-50 | 3,803 | 10 |
https://www.hitbullseye.com:443/Quant/How-to-Find-Average.php | math | Average is mainly defined as the sum of observations divided by the number of observations. Keeping in view the Quantitative Aptitude section of any competitive exam, 1-2 questions are asked from this chapter. It is not a difficulty chapter if you know the tricks to solve the question in very less time.
To understand the concept properly, let's try doing some questions.
Since, there difference between two consecutive terms, so the average will be taken as the middle term i.e. 27.
Question 2: Find the average of the following terms: 22, 23, 24, 25, 26 and 27.
Solution: We have discussed above that if the number of terms is even, then the average will be the average of the middle two terms.
So, the average here will be (24 + 25)/2 = 49/2 = 24.5
Must Read Average Articles
Question 3: The average weight of a class of 24 students is 36 years. When the weight of the teacher is also included, the average weight increases by 1kg. What is the weight of the teacher?
Solution: We know that, in case of increase in average,
Age of new member= Previous average+ (Increase in average X Number of members including new member)
Age of new member = 36 + (1 × 25)
Age of new member = 36 + 25 = 61
Question 4: Find the average of first 30 natural numbers.
Solution: Sum of first n natural numbers = n(n+1)/2
Therefore, Average=(30 (30+1))/(2*30)
= (30*31)/(2*31) = 15.5
Question 5: A merchant has a sale of Rs. 6435, Rs. 6927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 6500?
Solution: Total Sale of 5 months = 6435+6927+6855+7230+6562 = 34009
Required Sale = 6500 * 6 = 39000
Sale required in 6th month so that the average comes out to be 6500 = 39000 - 34009 = Rs 4991
Take this test to check your understanding of the topic: Averages.
Question 6: The average age of the teacher and six students is 12 which is reduced by 5 if the age of the teacher is excluded. What is the age of the teacher?
Solution: Total age of six students and teacher = 12 * 7 = 84
New average when teacher is excluded = 7
Therefore, total age of six students = 6 * 7 = 42
Therefore, age of teacher = 84 - 42 = 42
Question 7: 19 persons went to a hotel for a combined dinner party. 13 of them spent Rs 79 each on their dinner and the rest spent Rs 4 more than the average expenditure of all the 19. What was the total approximate money spent by them?
Solution: Assume that "×" is the average expenditure of 19 persons.
Then, 19× = 13 * 79 + 6 (×+4)
13× = 1051
× ≅81 ( approximately, as in the question approximate money is asked )
Therefore, total expenditure = 81 * 19= Rs 1539
Question 8: The average marks of 13 students 40. The average marks of first 7 students are 42 and that of the last seven are 35. Find the marks of the 7th student.
Solution: Total marks of 13 students = 13 * 40 = 520 Marks of first 7 students = 7 * 42 = 294
Marks of last 7 students = 7 * 35 = 245
Marks of 7th student = (294+245) - 520 = 19
Question 9: Aman has a certain average for 9 innings in the tenth innings; he scores 100 runs, thereby increasing his average by 8 runs. His new average is
Solution: Let his total average b "×"
His total runs in 9 innings will be 9×
New total; 9x + 100 = 10 (×+8)
× = 20
Therefore, new average = 20 + 8 = 28
Question 10: The average weight of 5 men is decreased by 3 kg when one of them weighing 150 kg is replaced by another person. This new person is again replaced by another person whose weight is 30 kg lower than the person he replaced. What is the overall change in the average due to the dual change?
Solution: The weight of the second man is 135 kg and that of the third is 105 kg.
Hence, net result is a drop of 45 for 5 people.
Hence, 9 kg is the overall drop.
Distance between two stations A and B is 778 km. A train covers the journey from A to B at 84 km/hr and returns back to A with a uniform speed of 56 km/hr. Find the average speed of train during the whole journey?
Solution: Required average speed = 2xy/(x+y)
(2*84*56)/(84+56)= 67.2 km/hr
- We have learnt ways to find the new average when there is replacement, addition or removal of a person in a group.
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Ohm’s Law Evan Deller and Charlie Rivera th January 27 , 2017 Abstract To illustrate the properties that make up Ohm’s law, an experiment was setup in order to measure the relationship between voltage, current and resistance. This was done using a series circuit combined with various resistors, a circuit, and power source. Two multi-meters were used to measure current and voltage, while resistance was given by 10 and 50 ohm resistors. Values of current and voltage were recorded for each resistor. This data served to illustrate the basis of Ohm’s law. Plugging the found data points into Ohm’s law ensured that the experiment | s3://commoncrawl/crawl-data/CC-MAIN-2021-04/segments/1610703561996.72/warc/CC-MAIN-20210124235054-20210125025054-00656.warc.gz | CC-MAIN-2021-04 | 818 | 2 |
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https://www.chemojo.com/post/fluid-mechanics-equations | math | Fluid mechanics is the branch of physics that studies the behavior of fluids at rest and in motion. It deals with the forces that fluids exert on other objects and how fluids respond to those forces. The fluids studied can be either liquids or gases.
This subject is important in many fields, including engineering, meteorology, oceanography, and aerospace. It is used in many industrial processes, such as internal combustion engines, turbine design, and many others.
What is a fluid?
Fluids are defined by their ability to flow and change shape, as opposed to solids, which maintain a fixed shape and volume.
There are two main types of fluids: liquids and gases. Liquids, such as water and oil, are a type of fluid that has a definite volume but no definite shape, meaning they will take the shape of their container. Gases, such as air and natural gas, have no definite shape or volume, meaning they will expand to fill their container.
Fluids can also be classified as incompressible or compressible. An incompressible fluid is a fluid that cannot be compressed, such as water. A compressible fluid is a fluid that can be compressed, such as a gas. The behavior of a fluid depends on its compressibility. For example, the speed of sound in a gas is affected by its compressibility.
Fluids are also classified as Newtonian or non-Newtonian. A Newtonian fluid is a fluid that behaves in a predictable way, following the laws of physics, such as liquids like water and oil. Non-Newtonian fluids are fluids that do not behave in a predictable way, such as toothpaste and blood. They can exhibit different behavior under different flow conditions.
In summary, understanding the properties and behavior of fluids is important in many industries and natural phenomena. The behavior of a fluid can be affected by its compressibility, viscosity and its ability to follow the laws of physics.
Here are 10 most important equations in fluid mechanics:
Newton's Law of Viscosity
It states that the shear stress (the force per unit area) in a fluid is proportional to the rate of change of velocity of the fluid with respect to distance in the direction perpendicular to the direction of flow. Mathematically, it is represented as :
τ = μ * (du/dy)
where τ is the shear stress, μ is the viscosity of the fluid, and (du/dy) is the rate of change of velocity of the fluid in the direction perpendicular to the flow. The proportionality constant μ is known as the coefficient of viscosity.
This law applies to fluids that behave in a predictable way, following the laws of physics, such as liquids like water and oil, which are known as Newtonian fluids.
The viscosity of a fluid is a measure of its resistance to flow. Fluids with high viscosity are more resistant to flow, while fluids with low viscosity flow more easily.
Pascal's law states that the pressure applied to an enclosed fluid is transmitted equally in all directions and at right angles to the container walls. Mathematically, it is represented as :
P1 = P2 = P3 = .... = Pn
where P1, P2, P3, ..., Pn are the pressures at different points within the fluid. This means that if an external force is applied to a fluid at one point, it will be transmitted throughout the entire fluid.
This law is the basis of many hydraulic systems, such as brakes, lifts, and construction equipment. It is also used in many industrial processes such as oil and gas extraction.
Hydrostatic law, also known as Pascal's law of fluids, states that the pressure exerted by a fluid at rest is transmitted equally in all directions and at right angles to the surface on which it acts. This means that if an external force is applied to a fluid at one point, it will be transmitted throughout the entire fluid. The pressure at a given point in a fluid at rest is determined by the weight of the fluid above it. Mathematically, it is represented as:
P = ρgh
where P is the pressure, ρ is the density of the fluid, g is the acceleration due to gravity, and h is the height of the fluid above the point in question. This law is widely used in fluid mechanics and many engineering applications such as pumps, valves, and pipelines.
In fluid mechanics, the continuity equation is a fundamental principle that states that the mass flow rate of a fluid through any given cross-sectional area must remain constant. Mathematically, it is represented as:
∑(mass flow rate)in = ∑(mass flow rate)out
A1V1 = A2V2 = A3V3 = .... = AnVn
where A1, A2, A3, ..., An are the cross-sectional areas and V1, V2, V3, ..., Vn are the velocities of the fluid at different points within the fluid.
This equation states that the mass of fluid flowing into any given point must be equal to the mass of fluid flowing out of that point. It is based on the principle of conservation of mass. It is a general statement of the conservation of mass, which applies to all systems, including fluids, gases and solids.
The continuity equation is also related to other principles in fluid mechanics such as the conservation of mass, the equation of motion and the energy equation.
It is used in many engineering applications such as fluid flow in pipes, pumps, and valves, and in the analysis of fluid systems. It is also used in the design and optimization of fluid systems.
This is a fundamental principle in fluid dynamics that describes the relationship between the pressure, velocity, and height of a fluid as it flows through a pipe or over a surface. The equation states that "in an ideal incompressible fluid when the flow is steady and continuous, the sum of the pressure energy, kinetic energy and potential energy is constant at any point along a streamline". Bernoulli's equation is given by:
P + 1/2 * ρu^2 + ρgh = constant
where, P is the pressure of the fluid, ρ is the density of the fluid, u is the velocity of the fluid, g is the acceleration due to gravity, h is the height of the fluid above a reference point.
**Applicable for incompressible, non-viscous, steady flow fluids**.
This equation is important in the study of fluid flow, as it can be used to predict the behavior of fluids in a variety of situations, including the flow of air over an airplane wing, the flow of water through a pipe, and the flow of fluids in pumps and turbines. For example, in the case of an airplane wing, the air flowing over the top of the wing is moving faster than the air flowing underneath the wing, which results in a lower pressure above the wing and a higher pressure below the wing. This creates lift, which is what allows the airplane to fly.
Navier Stokes Equation
The Navier-Stokes equations are a set of partial differential equations that describe the motion of a fluid, including its velocity, pressure, and temperature. These equations are based on the conservation of mass, momentum, and energy.
They take into account the effects of viscosity, which is the resistance of a fluid to flow, and turbulence, which is the chaotic, irregular motion of a fluid. The equations also include the effects of forces such as gravity and pressure gradients, and can be used to model fluid flow in a wide range of situations, including laminar flow, turbulent flow, and boundary layer flow. These equations can be represented in vector form as:
∂u/∂t + (u.∇)u = -1/ρ ∇p + μ/ρ ∇²u + g
where, u is the velocity vector of the fluid t is time ρ is the density of the fluid p is the pressure of the fluid μ is the dynamic viscosity of the fluid f is any external forces acting on the fluid. | s3://commoncrawl/crawl-data/CC-MAIN-2024-10/segments/1707948217723.97/warc/CC-MAIN-20240305024700-20240305054700-00767.warc.gz | CC-MAIN-2024-10 | 7,511 | 39 |
http://myeducationpath.com/search/tag/Taking+derivatives.htm?sortby=rating&categoryid=7&start=20&limit=20 | math | Courses tagged with "Taking derivatives" (22)
Calculus AB is primarily concerned with developing your understanding of the concepts of calculus and providing you with its methods and applications. The course emphasizes a multi-representational approach to calculus, with concepts, results, and problems being expressed graphically, numerically, analytically, and verbally. Broad concepts and widely applicable methods are also emphasized. The focus of the course is neither manipulation nor memorization of an extensive taxonomy of functions, curves, theorems, or problem types, but rather, the course uses the unifying themes of derivatives, integrals, limits, approximation, and applications and modeling to become a cohesive whole. The course is a yearlong high school mathematics course designed to prepare you to write and pass the AP Calculus AB test in May. Passing the test can result in one semester of college credit in mathematics.
Geometry comes from the Greek roots geo-, meaning Earth, and metron, meaning measure. Thus, geometry literally means the process of measuring the Earth. In a more mathematical sense, this course looks at geometric figures that we see in everyday life to understand the patterns in their attributes and how their measures relate to these patterns. It expands on the basic geometric concepts learned in previous math courses, through the applications of these concepts in new contexts. You will learn to develop formal proofs that support patterns and rules of geometric figures previously investigated, including congruent and similar figures, triangles, quadrilaterals, and circles. From here, the course expands on your knowledge about triangles and the Pythagorean theorem, introducing trigonometry of both right triangles and general triangles. The course will help you develop links between the attributes of two-dimensional and three-dimensional figures; help you develop formulas for calculating the volume of prisms…
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http://www.schuylervilleprephs.org/mathematics | math | Mathematics @ SPHS
3 years of Mathematics are required to complete a high school diploma in New York State, though four is recommended because certain colleges require it. At Schuylerville we seek to offer students a variety of math courses to build both foundation knowledge, as well as interest. Mathematical concepts are explored though students centered learning, with teachers who have both deep knowledge of their content as well real life experience in fields that require mathematical backgrounds.
Math @ SPHS
The fundamental purpose of this course is to formalize and extend the mathematics that students learned in the middle grades. Algebra 1 will deepen and extend understanding of linear and exponential relationships by contrasting them with each other and by applying linear models to data that exhibit a linear trend, and scholars engage in methods for analyzing, solving, and using quadratic functions.
Building on work with linear, quadratic, and exponential functions from Algebra I, scholars will add their knowledge of functions to include polynomial, rational, and radical functions. Scholars will work closely with the expressions that define the functions, and continue to expand and hone their abilities to model situations and to solve equations, including solving quadratic equations over the set of complex numbers and solving exponential equations using the properties of logarithms.
Welcome to the world of Geometry! This course will introduce you to axiomatic (Euclidean) geometry, transformations, proofs, and properties of two to three-dimensional figures. A major emphasis will be placed on developing your ability to explore and solve real-world application problems, appropriately use technology, and communicate mathematical ideas clearly. Writing samples, projects and presentations, and classwork activities are only a few of the many ways you will be demonstrating your understanding of the concepts we will cover this year. While we do hope that you enjoy your time in geometry, this class is meant to challenge you and prepare
you for subsequent courses in mathematics while providing you with the necessary tools to become a successful individual.
This one semester course provides scholars with the tools for describing variability in data and for making informed decisions or predictions. These tools include data collection, descriptive and inferential statistics,
probability, and the use of technology. Scholars will explore collected data, plan a study, produce statistical models using probability theory, and make statistical inferences. Ultimately scholars’ understanding of these
basic skills will build and solidify concepts and prepare them to succeed in the use of the afore mentioned mathematical tools in any college or career pathway they choose. As such, this course not only serves as a
4th -year mathematics course, but also as a practical course that prepares students to use these mathematical tools routinely as an integral part of their reasoning strategies.
This elective course highlights a branch of mathematics, which uses algebraic equations to describe the size and position of geometry figures on a coordinate system. A major emphasis will be placed on developing your ability to explore and solve real-world application problems, appropriately use technology, and communicate mathematical ideas clearly. Concepts presented in this course laid the foundation for modern mathematics as well as aided the development of calculus.
This elective course will strengthen and advance your understanding of variables, algebraic expressions, equations, functions, inequalities, and their multiple representations. A major emphasis will be placed on developing your ability to explore and solve real-world application problems, appropriately use technology, and communicate mathematical ideas clearly. This course is a prerequisite for Finite Math 2 where advanced and discrete topics are explored such as matrix algebra, linear programming, combinatorics, and probability.
A department's grading policy is the way in which the members of that department have chosen to weigh the different types of works that students do in their classrooms. Grading policies are used across the board by all teachers in that department. Please note that anywhere the word "assessment" appears can be meant to refer to quizzes, tests/exams, essays or any major work that is used to measure a students knowledge.
Daily/Weekly Assignments: 35%
● Exit Slips
Summative Assessments: 35%
Student Self-Assessments: 10% | s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570987817685.87/warc/CC-MAIN-20191022104415-20191022131915-00402.warc.gz | CC-MAIN-2019-43 | 4,562 | 18 |
https://www.alc.qld.edu.au/cms/index.php/en/courses/maths | math | Abacus Mental Calculations
The abacus is a mathematical calculation method. The abacus is used to add, subtract, multiply and divide. By using the abacus, the brain completes the computation, thereby raising the ability of the students to do mental arithmetic.
The abacus can be used at an astonishing speed. Often, as long as students can hear the numbers, or see the problem, the operator can immediately tell you the answer or write it down. This is the fundamental technique of computation using an abacus. | s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600401617641.86/warc/CC-MAIN-20200928234043-20200929024043-00488.warc.gz | CC-MAIN-2020-40 | 510 | 3 |
https://go.gale.com/ps/anonymous?id=GALE%7CA92528772&sid=googleScholar&v=2.1&it=r&linkaccess=abs&issn=01621459&p=AONE&sw=w | math | L. E. SADOVSKII and A. L. SADOVSKII. Providence, RI: American Mathematical Society, 1993. ISBN 0-8218-9500-1. ix + 152 pp. $20.00 (P).
This short paperback book is a translation (from Russian) of a collection of materials illustrating applications of mathematical ideas to sports. The authors intend it to be "for high school and college students" (p. ix). The level is certainly beyond most American high school students, but there are a number of interesting applications that might appeal to a good undergraduate student looking for an independent project topic. Mathematical application areas include probability and Markov chains (applied to tennis and basketball), voter theory (judging figure skaters and gymnasts), statistics (looking at progressions of world records), linear programming (to determine the lineup for a basketball team, stock players on soccer clubs, and plan a healthy athletic diet), game theory (for making substitutions in soccer, exerting a final spurt in speed skating, waxing skis, choosing to pass in weightlifting, and matching lines in ice hockey), tournament organization (Olympic format, round robins, and Latin squares) a nd rating systems (Elo's method for chess and tennis player rankings). Unfortunately, over half of the references are in Russian, so students may have some initial difficulty in following up on a particular topic.
Readers will notice that many of the examples are somewhat dated. Although the publication date is 1993, this fourth printing was issued in 2000. The original Russian manuscript was written several years earlier and, other than a few marginal notes by the editor, was not updated. One dated example is the excellent discussion in Chapter 2 of a model for examining the...
This is a preview. Get the full text through your school or public library. | s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243991207.44/warc/CC-MAIN-20210514183414-20210514213414-00287.warc.gz | CC-MAIN-2021-21 | 1,821 | 4 |
https://reference.wolfram.com/language/ref/NakagamiDistribution.html | math | represents a Nakagami distribution with shape parameter μ and spread parameter ω.
- NakagamiDistribution is also known as Nakagami- distribution.
- The probability density for value is proportional to for , and is zero for .
- NakagamiDistribution allows μ and ω to be any positive real numbers.
- NakagamiDistribution allows ω to be a quantity of any unit dimension and μ to be a dimensionless quantity. »
- NakagamiDistribution can be used with such functions as Mean, CDF, and RandomVariate.
Background & Context
- NakagamiDistribution[μ,ω] represents a continuous statistical distribution supported on the interval and parametrized by positive real numbers μ and ω (called a "shape parameter" and a "spread parameter", respectively), which together determine the overall behavior of its probability density function (PDF). Depending on the values of μ and ω, the PDF of a Nakagami distribution may have any of a number of shapes, including unimodal with a single "peak" (i.e. a global maximum) or monotone decreasing with potential singularities approaching the lower boundary of its domain. In addition, the tails of the PDF are "thin" in the sense that the PDF decreases exponentially rather than decreasing algebraically for large values of . (This behavior can be made quantitatively precise by analyzing the SurvivalFunction of the distribution.) The Nakagami distribution is sometimes referred to as the Nakagami -distribution or Nakagami -distribution.
- The Nakagami distribution was first proposed in a 1960 article by Minoru Nakagami as a mathematical model for small-scale fading in long-distance high-frequency radio wave propagation. In the years since, many applications of the distribution have been wave related. In particular, the Nakagami distribution has been used to model phenomena related to medical ultrasound imaging, communications engineering, and meteorology. It has also been used in various other fields, including hydrology, multimedia, and seismology.
- RandomVariate can be used to give one or more machine- or arbitrary-precision (the latter via the WorkingPrecision option) pseudorandom variates from a Nakagami distribution. Distributed[x,NakagamiDistribution[μ,ω]], written more concisely as xNakagamiDistribution[μ,ω], can be used to assert that a random variable x is distributed according to a Nakagami distribution. Such an assertion can then be used in functions such as Probability, NProbability, Expectation, and NExpectation.
- The probability density and cumulative distribution functions for Nakagami distributions may be given using PDF[NakagamiDistribution[μ,ω],x] and CDF[NakagamiDistribution[μ,ω],x]. The mean, median, variance, raw moments, and central moments may be computed using Mean, Median, Variance, Moment, and CentralMoment, respectively.
- DistributionFitTest can be used to test if a given dataset is consistent with a Nakagami distribution, EstimatedDistribution to estimate a Nakagami parametric distribution from given data, and FindDistributionParameters to fit data to a Nakagami distribution. ProbabilityPlot can be used to generate a plot of the CDF of given data against the CDF of a symbolic Nakagami distribution, and QuantilePlot to generate a plot of the quantiles of given data against the quantiles of a symbolic Nakagami distribution.
- TransformedDistribution can be used to represent a transformed Nakagami distribution, CensoredDistribution to represent the distribution of values censored between upper and lower values, and TruncatedDistribution to represent the distribution of values truncated between upper and lower values. CopulaDistribution can be used to build higher-dimensional distributions that contain a Nakagami distribution, and ProductDistribution can be used to compute a joint distribution with independent component distributions involving Nakagami distributions.
- NakagamiDistribution is related to a number of other distributions. Before the formulation of the Nakagami distribution, the RayleighDistribution and RiceDistribution were commonly used models for wave fading, and the three distributions are qualitatively very similar. In addition, NakagamiDistribution generalizes both RayleighDistribution and HalfNormalDistribution, in the sense that the CDF of NakagamiDistribution[1,2 σ^2] is precisely that of RayleighDistribution[σ], while the PDF of NakagamiDistribution[1/2, π/(2 θ^2)] is exactly that of HalfNormalDistribution[θ]. Moreover, NakagamiDistribution[μ,ω] has the same PDF as both GammaDistribution[μ,Sqrt[ω]/Sqrt[μ],2,0] and as the limit of RiceDistribution[μ,α,Sqrt[ω/2]] as α→0. NakagamiDistribution is also related to HoytDistribution, NormalDistribution, and LogNormalDistribution.
Examplesopen allclose all
Basic Examples (4)
In the theory of fading channels, NakagamiDistribution is used to model fading amplitude for land-mobile and indoor-mobile multipath propagation and also in the presence of ionospheric scintillation. Find the distribution of instantaneous signal-to-noise ratio where , is the energy per symbol, and is the spectral density of white noise:
Show that SNRdist is a GammaDistribution:
Properties & Relations (7)
RayleighDistribution is a special case of Nakagami distribution:
HoytDistribution is related to Nakagami distribution:
Wolfram Research (2010), NakagamiDistribution, Wolfram Language function, https://reference.wolfram.com/language/ref/NakagamiDistribution.html (updated 2016).
Wolfram Language. 2010. "NakagamiDistribution." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2016. https://reference.wolfram.com/language/ref/NakagamiDistribution.html.
Wolfram Language. (2010). NakagamiDistribution. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/NakagamiDistribution.html | s3://commoncrawl/crawl-data/CC-MAIN-2023-50/segments/1700679100745.32/warc/CC-MAIN-20231208112926-20231208142926-00814.warc.gz | CC-MAIN-2023-50 | 5,863 | 24 |
https://ip-numaram.com/ip2c.php | math | How to solve the distance formula
In this blog post, we will be discussing how to solve the distance formula.
How can we solve the distance formula
What is the difficulty in solving problems with formula or model thinking? In the simple example of throwing stones to find the distance, the difficulty is not to solve the quadratic equation of one variable, but that your thinking ability can transform the problem in this business scenario into a problem of solving the company. After completing this transformation, all that remains is the process of matching using your formula library. You can think about how much education at the current school stage teaches students how to transform their thinking ability? More school learning often relies on a large number of question type exercises and produces mechanical memory. For example, when you see the business scenario of stone throwing, you already know that it is converted into equation solving. This problem is not that you know how to analyze and convert, but that you have done similar problems. [answer] a. Analysis: calculate the growth of the average of each business income compared with the previous year. Since the options give percentages, the average growth rate is obtained. According to the formula and the options, item a is selected for this question. Calculate the growth of the average in the first half of 2017 compared with the same period of the previous year. The data in the options are all in units (yuan / set), so the average growth is obtained. According to the formula: In the school learning stage, the most impressive thinking framework is the formula and model, that is, all kinds of problems in the real world can be finally transformed or abstracted into specific formulas or models to solve. For example, when you throw a stone with a parabola, how far can the stone be thrown? Based on the knowledge of physics and mathematics, problems in reality will be transformed into solving a quadratic equation of one variable. The solution of the quadratic equation of one variable can be directly brought into the standard formula to get the answer. Various formula models themselves are the most basic thinking framework, because formula itself is a commonly used axiomatic post theorem obtained by human beings through induction and abstraction after studying various phenomena in the real world. And your actual process of solving the problem is only to apply the formula for deduction. Through the explanation of the above questions, I believe that we have a better grasp of solving such problems. We need to accurately find the total amount and the number of copies through the description of the question stem. When it comes to growth related problems, we need to determine the content of the examination according to whether there is a unit in the final request, and finally substitute it into the corresponding formula to solve it. I believe that through today's study, we can have a better understanding of the problem of average growth. We should practice more on weekdays so that practice makes perfect. Through the explanation of the above questions, I believe that we have a better grasp of solving such problems. We need to accurately find the total amount and the number of copies through the description of the question stem. When it comes to growth related problems, we need to determine the content of the examination according to whether there is a unit in the final request, and finally substitute it into the corresponding formula to solve it. I believe that through the introduction of public education in China, we can have a better understanding of the problem of average growth. We should practice more on weekdays so that practice makes perfect. If the formula related to the proportion of the current period is used, the stem usually gives the partial rate, that is, the molecular rate, and the value of the proportion. It is necessary to find the rate of the proportion before using the formula of the denominator rate to solve the denominator, that is, the overall rate. Basic formula of growth problem (Solving growth volume, growth rate, base period value, current period value), proportion (basic formula and modification of proportion, growth volume of proportion, judging the rise / fall of proportion), multiple, average (basic formula and modification of average, growth rate of average, judging the rise / fall of average), cross, etc.
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It has helped me so much, especially since the lockdown because the corona virus. I can't always ask my teacher to explain the question so it's easier just to use the app. I love the fact that the app gives you the solution instead of just the answer. the app has really helped during this pandemic!!
the app is a best App It helps me when I am confused It is based with kinds of Mathematical expression like Algebra. This app is best because it will help you It's a good app but it was offline now it is online if it is possible to make it usable offline, please! | s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710771.39/warc/CC-MAIN-20221130192708-20221130222708-00417.warc.gz | CC-MAIN-2022-49 | 5,064 | 7 |
https://www.mdpi.com/2227-7390/7/12/1232/htm | math | Reinforced concrete retaining walls (RCRWs) are referred to as structures that withstand the pressure resulting from the difference in the levels caused by embankments, excavations, and/or natural processes. Such situations frequently occur in the construction of several structures, such as bridges, railways, and highways. Due to the frequent application of RCRWs in civil engineering projects, minimizing the construction cost of such structures is an issue of crucial importance.
The satisfaction of both geotechnical and structural design constraints is a key component in the design of RCRWs. In most cases, primary dimensions are initially estimated based on reasonable assumptions and the experience of the designer. Then, in order to reach a cost-effective design while satisfying the design constraints, the design variables (particularly the wall dimensions) need to be revised by using a trial-and-error process, which makes it rather grueling. On the other hand, there is no guarantee that the final design will be the best possible one. To eliminate this problem, which can hinder the designer from reaching a cost-effective solution, and by considering the advances in computational technologies during the recent decades, it makes sense to express the design in the form of a formal optimization problem.
The design optimization of RCRWs has received significant attention during the last two decades. Some of the pertinent works are briefly investigated herein. As a benchmark work, Saribas and Erbatur [1
] used a nonlinear programming method and investigated the sensitivity of the optimum solutions to parameters such as backfill slope, surcharge load, internal friction angle of retained soil, and yield strength of reinforcing steel. The simulated annealing (SA) algorithm has been also applied to minimize the construction cost of RCRWs [2
]. Camp and Akin [4
] developed a procedure to design cantilever RCRWs using Big Bang–Big Crunch optimization. They captured the effects of surcharge load, backfill slope, and internal friction angle of the retained soil on the values of low-cost and low-weight designs with and without a base shear key. Khajehzadeh et al. [5
] used the particle swarm optimization with passive congregation (PSOPC), claiming that the proposed algorithm was able to find an optimal solution better than the original PSO and nonlinear programming. In their work, the weight, cost, and CO2
emissions were chosen as the three objective functions to be minimized. Gandomi et al. [6
] optimized RCRWs by using swarm intelligence techniques, such as accelerated particle swarm optimization (APSO), firefly algorithm (FA), and cuckoo search (CS). They concluded that the CS algorithm outperforms the other ones. They also investigated the sensitivity of the algorithms to surcharge load, base soil friction angle, and backfill slope with respect to the geometry and design parameters. Kaveh and his colleagues (e.g., [7
]) optimized the RCRWs using nature-inspired optimization algorithms, including charged system search (CSS), ray optimization algorithm (RO), dolphin echolocation optimization (DEO), colliding bodies of optimization (CBO), vibrating particles system (VPS), enhanced colliding bodies of optimization (ECBO), and democratic particle swarm optimization (DPSO). Temur and Bekdas [11
] employed the teaching–learning-based optimization (TLBO) algorithm to find the optimum design of cantilever RCRWs. They concluded that the minimum weight of the RCRWs decreases as the internal friction angle of the retained soil increases, and increases with the values of the surcharge load. Ukritchon et al. [12
] presented a framework for finding the optimum design of RCRWs, considering the slope stability. Aydogdu [13
] introduced a new version of a biogeography-based optimization (BBO) algorithm with levy light distribution (LFBBO) and, by using five examples, it was shown that this algorithm outperforms some other metaheuristic algorithms. In this work, the cost of the RCRWs was used as the criterion to find the optimum design. Nandha Kumar and Suribabu [14
] adopted the differential evolution (DE) algorithm to solve the design optimization problem of RCRWs. The results of sensitivity analysis showed that width and thickness of the base slab and toe width increases as the height of stem increases. Gandomi et al. [15
] studied the importance of different boundary constraint handling mechanisms on the performance of the interior search algorithm (ISA). Gandomi and Kashani [16
] minimized the construction cost and weight of RCRWs analyzed by the pseudo-static method. They employed three evolutionary algorithms, DE, evolutionary strategy (ES), and BBO, and concluded that BBO outperforms the others in finding the optimum design of RCRWs. More recently, Mergos and Mantoglou [17
] optimized concrete retaining walls by using the flower pollination algorithm, claiming that this method outperforms PSO and GA.
By taking a look at the studies so far reported, it can be noticed that there has been no work done in assessing the effect of using different available methods of determining the bearing capacity on the optimum design of the RCRWs. The current study investigates this important issue. In order to model and design the RCRWs, a code is developed in MATLAB [18
]. To reach a design with minimum construction cost, an optimization problem is defined and the construction cost is considered as the single objective function to be minimized. The design criteria, including both geotechnical and structural limitations, are considered as the optimization constraints. The wall geometrical dimensions and the amount of steel reinforcement are used as the design variables. The particle swarm optimization (PSO) [19
] algorithm is used to find the optimum solution. | s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623487621450.29/warc/CC-MAIN-20210615145601-20210615175601-00175.warc.gz | CC-MAIN-2021-25 | 5,834 | 20 |
https://nz.pinterest.com/explore/math-formulas/ | math | Definition of Area and Perimeter http://www.khanacademy.org/math/geometry/basic-geometry/perimeter_area_tutorial/v/perimeter-and-area-basics Finding Perimeter in a Coordinate Plane...
Electrical Engineering Community's Tools - geometry reference sheet - many more on this site
Algebra Tool Kit Reference Sheet - Free Printable Cheat Sheets. Four pages of easy-to-memorize algebra formulas.-Homeschool Encouragement
Algebra formula chart.
Handy Chart with Math Formulas.
Mensuration RS Aggarwal Class 7 Maths Solutions Exercise 20C http://www.aplustopper.com/mensuration-rs-aggarwal-class-7-maths-solutions-exercise-20c/
A good breakdown of a few of the most notable relativistic physics equations. They really are rather simple, which is why they are so famous and appreciated.
Circle Formulas that are frequently used. The symbolic notation is briefly explained, and the parts are color coordinated. I'd love to print this off and hang it while teaching geometry!
Geometry Formulas Cheat Sheet | eocgeom05geomformulas.gif | s3://commoncrawl/crawl-data/CC-MAIN-2017-22/segments/1495463607813.12/warc/CC-MAIN-20170524112717-20170524132717-00331.warc.gz | CC-MAIN-2017-22 | 1,022 | 9 |
https://www.internations.org/paris-expats/forum/is-a-french-degree-not-accepted-anywhere-else-1250159?ref=frp_gft | math | Is a French Degree not accepted anywhere else? (Paris)
I have heard that french universities issue degree with Diplome written instead of Degree. This makes it impossible to find a job anywhere else in the world as they reject french degree by calling it a diploma. Is it true?
My daughter wants to go for a law degree in France and if the degree is not accepted anywhere in the world than it is a big gamble.
Can someone please help me? | s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243989614.9/warc/CC-MAIN-20210511122905-20210511152905-00003.warc.gz | CC-MAIN-2021-21 | 437 | 4 |
https://www.vedantu.com/ncert-solutions/ncert-solutions-class-9-maths-chapter-2-exercise-2-2 | math | NCERT Solutions for Class 9 Maths Chapter 2 Polynomials (Ex 2.2) Exercise 2.2
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Vedantu’s Class 9 Maths Chapter 2 Exercise 2.2 includes the following problems from polynomial-
Before discussing polynomials, it is necessary that you have a clear idea about variables and exponents. Consider the following equation -
2x + 3x = 10
Here we don't know at first what X is. When we solve the equation, we come to the conclusion that here X is 2. So, what X does here is it answers the ‘what’ of a question. In this equation, the question that is implied is - what should we multiply 2 and 3 with so that the addition of the product results in 10?
Again when we are confronted with the following equation -
2x + 3x = 20
the result of X changes. So, the value of X varies the situation.
This is what we call variable. This variable is generally denoted by x,y,z etc.
Again, if you look at the above two examples, the values of 2 and 3 never change. In both situations, the values of 2 and 3 remain fixed. These are called constants.
Now, look at this,
Here the value of 2 increases exponentially ( 2*2*2). The power 3 is known as an exponent.
If you look at the algebraic expression - 2x + 3x - written above, you will see there are two parts in it - 2x and 3x. These parts are called terms.
Polynomial is a mathematical expression that has multiple terms and consists of constants, variables and non-negative or non-fractionated exponents. The polynomial will only involve addition, subtraction or multiplication.
So 2x + 3x is a polynomial in the variable X.
Again, 2³ + X³ + 3² is a polynomial.
But X + 1∕X is not a polynomial since 1/x can be written as . As said earlier, a polynomial does not allow negative exponents.
Expressions that have √X are not polynomials too since √X can be written as and we know that this is not accepted by polynomials.
If you look at the expression 2x + 3x, the numbers before the variables are called coefficients.
Here are a few other exercises that you will find in the NCERT Solutions for Class 9 Maths Chapter 2 PDF –
In this exercise of Class 9 Maths Chapter 2, students will be introduced to the concept of polynomials. They will obtain an indent knowledge regarding polynomials in one variable and how to solve the associated sums through shortcut techniques. Here are some important questions for exams that are provided in the exercise.
Question 1: Finding the polynomials among the expressions in one variable and stating reasons for the answers.
Question 2: Finding the coefficients of x2 in the provided expressions.
Question 3: Examples of a binomial of degree 35 and monomial of degree 100.
Question 4: Determining the degree of polynomials.
Question 5: Classifying linear, quadratic and cubic polynomial expressions.
This chapter is a continuation of Exercise 2.2 Class 9 of NCERT maths book. Students will get in-depth knowledge about the Factor Theorem by solving all questions provided in this exercise step by step.
Question 1: Finding the remainder when divided by expressions provided.
Question 2: Determining remainders.
Question 3: Checking if provided expressions are factors.
Vedantu's Polynomials Class 9 solutions will help you understand all the topics included in the Polynomials chapter. NCERT guidelines specifically advise teachers to build the fundamental knowledge of the subjects in the students. Vedantu follows this NCERT advice thoroughly. That is why you will find not only solutions to the questions on polynomials but also the explanations on the logic behind our solutions. For example - in question number 2 of Ex 2.1 of our Polynomials Class 9 NCERT Solutions when we are asked to find the coefficients of given polynomials we showed how has an invisible 1 before it. So the coefficient of X² is 1.
Our answers in Class 9th Maths NCERT Solutions Chapter 2 include every step. No step has been skipped. You will not struggle to understand how we reached the result from a given equation. So in question 1(i) of Ex 2.2, we showed how we arrived at the answer 3 by solving the equation step by step. This will not only help the students to understand the granularities in the chapter but will also help them to get good marks.
Every Polynomial formula Class 9 has been used in our solution. The students will get to learn all the aspects of the chapter. Reading our PDF, a student can answer any question from this chapter with confidence.
The Polynomials Class 9 PDF is written in a lucid language. Apart from the Maths expressions, we have used simple, easy to understand words so that students can understand the solutions. Even the math expressions are adequately explained wherever deemed fit.
The Class 9 Maths Chapter 2 PDF has accurate solutions to every polynomials problem. The answers are written by expert teachers who know how to solve a Maths problem so that students understand the process and even the examiners get impressed by the detailed process. These teachers are well aware of NCERT guidelines and follow them to write their answers. There is no unnecessary information in our solutions.
Vedantu’s Polynomial Class 9 PDF is neatly organised. The solutions are written in an uncluttered, easy to understand way. That is why in question 1 of Ex2.3, you will find that we have used red ink to indicate the cutting off of -2x² and +2x². This visually pleasurable way of reading the solutions will help the students to maintain their focus on the solutions.
You can use our NCERT Solutions for Class 9 Maths Chapter 2 Exercise 2.2 to learn all the intricacies of polynomials. These solutions can provide you with everything that you need to excel in the chapter. The answers in our PDF are not written by part-time bloggers, but they are written by professional teachers who took care to make the solutions as helpful as possible.
The Class 9 Maths Chapter 2 Exercise 2.2 Solutions are absolutely free of cost. You don’t need to pay a single penny to download our PDF. You can simply enter your email id and we will send the download link to your email. Vedantu is not motivated by profit; we are genuinely interested in making the learning process of students better. We believe every Indian student has the right to get a quality education.
Our PDF on polynomials is exhaustive and can help you in finding solutions to all the questions asked in the textbook. Maths needs explanation - countless of times. You might want to ask questions about a particular solution in our PDF. So to help you, Vedantu holds online classes where you can ask questions directly to the teachers. This interaction is particularly necessary for understanding Maths chapters. The schedule of the classes is announced beforehand. We have helpful videos too which will help you understand the solutions in a much more easy and efficient way.
Our online teachers are experts in their subjects and come from respectable institutions like IITs. These teachers know how to teach Maths to students in such a way that students do not get bored. The teachers are aided by simultaneous images, videos and slides. This visual way of teaching ensures easy retention in students.
With our Master Class, you can experience a whole new learning experience. We are offering free seats in our master class for a limited period of time. These masterclasses can enhance your knowledge in ways you cannot fathom. We do not employ cheap tricks and tips. Our main focus is on building the basic knowledge of the students. Our Master Class is not just for advanced students, intermediate students can get benefit from the Master Classes as they will shed fear for Maths and grow a love for the subject.
Vedantu also has its app. This application will help the students to stay in the learning mode 24*7. The app, as of now, boasts of 1 million-plus downloads on Play Store.
Vedantu is here to help the students move forward with confidence. With Vedantu, you have a golden opportunity to make the pillars of your knowledge strong.
Share your contact information
Vedantu academic counsellor will be calling you shortly for your Online Counselling session. | s3://commoncrawl/crawl-data/CC-MAIN-2020-29/segments/1593655911896.73/warc/CC-MAIN-20200710175432-20200710205432-00054.warc.gz | CC-MAIN-2020-29 | 8,146 | 46 |
https://repository.lsu.edu/gradschool_disstheses/4546/ | math | Date of Award
Doctor of Philosophy (PhD)
James M. Pruett
The key to the successful "factory of the future" will be the effective coordination of managerial functions and production operations. The research presented in this dissertation addresses this "coordination" issue, especially in terms of understanding the impact and possibilities which exist in an information-rich environment. Such an environment is often referred to in the literature as being a computer-integrated manufacturing (CIM) environment. An interactive simulation modeling program, MOSES (Manufacturing Organization Simulation and Evaluation System), was developed for the purpose of describing, analyzing, and understanding such manufacturing. MOSES is a copyrighted computer program, a menu-driven, interactive, simulation modeling tool. MOSES users are able to define the manufacturing environment to be simulated by keying in data values (e.g., products, bills of material, and production rates) which describe the organization. MOSES then uses these data values to "build the manufacturing simulation model." That is, once the manufacturing parameters have been defined, MOSES can simulate the manufacturing organization (from orders through distribution) without the user having to write any computer code or having to understand the principles of simulation modeling. MOSES users are then able to interact with the manufacturing organization as "managers" in the dynamic simulation environment. This interactive capability allows MOSES users to test various manufacturing scenarios, watch the model's progress from the perspectives of different organizational functions (e.g., from marketing or from production), override model-generated decisions (e.g., by changing the demand forecast), and view the results. The MOSES approach to simulation modeling differs from traditional approaches. In short, MOSES uses both mathematic and logical modeling principles, employs traditional simulation modeling techniques but in combination with database technology, and includes the user as an integral component in the simulation process.
Vasudev, Vinay Kumar, "Development of a Computer-Integrated Manufacturing Simulation Model: A Hybrid Systems Approach." (1988). LSU Historical Dissertations and Theses. 4546. | s3://commoncrawl/crawl-data/CC-MAIN-2023-50/segments/1700679100599.20/warc/CC-MAIN-20231206130723-20231206160723-00262.warc.gz | CC-MAIN-2023-50 | 2,284 | 5 |
https://perfectessayist.com/let-d-be-the-set-of-all-calendar-dates-from-4-30-1789-to-9-2-2/ | math | Let D be the set of all calendar dates from 4/30/1789 to 9/25/2014. Let P be the set of names of U.S. presidents. Let F be the set of names of first ladies of the U.S. Consider the following two functions press : D ⇒ P where pres(d) is the name of the president of the U.S. on date d (the incumbent on inauguration days, to avoid ambiguity) and lady : P ⇒ F where lady(p) is the name of the first lady of the U.S. during the presidency of president P. 1. Can the composition pres ° lady be defined? What about lady ° pres ?2. Which of the following functional inverses exist and which do not? pres-1, lady-1, (lady°pres)-1, (pres°lady)-1 (the -1 should be in superscript)Thank you. | s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764499710.49/warc/CC-MAIN-20230129080341-20230129110341-00533.warc.gz | CC-MAIN-2023-06 | 689 | 1 |
https://forum.duolingo.com/comment/5524574/Vet-du-vad-Sveriges-kronprinsessa-heter | math | Translation:Do you know what the crown princess of Sweden is called?
This is slightly off the topic of language, but....
Is a "crown prince" or "crown princess" a royal child?
Does a "crown princess" become a "princess" at a certain age?
Or is the "crown prince" the one who is in line for the throne, and his brothers are just called "prince"?
Sorry if this is obvious but we don't have these people in my country and I'm not sure what the difference is between a prince/ss and a crown prince/ss.
Actually, I don't like this question because I thought 'heter' was specifically asking about a person's name even though I think it literally means 'be called.' The reason I bring this up is, in English, it is easy to interpret this sentence to mean 'Do you know what (mean) names the crown princess of Sweden is called?' Alternatively, it could also ask the question as stated, but the answer would be something like "Yes, she is called the crown princess because that is her title." Am I mistaken in thinking the intention of the sentence is to see if we can answer that her name is Victoria?
In English, this word order is wrong.
If you start with, "Do you know what....," then the word "is" has to go to the end of the sentence, like this:
"Do you know what the name of the crown princess of Sweden is?"
Now it is grammatically correct.
However, the "what" and the "is" are not necessary. As a native English speaker, I would not put all of those words in the sentence. I would say it like this:
"Do you know the name of the crown princess of Sweden?" | s3://commoncrawl/crawl-data/CC-MAIN-2021-04/segments/1610703518201.29/warc/CC-MAIN-20210119072933-20210119102933-00541.warc.gz | CC-MAIN-2021-04 | 1,553 | 13 |
http://www.germanshepherds.com/forum/2722938-post3.html | math | Hi Llombardo... thanks for replying! Yes, it seems like Sugarland is pending... hopefully it works out. I thought I would post her anyway as sometimes it doesn't : )
I am thinking I will start to regularly post GSDs from MagMutts on the site. If only I could figure out how to get the pics to show up as pics and not just URLs... can anyone help me with that? Thanks in advance if you can!!!! | s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368702777399/warc/CC-MAIN-20130516111257-00062-ip-10-60-113-184.ec2.internal.warc.gz | CC-MAIN-2013-20 | 392 | 2 |
https://www.nextclima.eu/winter-storm/ | math | A long duration winter storm will begin today across the Southern Plains and then stretch as far as New England by Friday.
A mixture of snow, sleet, and freezing rain is expected, some of which will be heavy. Significant impacts to travel are likely in many areas.Significant ice accumulations greater than 0.25″ are likely from the Red River Valley of Texas through the Ozarks and southeast Missouri.Locally, damaging ice of 0.5″ or more is possible which could lead to scattered power outages, tree damage and dangerous travel.
Another area of freezing rain is likely from the eastern Ohio Valley through the mid-Atlantic states.Significant ice accumulations are possible across south-central Pennsylvania and western Maryland, with hazardous travel possible.Heavy snow is expected across Upstate New York and New England on Friday when snowfall rates will likely eclipse 1″/hr at times.Dangerous travel is likely.
Credits: NOAA and Weathermodels#nextclima#winterstorm#southernplains#newengland#newyorkstate#pennsylvania#maryland#ohiovalley#missouri#texas#ozarks#redrivervalley#extremeweather#severeweather | s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296948858.7/warc/CC-MAIN-20230328104523-20230328134523-00035.warc.gz | CC-MAIN-2023-14 | 1,114 | 4 |
http://www.slideshare.net/jthiessen/medorientation-sept2013session12013 | math | M.Ed. Orientation Library Session: Introduction to Library Research In Education (Sept. 2013)
LIBRARY RESEARCH IN
Liaison Librarian, Education
James A. Gibson Library
The James A. Gibson
Floors 2, 5-10
PatioLSE002 by JISC
Goals for today’s session
• Services (a very brief look)
• MY LIBRARY ACCOUNT
• RACER (Interlibrary Loan)
• Study Space
• RefWorks/Citation management
• Getting started with Library Research
• Finding books and ebooks
• Finding journal articles
• Where to find more…
What library services do you want to
My Library Account
• See items you have signed out
• Place holds
• See if you have any fines
• log in to library databases
from off campus
• Photocopy cards
• Colour and transparency copying
• Posters, photos, banners and other large format prints
• Interlibrary loan system
• Submit requests online for articles, books, book chapters
that Brock does not have
• Books: pick them up and return them at our Circulation
• Articles/book chapters: Get link to online copy emailed to
you (link expires after 5 views or 21 days)
Study spaces on library floors
• Floors 8, 9 and 10: SILENT STUDY
• One-person study rooms; first come, first serve
• Floors 5 and 7: low level talking
• Graduate Study room
• Floor 6
• Swipe card access
• Study carrels, bookable meeting room, lockers
•Save references to books and articles from catalogue
•Automatically create bibliographies or works cited pages
in APA style format.
* optional *
Library Research in Education
• Research Guide
Hint: Start with the Research tab.
• Use the Catalogue to find books (both print and e-books)
• Use the Databases to find journal articles
• Use SuperSearch to search it all
3/365 Research Aspirations by catspyjamasnz
• Go to the Library Catalogue. Do a keyword search on
narrative inquiry. Now do a keyword search on “narrative
inquiry.” Why is there a difference in results?
• Do the same search in Super Search
• What changes?
Click on Education to
see a list of databases
for that subject area.
Click on Research,
• Use library databases
• Try Google Scholar
For finding info
• Looks for full text in other locations (Does not guarantee
• Use Google Scholar from
the Quick Search toolbar
OR set up Library Links in
• Why use Google
• Another database
• Find works that cite a
• See who the important
• Watch: Get Better Results
with Google Scholar
• Find the Education databases.
• Select Education Research Complete.
• Search “international students.” How are the results
arranged? How can you limit your results to peer
reviewed journal articles?
More Search Tips
• Use quotation marks for phrases
• “grounded theory”; “educational leadership”
• Use * to search for alternate endings
• Canad* = Canada, Canadian, etc.; reflect* = reflect, reflection, reflective, etc.
• Use synonyms
• Teenager, adolescent, adolescence, teens, etc.
• Too many results?
• Use limits (peer-reviewed, date, language, etc.)
• Add additional keywords; get more specific
• Too few results?
• Remove one or more keywords
• Go broader (e.g. search Canada instead of Ontario)
Your Research Guide
• Review of what we’ve covered today and more
Information about library services for graduate students can be found
The most important services you should know about are:
My Library Account
Library catalogue – books
Library databases – journal articles
Contact me if you need help:
A particular slide catching your eye?
Clipping is a handy way to collect important slides you want to go back to later. | s3://commoncrawl/crawl-data/CC-MAIN-2015-48/segments/1448398446286.32/warc/CC-MAIN-20151124205406-00128-ip-10-71-132-137.ec2.internal.warc.gz | CC-MAIN-2015-48 | 3,618 | 102 |
https://www.bestdesignsblog.com/using-the-golden-ratio-in-logo-design/ | math | Also known as the golden number, golden ratio, golden number, golden ratio.
Remember those times in math class when you questioned how and when you would ever use math in the real world? I also. But now that I’m a designer, I really wish I had stayed up in Geometry and learned about the golden ratio.
Well in my design career, I learned about the golden ratio and how to use it in design. When I studied it, I realized that this knowledge was one of the missing pieces of my design education. Who knows?!
In this post, you will get a crash course on what the golden ratio is, why and how I use it in logo design, and how you can start applying it to your work.
The golden ratio is a mathematical principle that can be found in nature, anatomy, color, and even sound waves. Due to its pleasant nature, it has been used in art, paintings, architecture, music, and design for thousands of years. Scientific studies have shown that we perceive things that contain the Golden Ratio as a beautiful, harmonious, and bordering perfection, even when we do not know it.
I found that the more I incorporate the golden ratio into my design, the more satisfying the result is. Similar to using a grid in layout design, using Golden Ratio provides a framework for my layout decisions. Of course, you cannot superficially use the Golden Ratio and think that everything will always be perfect. Using these proportions in your design work will take time and practice. But the more you use it, the more you start to see the relationships between the elements of your design and begin to detect and correct areas that are inconsistent in your work and that just don’t feel right.
Now to get technical.
Let’s look at some key terms and concepts. Each builds on the previous one.
To get to the Golden Ratio, we must first understand the Fibonacci number sequence. It can be found everywhere; from the number of petals, there are in a flower to the spirals in sunflower or pineapple to the pattern of keys in a piano. Once you get familiar with this sequence, you will start to see it everywhere.
The sequence is as follows:
1, 1, 2, 3, 5, 8, 13, 21 …
So let’s see how this works. Each number after the first two in the sequence is the sum of the 2 previous numbers.
… and so.
Now let’s put this in visual terms that designers can appreciate.
If we square each number to identify the spatial area, our sequence will now look like this:
And if you are an expert in puzzles, you will begin to see that the progression of the numbers forms a visual pattern:
Crazy, right? You just wait. It gets even better.
The golden ratio
This is where the Golden Ratio comes in.
The ratio of the numbers in the Fibonacci sequence tends towards the golden ratio. The ratio of two consecutive numbers in the sequence gets closer and closer to the golden ratio, 1.618.
The golden ratio is the ratio of two quantities where the ratio of the small quantity (a) to the large quantity (b) is the ratio of the large quantity (b) to the set (a + b).
The golden spiral
The Fibonacci pattern is not only found in nature but there is another pattern within it, called the Fibonacci Spiral (also known as the Golden Spiral). By adding a circular arc to each square, we will produce a perfect spiral:
This spiral may look quite familiar to you if you’ve ever examined a seashell or even seen a picture of a galaxy.
Now that you know what the golden ratio is, let’s use it in the logo design. This is where the fun begins!
Note: for the sake of simplicity, I use the term “golden ratio” when I’m talking about the golden rectangle, spiral, or ratio, as the terms are often used interchangeably.
One of the ways I design logos is by taking all the main forms of the Golden Ratio so that the proportions are harmonious.
Then I combined the shapes and used a grid to align all the parts.
And finally, I refine the points, the shapes and the connections.
Pro Tip: Don’t use more than one golden ratio when designing. If you need a smaller ratio, take it from the golden ratio you started with.
Another way I use the Golden Ratio is to determine the height and width of the logo, as well as the proportions of the strokes.
Pro Tip: Not all strokes can align with the Gold Ratio. In this example, the horizontal strokes must be slightly thinner than the vertical strokes to appear optically the same. Even the Greeks altered it a bit .
Lastly, I use the golden ratio to help me decide the location, size, and length of key elements in a logo.
So you want to use the golden ratio?
Incorporating the golden ratio into your workflow will help you make better and faster design decisions.
Wondering how you can use the golden ratio in your next logo to create a more harmonious and pleasing design?
To really understand it, I would suggest studying first the logos of the Masters, like Paul Rand and Saul Bass, and observe the Golden Relationship in their work. The goal is to train your eye to see. Trace the logos and take note of what you discover. Did the logo use the golden ratio? Did the points within the Golden Ratio of various parts of the logo intersect? Not far from your studio, you will begin to notice the proportions, the relationships between the forms, and the alignment. When you learn to see, you will inevitably make better design decisions.
Next, use the golden ratio as a way to correct the proportions once you have the logo design 90% complete. As you use the golden ratio to refine your work, you will begin to notice how you will incorporate it earlier in your design process. Even if you don’t rush. The goal is to use it as you would a guide and not force it.
Final tip: use it as a guide, not as a rule. Your eyes have the last word. | s3://commoncrawl/crawl-data/CC-MAIN-2024-18/segments/1712297295329.99/warc/CC-MAIN-20240425130216-20240425160216-00694.warc.gz | CC-MAIN-2024-18 | 5,729 | 39 |
http://graphicdesign.stackexchange.com/questions/tagged/color-reproduction+transparency | math | Graphic Design Meta
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cc by-sa 3.0 | s3://commoncrawl/crawl-data/CC-MAIN-2014-35/segments/1409535917463.1/warc/CC-MAIN-20140901014517-00216-ip-10-180-136-8.ec2.internal.warc.gz | CC-MAIN-2014-35 | 2,218 | 53 |
https://thescienceteacher.co.uk/speed-and-motion/ | math | Speed, acceleration and motion teaching resources
Worksheets and lesson ideas to challenge students aged 11 to 16 to think hard about speed, distance-time, acceleration and motion (GCSE and Key Stage 3)
Watch this clip below of a man versus a plane. Who is going to win the race? This clip can serve as an excellent platform to begin thinking about the difference between average speed, instantaneous speed and acceleration.
Distance-time graphs and calculating speed
Key Stage 3 activity on distance-time graphs and speed. Students walk through a distance time graph in the classroom before sketching a distance-time graph for different activities. Ask students to draw a distance-time graph for their journey into school before modelling how to calculate speed from a distance-time graph. Focus on how the units of speed help us. (PDF)
Breaking distance, stopping distance and thinking distance
Why is the UK speed limit 70 mph? This is a great question to pose before you introduce the concept of stopping distance. Most students will believe the speed limit is set at 70 mph because travelling fast is dangerous. Although this is true, the real danger comes from the fact that travelling fast makes it hard to stop. The 70 mph speed limit was set in 1965 when cars weren’t quite so good at stopping. This clip from Top Gear will help students appreciate cars from the past! Should then the speed limit increase to reflect the advancements in motor car technology and if so, to what speed?! A good question that could be answered with some simple maths. | s3://commoncrawl/crawl-data/CC-MAIN-2023-50/segments/1700679100651.34/warc/CC-MAIN-20231207090036-20231207120036-00111.warc.gz | CC-MAIN-2023-50 | 1,558 | 7 |
https://socialcar-project.eu/en/a-certain-bank-assigns-one-unique-number-to-each-savings-account-the-amount-of-savings-in-each-acco.9902978.html | math | A certain bank assigns one unique number to each savings account. The amount of savings in each account depends on how much the owner deposits into the account. The interest paid on each account depends on how much money is in the account. Which of these relations is not a function? (interest paid, savings account number) (interest paid, amount in savings account) (savings account number, interest paid) (savings account number, amount in savings account)
All the ones with saving account number are not functions because the outcome does not depend on the account number. It depends on the amount in the account and the interest. | s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882571472.69/warc/CC-MAIN-20220811133823-20220811163823-00350.warc.gz | CC-MAIN-2022-33 | 633 | 2 |
https://donghiadigest.com/key-29 | math | Math helper online
There are a lot of Math helper online that are available online. Our website can solve math word problems.
The Best Math helper online
There is Math helper online that can make the process much easier. Unlike elementary functions and derivative functions, this section is relatively simple. As long as you master the core formulas and angle changes, and skillfully use them in brushing questions, you can flexibly solve problems! But the difficulty is that many students do not thoroughly analyze the question type! I have no idea how to solve the problem! The main contents of this chapter include: acute angle trigonometric functions (sine, cosine and tangent), and solving right triangle. Acute angle trigonometric function is the trigonometric function when the independent variable is acute angle, that is, the trigonometric function after narrowing the definition domain. Solving right triangles is widely used in practice.
Secondly, we can also assign some oral homework. For example, in the second grade textbook, to let students know the direction, we can assign homework in this way. On the way home, tell me your way home. The route when you came.
After that, the function value in a specific state can be solved by substituting the independent variable in a specific state. For example, Newton's second law and the differential form of Maxwell's equations are all such differential equations. Note that the above formula integrates the independent variable x, and after integration, it becomes a function with only one parameter alpha, which is very important in understanding the variational method to solve differential equations. ① Clem's law There are two preconditions for solving the equations with Clem's law, one is that the number of equations should be equal to the number of unknowns, and the other is that the determinant of the coefficient matrix should not be equal to zero.
The free download website of design elements provides free download of a variety of design elements. There are also many poster templates for marketing creation, 80 fonts and 2000 materials, which are free and commercially available Unsplash, a free HD image download website, will also have a smaller number of pictures, but fortunately, it is also free to download and use. Above, the materials of these three websites can be used for nothing. If you feel that the resources of a single website can not meet the requirements, you can use them together, and you will always find the right pictures. For those who need material websites, there are a lot of materials on this website, including design, e-commerce, illustration, background pictures, videos and audio materials, which can be found here.
In the cross roller bearing, because the cylindrical rollers are vertically arranged on the V-shaped groove rolling surface with a 90 degree shape through spacer blocks, the cross roller bearing can bear radial load, axial load, torque load and other multi-directional loads. The size of the inner and outer rings is miniaturized, and the extremely thin form is a small size close to the limit, and has high rigidity. Therefore, it is most suitable for the joints and rotating parts of industrial robots, the rotating table of machining centers, the rotating part of robots, precision rotating tables, medical machines, calculators, IC manufacturing devices and other equipment. Structural characteristics of cross roller bearing: cross roller bearing is a cylindrical roller that is vertically arranged on the rolling surface with a 90 degree V-shaped groove through spacer blocks. The size of the inner and outer rings is miniaturized, and the extremely thin form is a small size close to the limit.
We will support you with math difficulties
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https://www.nber.org/papers/w2807 | math | The Excess Smoothness of Consumption: Identification and Interpretation
The paper investigates the implications of the omitted information problem -- that is, the econometric problem which arises because an econometrician cannot explicitly include the complete set of variables potentially used by agents -- in the context of the "excess smoothness" phenomenon posed by Deaton 11987]. The paper shows that an econometrician who fails to take into account the effects of omitted information will incorrectly conclude that an empirical finding of excess smoothness of consumption implies that the income process is nonstationary. By contrast, with a more thorough understanding of the omitted information problem, the finding of excess smoothness of consumption is easily explained with two assumptions: a) the consumption data is generated by the excess sensitivity alternative hypothesis, in which consumption is a weighted average of current income and permanent income, and b) agents are forecasting on the basis of a larger information set than the econometrician. Further, excess smoothness is revealed to be consistent with a wide range of stationary income processes as well as nonstationary income processes. Thus the common presumption that the excess smoothness phenomenon is linked in an essential way to the stationarity or nonstationarity of the income process evaporates when omitted information is taken into consideration. | s3://commoncrawl/crawl-data/CC-MAIN-2020-45/segments/1603107919459.92/warc/CC-MAIN-20201031151830-20201031181830-00253.warc.gz | CC-MAIN-2020-45 | 1,437 | 2 |
https://foxoyo.com/search?q=what%20is%20matrix?&noTracking=true | math | Showing results for
what is matrix?
What is Matrix Acidizing?
Treatment of a reservoir formation with fluid containing a surfactant
When the injection pressure is more than the fracture pressure
Treatment of a reservoir formation with fluid containing base
When the injection pressure is less than the fracture pressure
How will you find “What is Matrix?”
Ask the Oracle
Swallow the Red Pill
Pick up the Phone
Find the Key Maker
If the coefficient matrix of a linear system has rank 4, and the augmented matrix has rank 5, then
The system has infinitely many solutions
The system is inconsistent
There are fewer variables than equations
The system is homogeneous
A polymer matrix composite is reinforced with long continuous ceramic fibres aligned in one directio...
EC = (1 - f)Em + fEf
EC = (1 - f)Ef + fEm
1/EC = (1 - f)/Em + f/Ef
1/EC = (1 - f)/Ef + f/Em
A is a 2 * 2 matrix given below:A = The eigenvalues of A are
The approximate eigenvalue of the matrixobtained after two iterations of Power method, with the init...
If the transpose of a matrix is equal to its inverse, then the matrix is
Consider the following Assertion [a] and Reason [r] [a] M is an orthogonal matrix, but not a skew-sy...
[a] is right [r] is wrong
[a] is right [r] is right
[a] is wrong [r] is right
[a] is wrong [r] is wrong
The matrix A= can be decomposed uniquely into the product A = LU, where and The solution of the sys...
[1 1 1]t
[1 1 0]t
[0 1 1]t
[1 0 1]t
If a connected Graph (G) contains n vertices what would be the rank of its incidence matrix
values greater than n are possible
values less than n-1 are possible
Insufficient Information is given
If the A-matrix of the state space model of a SISO linear time invariant system is rank deficient, t...
a pole with a positive real part
a pole with a negative real part
a pole with a positive imaginary part
a pole at the origin
If row-major order is used, how is the following matrix stored in memory?a b cd e fg h i
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http://www.vvc.edu/academic/mathematics/math-63-pre-statistics-mathematics.shtml | math | MATH 63 - Pre-Statistics Mathematics
The math department began offering a new math course and pathway to graduation in the fall 2015 term. Math 63 is specifically designed for students who are not going into math-intensive careers. For those of you going into fields involving lots of math (math, any science, computer science, business, engineering, nursing, EMT, RT, or teaching) this will not be of concern to you. For the rest of you, though, Math 63 is a new course which comes right after Math 12 or Math 42. It is a 5-unit course which will allow you to bypass Math 42 and Math 90, and move straight into Math 120, Intro to Statistics! Math 120 will meet your graduation requirement and also satisfies transfer GE requirements for many majors at many universities (i.e., Criminal Justice, Child Development, Communication Studies, History, Sociology, Psychology, Geography, Political Science, English, and many others).
Math 63 will not be your standard math class! It will utilize graphing calculators, group activities, and will be highly interactive. For those of you who struggle with the typical algebra, the course may help, as you will only be learning the core topics that will be expressly useful to help you master Math 120 (Intro to Statistics). It will be challenging in a different sort of way, focusing on the concepts, reasoning and logic needed to be successful, rather than just having an emphasis on the arithmetic. The focus will be on real-life applications that will make sense; you won’t be asking “When will I ever use this?”
To summarize, if you are in Math 12 now (for example), instead of taking Math 42 followed by Math 90, you will be able to take Math 63 followed by Math 120 instead.
If you have other questions, ask your math teacher or counselor. If they don’t know the answer, they will get the answer for you and report back to you.
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http://relativity.livingreviews.org/Articles/lrr-2003-1/articlese3.html | math | In the GPS, the time variable becomes a coordinate time in the rotating frame of the earth, which is realized by applying appropriate corrections while performing synchronization processes. Synchronization is thus performed in the underlying inertial frame in which self-consistency can be achieved.
With this understanding, I next need to describe the gravitational fields near the earth due to the earth’s mass itself. Assume for the moment that earth’s mass distribution is static, and that there exists a locally inertial, non-rotating, freely falling coordinate system with origin at the earth’s center of mass, and write an approximate solution of Einstein’s field equations in isotropic coordinates:1. The angle is the polar angle measured downward from the axis of rotational symmetry; is the Legendre polynomial of degree 2. In using Eq. (12), it is an adequate approximation to retain only terms of first order in the small quantity . Higher multipole moment contributions to Eq. (13) have a very small effect for relativity in GPS.
One additional expression for the invariant interval is needed: the transformation of Eq. (12) to a rotating, ECEF coordinate system by means of transformations equivalent to Eqs. (3). The transformations for spherical polar coordinates are:
The Earth’s geoid. In Eqs. (12) and (15), the rate of coordinate time is determined by atomic clocks at rest at infinity. The rate of GPS coordinate time, however, is closely related to International Atomic Time (TAI), which is a time scale computed by the BIPM in Paris on the basis of inputs from hundreds of primary time standards, hydrogen masers, and other clocks from all over the world. In producing this time scale, corrections are applied to reduce the elapsed proper times on the contributing clocks to earth’s geoid, a surface of constant effective gravitational equipotential at mean sea level in the ECEF.
Universal Coordinated Time (UTC) is another time scale, which differs from TAI by a whole number of leap seconds. These leap seconds are inserted every so often into UTC so that UTC continues to correspond to time determined by earth’s rotation. Time standards organizations that contribute to TAI and UTC generally maintain their own time scales. For example, the time scale of the U.S. Naval Observatory, based on an ensemble of Hydrogen masers and Cs clocks, is denoted UTC(USNO). GPS time is steered so that, apart from the leap second differences, it stays within 100 ns UTC(USNO). Usually, this steering is so successful that the difference between GPS time and UTC(USNO) is less than about 40 ns. GPS equipment cannot tolerate leap seconds, as such sudden jumps in time would cause receivers to lose their lock on transmitted signals, and other undesirable transients would occur.
To account for the fact that reference clocks for the GPS are not at infinity, I shall consider the rates of atomic clocks at rest on the earth’s geoid. These clocks move because of the earth’s spin; also, they are at varying distances from the earth’s center of mass since the earth is slightly oblate. In order to proceed one needs a model expression for the shape of this surface, and a value for the effective gravitational potential on this surface in the rotating frame.
For this calculation, I use Eq. (15) in the ECEF. For a clock at rest on earth, Eq. (15) reduces to, a “Terrestrial Time” scale (TT) has been defined by adopting the value . Eq. (18) agrees with this definition to within the accuracy needed for the GPS.
From Eq. (15), for clocks on the geoid,10. Note that these effects sum to about 10,000 times larger than the fractional frequency stability of a high-performance Cesium clock. The shape of the geoid in this model can be obtained by setting and solving Eq. (16) for in terms of . The first few terms in a power series in the variable can be expressed as
Better models can be found in the literature of geophysics [18, 9, 15]. The next term in the multipole expansion of the earth’s gravity field is about a thousand times smaller than the contribution from ; although the actual shape of the geoid can differ from Eq. (20) by as much as 100 meters, the effects of such terms on timing in the GPS are small. Incorporating up to 20 higher zonal harmonics in the calculation affects the value of only in the sixth significant figure.
Observers at rest on the geoid define the unit of time in terms of the proper rate of atomic clocks. In Eq. (19), is a constant. On the left side of Eq. (19), is the increment of proper time elapsed on a standard clock at rest, in terms of the elapsed coordinate time . Thus, the very useful result has emerged, that ideal clocks at rest on the geoid of the rotating earth all beat at the same rate. This is reasonable since the earth’s surface is a gravitational equipotential surface in the rotating frame. (It is true for the actual geoid whereas I have constructed a model.) Considering clocks at two different latitudes, the one further north will be closer to the earth’s center because of the flattening – it will therefore be more redshifted. However, it is also closer to the axis of rotation, and going more slowly, so it suffers less second-order Doppler shift. The earth’s oblateness gives rise to an important quadrupole correction. This combination of effects cancels exactly on the reference surface.
Since all clocks at rest on the geoid beat at the same rate, it is advantageous to exploit this fact to redefine the rate of coordinate time. In Eq. (12) the rate of coordinate time is defined by standard clocks at rest at infinity. I want instead to define the rate of coordinate time by standard clocks at rest on the surface of the earth. Therefore, I shall define a new coordinate time by means of a constant rate change:10 (see Eq. (18)).
When this time scale change is made, the metric of Eq. (15) in the earth-fixed rotating frame becomes
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https://www.grasshopper3d.com/forum/topics/cross-pattern-for-list-management | math | algorithmic modeling for Rhino
Here is an example definition which I use to teach my students about List Management..
There are materials showing some different ways managing list..
Please enable display components each by each..
It works with GH 0.9.0006..
thank you, this is helpful | s3://commoncrawl/crawl-data/CC-MAIN-2020-24/segments/1590347413097.49/warc/CC-MAIN-20200531085047-20200531115047-00031.warc.gz | CC-MAIN-2020-24 | 284 | 6 |
http://bado-shanai.net/Map%20of%20Physics/mopPhotodynamics.htm | math | The Photodynamics of Moving Bodies
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In the quantum theory we associate with a photon two kinematic properties that correspond to two dynamic properties. We associate the photon=s energy with an angular frequency,
and we associate the photon=s linear momentum with a wave number,
Those kinematic properties come to us as the reciprocals of the elapsed time and the spanned distance that we associate with one radian of one cycle of the electromagnetic wave of which the photon is a curd (ah, yes, the cottage cheese theory of light). I now want to work out the equations that will transform those properties as one observer would measure them into the same properties as another observer, moving relative to the first along their common x-axis, would measure them. In doing so I will obtain something like a reciprocal Lorentz Transformation.
As usual, we will use a series of imaginary experiments to work out the equations that we want. As we do with real experiments, we so design our imaginary experiments that they will produce events that will reveal the information we want. Our imaginary measurements of those events will have missing pieces whose mathematical form we infer from the requirement that they be consistent with the known laws of physics and of logic.
We begin with Observer Stationary Stan, who has a body of mass M floating at the origin of a coordinate grid that he has etched into the phlogistonic emulsion embedded in the Šther filling the region in which he will conduct his experiment. We can use non-existent fantasy materials, such as phlogiston and Šther, in these experiments as aids to the imagination so long as they do not interfere with the action of the experiment: in this case we use the phlogistonic emulsion as a medium on which we can draw and make measurements without in any way changing the properties of the experimental body or of any photons involved in Stan=s experiments.
Stan contrives to make his experimental body emit two identical photons in opposite directions in the x-y plane (I will ignore the z-direction in this essay for convenience, since whatever we infer for the y-direction applies also to the z-direction). Emission of those photons reduces the mass of the emitting body byΔM, so each photon carries energy
Because photons possess no rest mass, they have the relationship E=pA c between their energies and their linear momenta. Thus each of Stan=s photons carries linear momentum
in which the vector c designates the fact that the photon moves at the speed of light in a specific direction. Because the two photons go in opposite directions, their linear momenta cancel out and the linear momentum of the emitting body remains equal to zero.
Stan has put three clocks into his setup. The clock on the emitting body stops at time t0 when the body emits the two photons. The two other clocks, one at y=a, x=b and the other at y=-a, x=-b, stop at time t1 when they absorb the photons. As the photons travel they etch a trace of their passage into the phlogistonic emulsion, thereby drawing straight lines that make an angleθ with the x-axis such that
Now let=s turn our attention to Observer Mobile Monica. She moves at speed V in the negative direction parallel to Stan=s x-axis and she has contrived for her x=-axis to coincide with Stan= s x-axis for convenience. She has also established her y=-axis parallel to Stan= s y-axis. Thus, as Monica observes them, Stan, his coordinate grid, and his apparatus move at the speed V in her positive x= -direction. If Stan measures between two events the distances and duration x, y, and t, then Monica will measure between those same two events the distances and duration x=, y=, and t=, which she can relate to Stan=s measurements through the Lorentz Transformation:
1. In Monica=s frame Stan=s frame moves a distance Vt= between the two events, so Monica must add that distance to the dilated version of the distance that Stan measures between the events in the x-direction. Further, because Stan=s clocks tick off time that has dilated in Monica=s frame to fill more time ticked off Monica=s clocks, Monica must account for that dilation in her calculation;
2. Oriented perpendicular to the direction of relative motion, the y-direction doesn=t change for either observer;
3. As noted, Monica must account for the dilation of time elapsed on Stan=s clocks. If Stan=s clocks are separated from each other by some distance in the x-direction, Monica must add a temporal offset to the dilated time to compensate the fact that in her frame Stan=s fore clock appears pushed into the past relative to his aft clock;
Monica also knows that in her frame Stan=s emitting body initially ponders a mass
That fact implies that the photons carry away an energy that corresponds to
but Monica wants a proof. Conservation of energy should give her a good enough proof, but she wants to augment it with a proof that involves a different conservation law.
Imagine that a rod made of massless, transparent unobtainium extends in the negative y-direction from Stan=s emitting body. The body emits a burst of photons into the rod, they propagate to its far end, and there they condense into a body of massμ (the physical laws that process would violate are irrelevant to the subject of our imaginary experiment, so we can ignore them just as we ignore other irrelevant details, such as the color of the emitting body). Because of Newton=s third law of motion, the emitting body recoiled when it emitted the photons, so it moved a small distance y1 from the origin of Stan=s coordinate grid as the photons moved a distance y2 before condensing into a small body. No external forces acted on that little system, so it remains balanced on the origin of Stan=s coordinate grid; that is, the system=s center of mass remains on the grid=s origin. That fact means that if Stan puts a needle on his x-axis and pushes it against the unobtainium rod where it crosses the grid=s origin, the compound body will accelerate but it will not rotate. From the counterbalancing of the inertially instigated torques in the composite body Stan can then calculate
Reality has the fundamental property that any event that exists for one observer necessarily exists for all observers (even if they don=t actually observe it). Thus Monica will also observe Stan=s composite body accelerating (though at a rate different from the one that Stan calculates from his measurements) and not rotating. That latter observation tells Monica that the composite body is balanced in her frame, that the inertially induced torques acting on the component bodies counterbalance each other, so she writes her own version of Equation 11 as
Monica knows that y=2=y2 and y=1=y1. She also has Equation 9, so now she knows that the law of conservation of angular momentum necessitates that Equation 10 stand true to Reality.
Referring back to Stan=s original experiment, Monica now knows for certain that the two photons each carry an amount of energy equal to
By way of Equation 1 and Stan=s measurement of each photon=s angular frequency, Monica also knows that
This puzzles Monica because she knows that frequency corresponds to the reciprocal of an elapsed time, so time dilation should make the frequencies of the photons in her frame smaller, not larger. For the moment she leaves it as a paradox that she will resolve later and turns her attention to the photons= linear momenta.
In Stan=s frame the emitting body doesn=t move, so it suffers no change of linear momentum when it emits the photons. But in Monica=s frame the body initially carries momentum M=V, so when it emits the two photons it loses an amount of linear momentum equal toΔM=V. To satisfy the laws of conservation of linear momentum, the photons must have taken that momentum with them, so now Monica knows that each photon took
to add to the linear momentum conferred upon it by its emission.
She must add that amount to the x-component of the basic momentum of the photon as it appears in her frame. If she and Stan were to observe a photon propagating in the x-direction only and if, at some instant, they could take a picture of it by way of some Štherial camera, they would find that the photon spans the distance between two points. But that distance is shorter for Monica than it is for Stan, so the wave number of the photon and, therefore, its momentum must be correspondingly larger; that is, Monica has
When she adds in the momentum from Equation 15, she gets
She knows right away that the component of the momentum in the y-direction cannot differ between her frame and Stan=s, so she has
And lastly Monica looks at the photon=s energy and associated angular frequency. She already has Equation 14, which tells her how the photon=s fundamental energy differs in her frame from its value in Stan=s frame. But in her frame another phenomenon comes into play. Whenever a body absorbs or emits light, that light exerts a force upon the body as it enacts the transfer of momentum, thereby obliging the body to exert the necessary equal and oppositely directed force upon the light. If the body is moving, then the latter force does work upon the light, changing its energy. For a single photon emitted in the direction of the body=s motion (or for the component of a photon=s momentum parallel to the direction of motion) the net work done on the photon corresponds to
Adding that result to Equation 14 gives Monica
In accordance with Equations 1 and 2, Monica divides Equations 17, 18, and 20 by Planck=s constant (S) and obtains the wave-parameter analogue of the Lorentz Transformation:
With those equations she conducts a simple test. She calculates
which gives her the wave-parameter analogue of the Minkowski metric.
Now she can go back and resolve a minor paradox that she discerned earlier. She takes the case in which k=x=0, which represents a photon moving only in the y-direction in her frame, and calculates from Equation 21 that
Substituting that into Equation 23 to calculate the corresponding frequency gives her
which displays what she originally anticipated based on time dilation acting on the emitted photons. She now has the wave-parameter analogue of the Lorentz-Fitzgerald contraction.
And finally Monica substitutes kx=kCosθ and ω/c=k into Equation 21 to get
From her previous study she knows that Stan=s photons trace in her frame paths that make an angleθ= away from her x=-axis in accordance with
Monica substitutes that into Equation 27, divides the equation by Cosθ+V/c, and multiplies the equation by 1+Cosθ(V/c) to get
which is the reciprocal, to within a constant factor, of the relativistically Doppler shifted wavelength of the photon. Substituting kx=Cosθ(ω/c) into Equation 23 gives her
which describes the relativistic Doppler shift of the photon=s frequency.
Now Stan and Monica have a version of the Lorentz Transformation that they will find useful in the development of the quantum theory, among other things.
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https://au.mathworks.com/matlabcentral/fileexchange/38909-parametrized-uniform-triangulation-of-3d-circle-sphere?s_tid=prof_contriblnk | math | Function sphereTriangulation discretize a sphere parametrized with:
- radius R and,
- number of division.
Triangles are formed by spiting unit octahedron triangles, so nice mesh is retrieved. My usage was for FEM analysis - results are stored so that they could be used for saving in STL and further meshing.
Code is short and commented, if You have any question You can post.
Arso (2020). Parametrized uniform triangulation of 3D circle/sphere (https://www.mathworks.com/matlabcentral/fileexchange/38909-parametrized-uniform-triangulation-of-3d-circle-sphere), MATLAB Central File Exchange. Retrieved . | s3://commoncrawl/crawl-data/CC-MAIN-2020-24/segments/1590347436828.65/warc/CC-MAIN-20200604001115-20200604031115-00288.warc.gz | CC-MAIN-2020-24 | 603 | 6 |
http://bandersnatch.ca/to-my-sweet-babboo/ | math | Basic Encryption Techniques and Love Professions
Tired of waiting for JAC Secrets to post about your crush? Talking face-to-face is risky, and notes can be compromised…but not if they’re encoded.
Try the Caesar cipher by shifting the alphabet used by a given value. While the normal alphabet reads: ABCDEFGHIJKLMNOPQRSTUVWXYZ, one shifted by 3 starts on the third letter: CDEFGHIJKLMNOPQRSTUVWXYZAB. The word “VALENTINE” then reads “YDOHQWLGH.” Your crush can decode your message without knowing the number of shifts by the frequency with which each letter is used. An experiment at Cornell University showed that 12.02% of a 40,000 word sample consisted of the letter E, followed by 9.10% T, and 8.12% A; certain letters appear more frequently in the English language than others.
Your nosy friends could probably solve it too, so employ a polyalphabetic cipher, which requires multiple shifts indicated by a code word.
Say your code word is LOVE and your message is WILLYOUGOOUTWITHME. Shift the alphabet so that it starts on the first letter of the code word, L, and find the letter corresponding to W (the first letter of your message). Your alphabet is LMNOPQRSTUVWXYZABCDEFGHIJK, and the first encoded letter is H. For the second letter of the message, use the second letter of the code word’s Caesar cipher. Repeat the key word until your entire message is encoded as IXHQKD LAD QY IXPM YT. This cipher levels the letter frequencies, since the Caesar ciphers used cycle with the code word.
Not convinced that only your crush will know your true feelings? The one-time pad nearly ensures unpredictability. Randomly reorder the numbers 1 through 26. This sequence is the list of shifts that your beloved will use to decode your secret message. If you have 25-21-7-8-14-13-23-5-12-16-17-22-24-18-20-1-19-3-2-9-10-11-6-4-15-26, do a Caesar cipher with a shift of 25 for the first letter of your message, 21 for the second, 7 for the third, and so on.
A Caesar cipher yields 26 possible results for a given message and can be cracked with brute force. The one time pad creates 26^n combinations, where n is the number of letters in your message, since each letter is independently shifted by a random number. Now no one –not even your paramour– will decode your message! | s3://commoncrawl/crawl-data/CC-MAIN-2023-50/segments/1700679100550.40/warc/CC-MAIN-20231205073336-20231205103336-00835.warc.gz | CC-MAIN-2023-50 | 2,290 | 7 |
http://shailpatels.me/EG/index.html | math | About 100 years ago, one of the founders of modern formal logic, the American logician and philosopher of language Charles Sanders Peirce, expressed concerns regarding the traditional linear notation of formal logic. Thus, Peirce proposed an alternative system with a more graphical notation, called Existential Graphs (Peirce, 1933) .
Existential Graphs are a little-known diagrammatic representation that can be used for propositional, first-order, and modal logic. They hardly use any special symbols and contain only 4 rules of inferences but are sound and complete.
Alpha is the part of Existential Graphs (EG) corresponding to propositional logic (PL).
To assert some statement in EG, you put the symbolization of that statement on a sheet of paper, called the 'Sheet of Assertion' (SA) .
Notice that the location of the symbolization on the SA does not matter:
By drawing the symbolization of two statements on the SA, you are asserting the truth of both statements at once. Therefore, mere juxtaposition of two symbolizations on the SA can be interpreted as the assertion of a single conjunction.
This EG can be interpreted as the assertion of two statements: P, Q or as a conjunction: P ∧ Q
Since any number of symbolizations can be juxtaposed on the SA, juxtaposition becomes a kind of generalized conjunction. Since the location of each of the symbolizations on the SA does not matter, no particular order on these conjuncts is imposed. This coincides with our abstract understanding of conjunction which gives Existential Graphs an important advantage over the linear notation of traditional propositional logic.
For example by symbolizing P, Q on the SA, the EG can represent P , Q , P ∧ Q , and Q ∧ P all at once!
Asserting a negation can be done by drawing a cut around a symbol. A cut can be any enclosing figure. In Existential Graphs, an empty graph represents a tautology whereas an empty cut represents a contradiction.
This EG represents: ¬P
This EG represents a Tautology: ⊤
This EG represents a Contradiction: ⊥
Cuts can be nested, each nested symbol is one level above its parent.
In this EG P and Q is level 2, the cuts surrounding them are level 1, and the outermost cut is level 0
So far using these rules of symbolization can represent conjunction, negation, and simple letters for atomic statements, any compound or truth functional statement can be represented by an Existential Graph. Because conjunction and negation form an expressively complete set of operators, EG is also expressively complete.
Examples of EG to propositional logic
Insertion and Erasure are rules of inference while Double cut and Iteration/De-iteration are rules of Equivalence.
Insertion allows inserting a graph at any odd level.
Erasure allows erasing any graph from any even level.
Double Cut allows drawing or erasing a double cut around any subgraph. This is similar to a double negation in propositional logic.
Iteration/De-iteration allows placing or erasing a copy of any subgraph at any nested level.
A formal proof in Existential Graphs consists in the successive application of inference rules to transform one graph into another. Formal proofs in EG are used just as in traditional logic | s3://commoncrawl/crawl-data/CC-MAIN-2020-24/segments/1590347402885.41/warc/CC-MAIN-20200529085930-20200529115930-00116.warc.gz | CC-MAIN-2020-24 | 3,216 | 23 |
http://www.rawbw.com/~hinshaw/cgi-bin/id?3549 | math | +-- William Hinshaw | 1808-1885 | | Jacob Madison Hinshaw ---+ B: c1840 | D: 1861 | +-- Rhody - c1806-? M: Almarinda Walker +-- William A. Hinshaw, c1860-c1866 +-- Jacob Madison Hinshaw, Jr., 1862-1941
|Jacob Madison Hinshaw [ID 03549]||Click here to switch to Ahnentafel view:|
(Jacob Madison Hinshaw)159 (Jacob Madison Hensie)162 (Jacob Madison Hinchey)162,a,45,b (Madison J. Hinchy)c (Matt Hinshaw)159 (Matt Hincher)162
Born about 1840, Tennessee.d,174,e,159
He married Almarinda Walker, Sep 22 1858, Hawkins County, Tennessee.45,159,162,174,a,b (Almarind Walker)162,e (Lorinda Walker)45,162,a,f,b (Rinda Walker)g (Elias Beal, Security).f Almarinda, daughter of Gabriel Walker & Rebecca Jane Hinshaw, was born about 1843, Tennessee.162,g,h,i
Jacob and family were shown in the 1860 census (Jul 13-16 1860), Greene County, Tennessee:e
Jacob Madison Hinshaw died Nov 30 1861, Green County, Tennessee; age 22; buried Long Family Cemetery, near Bulls Gap, Tennessee.159
Jacob was hung for his Union loyalties. Tennessee voted for secession on June 8, 1861, with residents of eastern Tennessee voting two-to-one against secession but losing the vote to the state's larger western population. Rev. William Carter, who had been a delegate to an early 1861 convention of pro-Union loyalists at Greeneville, devised a plan to burn down the railroad bridge over Lick Creek, near Potterstown in Greene County. Carter went to Washington and met with President Abraham Lincoln, General George McClellan and Secretary of War William Seward. Lincoln gave his personal approval for the plan and assured Carter that the Union army would invade eastern Tennessee from Kentucky immediately after the bridge burning to protect the Union loyalists.159
Carter returned to Green County and, with the help of David Fry, assembled a party of 40 to 60 loyalist men. The men gathered at the home of Jacob Harmon on the night of November 8. In a corner of a large room was placed a small wooden table, over which was spread a United States flag. Each man stepped forward, one at a time, and placed his left hand on the flag, raised his right hand, and took an oath to "do what was ordered of him that night and to never disclose what he had done.".159
After midnight, the raiders set out on horseback for the two-mile ride to the wooden railroad bridge across Lick Creek. About 2:00 A.M. on November 9, they captured several Confederate guards inside a tent at one end of the bridge. Some of the men set fire to the bridge, while others gave the guards a choice: swear loyalty to the United States or die on the spot (none of the guards chose to die that night).159
By the next day (November 10), Confederate authorities had tracked down five of the conspirators, including Jacob Hinshaw. The promised invasion of Union soldiers never happened.159
On November 11, Confederate Colonel W.B. Wood sent a dispatch to General Samuel Cooper requesting instructions. Colonel Daniel Leadbetter, Provisional Army, was assigned to the command of troops to rebuild the bridge.159
By November 25, time was running out for Jacob and his co-conspirators. That day, J.C. Ramsey, district attorney for the Confederate District of Tennessee, sent a dispatch to Confederate War Secretary Benjamin: "The military authorities in command at this post have determined to try the bridge-burners and other men charged with treason by a court-martial. What shall I do? Answer.". Benjamin sent an immediate and abrupt reply: "I am very glad to hear of the action of the military authorities and hope to hear they have hung every bridge-burner at the end of the burned bridge".159
On November 30, a dispatch from Colonel Leadbetter was sent from Greeneville, Tennessee: "Two insurgents have to-day been tried for bridge-burning, found guilty, and hanged.". The two insurgents were Henry Fry and Jacob Madison "Matt" Hinshaw, who were both hanged from a large tree near the old railway depot in Greeneville. Colonel Leadbetter ordered their bodies be left hanging on display for hours, as a warning to others.159
Jacob left his wife with 18-month old son William, and two months after Jacob was hanged Almarinda gave birth to another son, who was named after his late father Jacob. After Jacob was hanged, his father William enlisted in the 2nd Illinois Light Artillery at age 53.159
In 1862, the U.S. Congress passed a special act that made Jacob and the other executed bridge-burners posthumous members of the Union Army. They were enrolled in Company F of the 2nd Tennessee Infantry. The act allowed the men's widows and their nearly 20 fatherless children to draw small pensions from the government that had abandoned the loyalist raiders it had promised to protect. The act also allowed the men's graves, all of which are in Pottertown-area cemeteries, to be marked with official U.S. government markers.159
In 1865 Almaranda Hinshaw applied for a Civil War Pension as widow of Jacob M. Hinshaw, Company F, 2nd Tennessee Infantry.k She also listed minor child James Hinshaw [sic].k
Almarinda ("Rinda") remarried on Jun 15 1865 to William B. Jenkins.159,h,f
Almarinda and family were shown in the 1870 census (Aug 11 1870), Hawkins County, Tennessee:h
Photo: Artist's rendition of Jacob's hanging 159
See also - "The Pottertown Bridgeburners" narrative on the events leading to the hanging of Jacob Madison Hinshaw: http://www.rootsweb.com/~tngreene/potter.html
See also - "Civil War Times", December 1997: http://www.britannica.com/bcom/magazine/article/0,5744,25823,00.html
See also - Dave Mathews' study of the 2nd Tennessee Infantry: http://home.fuse.net/damathew
45. The Church Of Jesus Christ of the Latter Day Saints (LDS) International Genealogical Index (IGI) - Tennessee.
159. "Civil War Times", December, 1997, pages 48-54 & 86-87, Contributed by Jeff Hatfield ().
162. Letter from Donahue Bible, historian and author, discussing Hinshaws of eastern Tennessee.
174. Family history information contributed by James C. Henshaw.
(a) "Early East Tennessee Marriages", Sistler, 1987.
(b) "Tennessee Marriages, 1851-1900"; http://www.ancestry.com.
(c) 1850 census, 9th Division, Greene County, Tennessee; roll 880, page 164, dwelling #387.
(d) 1850 census, 9th Division, Greene County, Tennessee; roll 880, page 168, dwelling #443.
(e) 1860 census, 23rd Civil District, Blue Spring P.O., Greene County, Tennessee; page 413A, line #36, dwelling #1405, family #1405.
(f) "Tennessee Marriage Records - Volume 2, Hawkins County 1789-1865",
by Prentiss Price; 1958, Clinchdale Press, Knoxville, Tennessee;
microfilm #0469471 Item 1 in the LDS Family History Library.
(g) Contribution from Andra Walker Clark () citing: records of genealogist Prentiss Price.
(h) 1870 census, White Horn P.O., District 14, Hawkins County, Tennessee; roll M593-1535, page 183, line #36, dwelling #107, family #107.
(i) 1880 census, District 14, Hawkins County, Tennessee; roll T9-1260, ED 75, page 168C, line #11, dwelling #147, family #147.
(j) 1860 census, 23rd Civil District, Blue Spring P.O., Greene County, Tennessee; page 413A-B, line #39, dwelling #1406, family #1406.
(k) National Archives and Records Administration. "General Index to Pension Files, 1861-1934":
"Civil War Pension Index". [database] Provo, UT: Ancestry.com, 2000.
(l) 1880 census, District 14, Hawkins County, Tennessee; roll T9-1260, ED 75, page 167B, line #46, dwelling #144, family #144.
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https://www.physicsforums.com/threads/rotating-motion-of-a-d-c-motor.201422/ | math | I am doing this project to check how the number of baldes of a turbine affects its output. So I used a D.C motor which can be used as a dynamo. I attached a blade to it and forced water on to it and as a result of the rotation motion of the D.C motor/dynamo current was produced. Then I attached two blades to the motor and noticed that more current was produced. There will be a certain point after which there will be so many blades that their mass will be too much and hence the current would drop. Can anyone tell me how I can find the optimum number of baldes at which the "turbine" will give maximum output current? Mass of one blade = 4.5 grams Force of water (flow rate) = 50 ml per sec And apart from that question above can someone tell me how i can analyse my results the best and draw up a good conclusion? | s3://commoncrawl/crawl-data/CC-MAIN-2018-22/segments/1526794865913.52/warc/CC-MAIN-20180524033910-20180524053910-00338.warc.gz | CC-MAIN-2018-22 | 818 | 1 |
https://eric.ed.gov/?id=ED325397 | math | ERIC Number: ED325397
Record Type: RIE
Publication Date: 1985
Reference Count: N/A
Time Comparison of Practical Mathematical Calculations Using Customary and Metric Systems.
Tew, E. James, Jr.
The purpose of this practicum was to determine if adult students engaged in training for high technology jobs can realize a time savings if customary or metric units of measure are used for practical mathematical calculations. Two quizzes were developed, and validated, using customary and metric units for the same type of problem, and the time to solve each problem was recorded. The objective was to determine if there was a significant difference in time per correct answer for either unit of measure. Both quizzes, each having both units of measure for different types of problems, were give to 20 industrial adult students without prior notification. Provided with each quiz was an instruction sheet regarding the procedures to be followed and method of recording time. The recommendation resulting from this study is that practical mathematical calculations be performed using metric units of measure to the extent permitted by limiting variables including measuring and test equipment, specifications, and blueprints which have not been converted to metric units. The paper includes an introduction to the problem, its background and significance, and procedures for the study, data resulting from the study, and conclusions. Copies of the quizzes and the statistical calculations are appended. (KR)
Descriptors: Adult Education, Adult Learning, Algorithms, Computation, Continuing Education, Education Work Relationship, Industrial Training, Job Training, Mathematical Applications, Mathematics Education, Mathematics Tests, Measurement, Metric System, Problem Solving, Skilled Occupations, Technical Education, Technical Mathematics, Technical Occupations, Technological Literacy, Technology, Test Content, Test Interpretation, Test Validity, Timed Tests, Trade and Industrial Education
Publication Type: Dissertations/Theses - Practicum Papers; Tests/Questionnaires
Education Level: N/A
Authoring Institution: N/A
Note: Ed.D. Practicum, Nova University. | s3://commoncrawl/crawl-data/CC-MAIN-2018-51/segments/1544376825098.68/warc/CC-MAIN-20181213193633-20181213215133-00150.warc.gz | CC-MAIN-2018-51 | 2,157 | 12 |
https://chemhomeworkhelp.com/homework-questions/lab-report-chemistry-homework-help/ | math | Answer the questions below. When you have finished, submit this assignment to your teacher by the due date for full credit.
- From Part 2 of the lab activity, plot a graph of volume vs. temperature (in kelvins) with the two data points that resulted from your experiment. Draw a straight line connecting the two points, thus assuming a linear relationship between volume and temperature. Extend this line back to intercept the x-axis.
The x-intercept corresponds to where the volume would be zero and the temperature can be no lower, defined as absolute zero. Absolute zero is 0 K. Compare your results to those expected. How close to absolute zero was your intercept? Why might your value be different from absolute zero?
- Consider all parts of the experiments that you have just performed.
- What conclusions can you make about the relationship between the volume of a gas and its temperature?
- What conclusions can you make about the relationship between the volume of a gas and its pressure?
- What possible variables have you not accounted for? As you did the procedures, is it possible that the atmospheric pressure may have changed? If it did change over the course of your experiment, then how would your results have been affected?
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https://www.hackmath.net/en/examples/reason | math | Reason - examples
- Profit per kilo
The trader sells apples at a profit of 20% per kilogram. Today, he decided to reduce the price of apples by 10%. How much profit does the trader have today?
- ABCD square
In the ABCD square, the X point lies on the diagonal AC. The length of the XC is three times the length of the AX segment. Point S is the center of the AB side. The length of the AB side is 1 cm. What is the length of the XS segment?
Several pieces of bread were in the store. Half of them plus a half of bread bought a cookbook. Of the remaining bread, half of it plus half of the bread was bought by Mr. Novák. The last bread was bought by Ms. Small. How many breads were in the store at.
Two tractors plow the field in 4 hours together. If the first tractor plow half of the field and then the second tractor completed the job, it would take 9 hours. How many hours does the field plow for each tractor separately?
- Class alphabet
All 29 pupils in the class are written in a class by alphabet. The number of pupils enrolled before Paul is three times higher than the number of pupils behind him. Calculate how many pupils are enrolled after Paul.
- Digit sum
The digit sum of the two-digit number is nine. When we turn figures and multiply by the original two-digit number, we get the number 2430. What is the original two-digit number?
- Endless lego set
The endless lego set contains only 6, 9, 20 kilograms blocks that can no longer be polished or broken. The workers took them to the gym and immediately started building different buildings. And of course, they wrote down how much the building weighed. They
- Pupil age
I am a pupil of the primary school, I spent 1/4 of my age on the exercise of parents with children, 1/3 on drawing, 1/6 on flute. I did not have a ring for the first three years of my life and never went to two rings at once. How old am I?
- Highway tunnel
The highway tunnel was built from two ends in the north-south direction. The average daily performance of the "northern party" rasters was higher than the average daily power of the "southern party" of the rasters. After 55 business days, both parties met.
One brick is 4 kg and half a brick heavy. What is the weight of one brick?
Area of square garden is 6/7 of triangle garden with sides 96 m, 60 m and 60 m. How many meters of fencing need to fence a square garden?
- Trapezoid MO
The rectangular trapezoid ABCD with right angle at point B, |AC| = 12, |CD| = 8, diagonals are perpendicular to each other. Calculate the perimeter and area of the trapezoid.
If water flows into the pool by two inlets, fill the whole for 9 hours. First inlet filled pool 8 hour longer than second. How long pool is filled with two inlets separately?
- Forestry workers
In the forest is employed 63 laborers planting trees in nurseries. For 11 hour work day would end job in 43 days. After 14 days, 22 laborers go forth. How many days is needed to complete a planting trees in nurseries by others, if they will work 15 hours
Gross wage was 1762 USD including 22% bonus. How many USD were bonuses?
Route is long 203 km and the first day first regiment went at an average speed 20 km/h and journey back 19 km/h. The second day went second regiment same route at an average speed 18 km/h there and back. Which regiment will take route longer?
- Three cats
If three cats eat three mice in three minutes, after which time 110 cats eat 110 mice?
- Motion problem
From Košíc to Bratislavy go car at speed 76 km/h. From Bratislavy to Košíc go another car at speed 60 km/h. How many minutes before the meeting will be cars 22 km away?
Mr. Radoslav calculated that excavation for a water connection dig for 10 days. His friend would take 7 days. Radoslav worked 3 days alone. Then his friend came to help and started on the other end. On what day since the beginning of excavation they met?
A man drinks a barrel of water for 31 days, woman for 58 days, for how many days they drink barrel together? | s3://commoncrawl/crawl-data/CC-MAIN-2018-05/segments/1516084886792.7/warc/CC-MAIN-20180117003801-20180117023801-00692.warc.gz | CC-MAIN-2018-05 | 3,971 | 32 |
http://texashuntingforum.com/forum/ubbthreads.php/topics/7181842 | math | Not a bad choice in the bunch. I don't own one, but know some that do, and they swear by Schmidt and Bender.
He needs to pick a scope, and read what travel it has available. Half is available on a 0 MOA base.
To convert MOA to Mil, divide MOA by 3.43, and you get the value in Mil. So a 20 MOA base is the same thing as a 5.3 Mil base.
Then he needs to go to a ballistic calculator and find out his worse case scenario environmental conditions elevation correction, for 2000 yards. Once he knows how far up is going to need to dial, he will kknow how much of an elevated base he needs to give the scope more POI up.
I like a Harris bipod better for prone, and an Atlas better for positional/ barricade shooting.
800 Yard Steel Range
Precision Rifle InstructionMemberships and Classes Available | s3://commoncrawl/crawl-data/CC-MAIN-2018-43/segments/1539583511889.43/warc/CC-MAIN-20181018152212-20181018173712-00089.warc.gz | CC-MAIN-2018-43 | 793 | 7 |
https://maniacs.info/percent-lakh/what-is-15-percent-of-21-lakh.html | math | What is 15 percent of 21 lakh? (15% of 21 lakh?) In other words, how do you calculate fifteen percent of twenty-one lakh? First, note that 15 percent means 15 per hundred, and 21 lakh is 21 followed by 5 zeros.
To calculate the percent of any amount of lakh, you multiply lakh by the percent and then divide the product by 100. Here is the formula:
Using the formula, we first multiply 21 lakh by 15 and then we divide that product by 100. Here is the math to show you how:
= 315 lakh
= 3.15 lakh
There you have it! Below is the answer to 15 percent of 21 lakh in numbers (digits).
Percent of Lakh Calculator
Calculate the percent of another lakh amount here!
What is 15 percent of 22 lakh?
Here is the next amount of lakh that we have calculated the percent of. | s3://commoncrawl/crawl-data/CC-MAIN-2023-40/segments/1695233510085.26/warc/CC-MAIN-20230925183615-20230925213615-00364.warc.gz | CC-MAIN-2023-40 | 762 | 10 |
http://markmail.org/message/fms6wrakursv2w46 | math | [Lars Marius Garshol}
I think Thomas means what he says, and that he disagrees with you.
(He agrees with ISO 13250:2000, BTW.)
Lars is right, I do mean "any". If any of the scopes that contribute to a
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http://adguard.mobi/f77-tutorial-22/ | math | F77 TUTORIAL PDF
May 27, 2020 | by admin
Fortran Tutorial for Beginners – Learn Fortran in simple and easy steps starting from basic to advanced concepts with examples including Overview, Environment. Fortran 77 has only one loop construct, called the do-loop. The do-loop corresponds to what is known as a for-loop in other languages. Other loop constructs. The goal of this Fortran tutorial is to give a quick introduction to the most common features of the Fortran 77 and Fortran 90 programming languages. It is not a.
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D77 are many different programming styles, but here are some general guidelines that are fairly non-controversial. Note that each read or write statement by default ends with a newline here Fortran differs from C. A quick reference to BLAS 1 can be found at http: In addition, the function r has to be defined as a Fortran function. You should know that the common statement should appear together with the variable declarations, before the executable statements.
The advantage of this is that the statement label can then be omitted since it is assumed that an enddo closes the nearest previous do statement. Consider again the example where we only use the upper 3 by 3 submatrix of the 3 by 5 array A tutoroal.
It should be mentioned that all the software listed above also comes in a C version or is at least callable from C. A single space character has ttutorial added to the beginning of each code line to tktorial the wiki framework from interpreting the first character as a markup command.
Many scientific computations use vectors and matrices. The elements in the submatrix A 1: First of all you should check if you already have BLAS on your system. Check if there is a graphical user interface available, like, e.
Here is a subroutine for this:. Fortran functions are quite similar to mathematical f7 The simplest form of an expression is a constant. Some old Fortran 77 programs may declare variable length arrays like this:. Books to be broken into subpages Subject: There are also several versions of Fortran aimed at parallel computers. Syntax errors are easy to find. The library file is an object file, so you only have to compile your additional main driver program and then link it tutogial library.
It also has support for analyzing and presenting statistical data in scientific and business applications. The format label is chosen somewhat arbitrarily, but it is common practice to number format statements with higher numbers than the control flow labels.
Here cos is the cosine function, so x will be assigned the value 0. It is ttutorial good programming style to use either the plus sign, an ampersand, or digits using 2 for the second line, 3 for the third, and so on.
Fortran 77 Tutorial
This is tjtorial simple to do in Fortran 77, some will say it is too easy! But in the write statement we try to print 50 numbers.
It is the responsibility of the programmer to make sure that the vectors x and y really have been declared to have length n or more in some other program unit. Fortran will do some type conversion implicitly. Notice especially the shorthand notation for assigning identical values repeatedly.
The index i is used as a row index 1 to m while the index j is used as a column index 1 to n.
The i’th row of A starts at the element A i,1. We give an example of a very simple subroutine.
Fortran 77 Tutorial – Wikibooks, open books for an open world
Naive implementations can generate worst-case memory access patterns which result in programs that are too slow to be worthwhile. Netlib the NET LIBrary is a large collection of freely available software, documents, and databases of interest to the numerical, scientific computing, and other communities.
Typically, all arrays are declared and dimensioned in the main program and then passed on to the subprograms as needed. This means that the following do-loop will multiply a non-negative j by two the hard wayrather than running forever as the equivalent rutorial might in another language.
The numerical value of statement labels have no significance, so any integers can be used, in any order. Some of these optimizations can be done by the Fortran compiler but others must be done by tutodial.
Of course you can initialize arrays to other values than zero. The list of variables should consist of variable names separated tuhorial commas. Fortran 77 is not a free-format language, but has a very strict set of rules for how the source code should be formatted.
The only difficulty is to figure out the correct indices and increments. By convention, Fortran arrays are indexed from 1 and up. | s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600400206329.28/warc/CC-MAIN-20200922161302-20200922191302-00176.warc.gz | CC-MAIN-2020-40 | 4,752 | 25 |
https://practice.geeksforgeeks.org/problems/minimum-product-pair/0/ | math | Given an array of positive integers. The task is to print the minimum product of any two numbers of the given array.
The first line of input contains an integer T denoting the number of test cases. Then T test cases follow. Each test case consists of two lines. First line of each test case contains a integer N and the second line contains N space separated array elements.
For each test case, print the minimum product of two numbers in new line.
2 7 3 4
5 3 6 4
If you have purchased any course from GeeksforGeeks then please ask your doubt on course discussion forum. You will get quick replies from GFG Moderators there. | s3://commoncrawl/crawl-data/CC-MAIN-2020-24/segments/1590347413624.48/warc/CC-MAIN-20200531182830-20200531212830-00595.warc.gz | CC-MAIN-2020-24 | 625 | 6 |
https://www.stoneyholme.lancsngfl.ac.uk/maths-642/ | math | Todays activity is going to test you on both area and perimeter of the shapes.
Area - The space taken up by an object. Find rectangles and use the formula: Length X Width. Alternatively, you can work out the area of 1 square and multiply this by the number of squares in the shape.
Perimeter - The distance around the outside of the shape. Add the lengths of each side of the shape to find its perimeter. Alternatively, You can count the squares number of squares you cross as you work you way all the way around the shape (once you have checked the key to find out the unit of measure for 1 square).
Go onto Purple Mash complete the 2Do named 'Area and Perimeter' | s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323587711.69/warc/CC-MAIN-20211025123123-20211025153123-00508.warc.gz | CC-MAIN-2021-43 | 664 | 4 |
https://zdroweporadniki.pl/how-to-find/how-to-find-median-the-essential-guide/ | math | Are you tired of searching for a simple and straightforward method to find the median? Look no further! In this article, we will demystify the process and provide you with a step-by-step guide on how to find the median with ease. Whether you’re a student struggling with math homework or simply curious about this statistical measure, our concise and jargon-free explanation will help you master the art of finding the median in no time. So, let’s dive in and unravel this mathematical mystery!
Introduction to Finding the Median
Finding the median is a fundamental statistical concept that allows us to understand the middle value of a set of data. Whether you’re analyzing a small sample or a large population, understanding how to find the median is crucial to gaining insights and drawing conclusions from your data. In this comprehensive guide, we will explore the concept of median, step-by-step instructions on finding it, techniques for dealing with outliers or missing values, practice exercises, and common mistakes to avoid.
The Importance of Finding the Median
The median is a measure of central tendency that is exceptionally useful in situations where the data may contain outliers or extreme values. Unlike the mean, which can be heavily influenced by outliers, the median provides a more robust representation of the „typical” value in a dataset. It is particularly handy in skewed distributions or when the data contains extreme values that do not reflect the overall trend.
The Relevance of Median in Various Fields
The concept of median finds its applications in a wide range of fields, such as economics, healthcare, finance, and social sciences. For example, in economics, the median household income is often used as a measure to understand the income distribution and inequality within a country. In healthcare, the median survival time can indicate the effectiveness of a treatment. The median price of a house can provide insights into the real estate market. Understanding how to find the median is, therefore, crucial for making informed decisions and drawing accurate conclusions from data.
Understanding the Concept of Median
To effectively find the median, it is essential to grasp the underlying concept. The median represents the middle value in a dataset, dividing it into two equal halves, with 50% of the values falling below and 50% above this central point. It is not affected by the actual values of the dataset but only by their order. In other words, the median is the value that separates the data into two halves, with an equal number of values on either side.
Benefits of Using the Median
Limitations of the Median
Step-by-Step Guide to Finding the Median
To find the median, follow these simple steps:
1. Arrange the dataset in ascending order from smallest to largest.
2. Calculate the total number of values (N) in the dataset.
3. Determine whether N is even or odd.
4. If N is odd, the median is the middle value in the ordered dataset.
5. If N is even, the median is the average of the two middle values.
6. The median is found!
It is important to remember that the dataset must be sorted in ascending order for these steps to work correctly. Now, let’s dive into finding the median in more detail under both odd and even scenarios.
Finding the Median in a Set of Data with an Odd Number of Values
Finding the median in a dataset with an odd number of values is relatively straightforward. Let’s say we have a dataset with nine values. We follow the step-by-step approach discussed above.
1. Arrange the dataset in ascending order: 12, 15, 18, 19, 20, 26, 28, 31, 40.
2. Calculate the total number of values: N = 9.
3. Since N is odd, the median is the middle value.
4. The middle value is the fifth value in the ordered dataset, which is 20. Therefore, the median is 20.
It’s important to note that in datasets with an odd number of values, there is always a single middle value. This value becomes the median, representing the center of the data distribution.
Finding the Median in a Set of Data with an Even Number of Values
Finding the median in a dataset with an even number of values requires one additional step compared to finding it in an odd-sized dataset. Let’s consider a dataset with 10 values.
1. Arrange the dataset in ascending order: 10, 12, 15, 18, 19, 21, 24, 30, 35, 40.
2. Calculate the total number of values: N = 10.
3. Since N is even, the median is the average of the two middle values.
4. The two middle values are the 5th and 6th values, which are 19 and 21.
5. Calculate the average of these two values: (19 + 21) / 2 = 20.
6. Therefore, the median is 20.
By taking the average of the two middle values, we can find the median in a dataset with an even number of values. This technique ensures a representative value that falls between the two central points.
Dealing with Missing or Outlier Values in Finding the Median
While calculating the median, missing or outlier values can pose challenges. However, there are strategies to handle these situations and ensure accurate results.
When dealing with missing values, the first step is to determine the reason for their absence. If it is a random or non-systematic issue, and the missing values are only a small fraction of the dataset, you may choose to exclude them. However, if the missing values are systematic or significant in number, they should be dealt with more carefully.
One approach is to impute missing values based on other available information or statistical techniques such as regression, mean, or median imputation. By doing so, you can estimate the missing values and proceed with finding the median using the complete dataset.
Outliers are extreme values that deviate significantly from the rest of the dataset. It’s important to assess whether these outliers are genuine, data entry errors, or a result of some other phenomenon. In some cases, outliers may need to be excluded if they do not represent the true nature of the data.
If you decide to include the outliers, it is essential to acknowledge their impact on the median. Outliers can shift the median towards their side, especially if they are located close to or within the middle of the ordered dataset. It’s crucial to consider the context of the data and the potential influence of outliers when interpreting the median.
Practice Exercises for Finding the Median
To enhance your understanding and skill in finding the median, it’s crucial to practice with various datasets. Here are some exercises to help you master the concept:
1. Dataset 1: 2, 5, 8, 11, 15, 18, 20
2. Dataset 2: 12, 15, 20, 32, 32, 36, 41, 42
3. Dataset 3: 17, 21, 24, 28, 30, 34, 39, 50, 78
4. Dataset 4: 9, 12, 15, 15, 21, 21, 26, 27, 29
By practicing with different datasets, you will gain confidence in finding the median and become more comfortable with its interpretation.
Common Mistakes to Avoid When Finding the Median
While finding the median may seem straightforward, there are common mistakes that even experienced analysts can make. By being aware of these pitfalls, you can ensure accurate results and proper interpretation of your data.
Mistake 1: Forgetting to Sort the Data
One of the most common mistakes is failing to sort the dataset in ascending order before finding the median. Without proper ordering, you may obtain incorrect results, leading to misinterpretation and flawed analysis. Always double-check that your dataset is appropriately arranged before proceeding.
Mistake 2: Mishandling Even-Sized Datasets
In datasets with an even number of values, determining the median requires calculating the average of the two middle values. Neglecting this additional step or calculating the average incorrectly can lead to inaccurate results. Pay close attention to the steps when dealing with even-sized datasets.
Mistake 3: Ignoring Missing or Outlier Values
Failing to account for missing values or not considering the impact of outliers can significantly affect the median. Make sure to address missing values appropriately through imputation techniques and critically assess the influence of outliers on the central tendency measure.
By avoiding these common mistakes, you can confidently find the median and utilize it effectively in your data analysis.
The median is a powerful statistical tool that allows us to understand and interpret a dataset’s central tendency accurately. By following the step-by-step guidelines outlined in this comprehensive guide, you can confidently find the median in both odd and even-sized datasets. Additionally, understanding how to handle missing or outlier values ensures accurate results despite potential challenges. Through practice exercises, you can hone your skills and avoid common mistakes associated with finding the median. Whether you’re analyzing data for business, research, or personal purposes, the ability to find and interpret the median is a valuable asset in making informed decisions and drawing reliable conclusions. | s3://commoncrawl/crawl-data/CC-MAIN-2023-50/segments/1700679100534.18/warc/CC-MAIN-20231204182901-20231204212901-00126.warc.gz | CC-MAIN-2023-50 | 9,007 | 59 |
https://www.quibblo.com/quiz/b2ElTth/Polygons | math | Completed 0 of 13 questions.
A rectangle is a polygon
A circle is a polygon
How many sides does a pentagon have?
Draw a hexagon. Divide it up into its least number of triangles. The number of triangles formed is:
The correct formula for the INTERIOR ANGLE SUM of a polygon is:
The angle sum of a nonagon (9 sides) is:
Find the number of sides of a polygon whose interior angle sum is 1980
Find the size of each angle of a 7 sided shape where the interior angle sum is 900 (to the nearest degree)
The sum of the EXTERIOR angles of any polygon is:
Find the size of each exterior angle of a decagon (10 sides)
Each pair of interior and exterior angles add to
If an interior angle is equal to 72, its exterior angle is equal to:
A polygon has angles equal to x, x, 2x and 2x. Find x | s3://commoncrawl/crawl-data/CC-MAIN-2017-43/segments/1508187823350.23/warc/CC-MAIN-20171019160040-20171019180040-00446.warc.gz | CC-MAIN-2017-43 | 778 | 14 |
http://www.fantasyfootballcafe.com/forums/viewtopic.php?t=494409 | math | Ok, my league has 12 Managers in it, and its standard scoring. RB get 1 point for every ten rushing yards and 6 for a touchdown, WR and TE get 1 point for every 10 receiving yards and 6 for a touchdown. QB gets 1 point for every 25 passing yards, 1 point for every 10 rushing yards and 6 for a touchdown. All players lose 2 points for a fumble of INT. K get 1 point for an extra point, 3 for a FG, and 5 for a FG over 50 yards. Finally, DST starts at 20 points each week and goes up or down based of stats such as points for and against, INT, fumbles, sacks, etc.
I know you can't see the free agents in my league, but who would you recommend going after to improve my RB core? | s3://commoncrawl/crawl-data/CC-MAIN-2014-23/segments/1405997886087.7/warc/CC-MAIN-20140722025806-00035-ip-10-33-131-23.ec2.internal.warc.gz | CC-MAIN-2014-23 | 677 | 2 |
http://www.zillow.com/homedetails/304-S-19th-St-Saint-Charles-IL-60174/4661146_zpid/ | math | This home is not currently listed for sale or rent on Zillow.
A Zestimate® home valuation is Zillow's estimated market value. It is not an appraisal. Use it as a starting point to determine a home's value. Learn more
A Rent Zestimate® is Zillow's estimated monthly rental price, computed using a proprietary formula. It is a starting point in determining the monthly rental price for a specific property.
- Lot: 8,712 sqft
- Single Family
- Built in 1961
- Views: 3,472 all time views
- Cooling: Central
- Heating: Forced air
- Last sold: Aug 2011 for $111,000
- Ceiling Fan
- Fenced Yard
- Flooring: Carpet, Hardwood, Tile
- Parking: Garage - Attached
- 2nd Bedroom Flooring \ Hardwood, 2nd Bedroom Level \ Main Level, 2nd Bedroom Window Treatments (Y\N) \ None, 3rd Bedroom Flooring \ Hardwood, 3rd Bedroom Level \ Main Level, 3rd Bedroom Window Treatments (Y\N) \ None, 4th Bedroom Level \ Not Applicable, Additional Rooms \ Recreation Room, Additional Sales Information \ None, Addtl Room 1 Flooring \ Carpet, Addtl Room 1 Level \ Basement, Addtl Room 1 Name \ Recreation Rm, Addtl Room 10 Level \ Not Applicable, Addtl Room 2 Level \ Not Applicable, Addtl Room 3 Level \ Not Applicable, Addtl Room 4 Level \ Not Applicable, Addtl Room 5 Level \ Not Applicable, Addtl Room 6 Level \ Not Applicable, Addtl Room 7 Level \ Not Applicable, Addtl Room 8 Level \ Not Applicable, Addtl Room 9 Level \ Not Applicable, Age \ 51-60 Years, Appliances \ Oven\Range, Avail Furnished (Y\N) \ No, Basement (Y\N) \ Full, Basement Bathrooms (Y\N) \ Yes, Basement \ Finished, Built Before 1978 (Y\N) \ Yes, Compensation paid on \ Net Sale Price, Dining Room Level \ Main Level, Dining Room \ Combined w\ LivRm, Disability Access and\or Equipped \ No, Driveway \ Concrete, Electricity \ Circuit Breakers, Equipment \ CO Detectors, Equipment \ Ceiling Fan, Equipment \ Fan-Attic Exhaust, Equipment \ Sump Pump, Equipment \ TV-Cable, Exterior Property Features \ Storms\Screens, Family Room Flooring \ Carpet, Family Room Level \ Basement, Family Room Window Treatments (Y\N) \ None, Fees\Approvals \ Credit Report, Fees\Approvals \ Letters of Reference, Fireplace Location \ Family Room, Fireplace Location \ Living Room, Fireplace Type\Details \ Gas Logs, Fireplace Type\Details \ Gas Starter, Fireplace Type\Details \ Wood Burning, Foundation \ Concrete, Franchisor Feed(y\n) \ No, Garage On-Site \ Yes, Garage Ownership \ Yes, Garage Type \ Attached, Heat\Fuel \ Forced Air, Heat\Fuel \ Gas, Interior Property Features \ 1st Floor Bedroom, Interior Property Features \ 1st Floor Full Bath, Interior Property Features \ Bar-Wet, Interior Property Features \ Hardwood Floors, Kitchen Flooring \ Ceramic Tile, Kitchen Level \ Main Level, Kitchen Type \ Galley, Kitchen Window Treatments (Y\N) \ None, Laundry Level \ Not Applicable, Lease Terms \ 1 Year Lease, Living Room Flooring \ Hardwood, Living Room Level \ Main Level, Living Room Window Treatments (Y\N) \ None, Lot Description \ Corner, Lot Description \ Fenced Yard, Management \ Self-Management, Master Bedroom Bath (Y\N) \ Full, Master Bedroom Flooring \ Hardwood, Master Bedroom Level \ Main Level, Master Bedroom Window Treatments (Y\N) \ None, Monthly Rent Incl \ None, Offered for Sale or Rent \ No, Other Information \ School Bus Service, Parking Type \ Garage, Pet Information \ Deposit Required, Pet Information \ Pet Count Limitation, Pets Allowed (Y\N) \ Yes, Property Address On IDX? (Y\N) \ Yes, Property Type \ Residential Rental, Roof Type \ Asphalt\Glass (Shingles), Sewer \ Sewer-Public, Short Term Lease Ok (Y\N) \ No, Special Compensation Info. \ None, Square Feet Source \ Assessor, Status \ Active, Type of Rental Property \ Detached, Water \ Public, Waterfront (Y\N) \ No
- Garbage disposal
- Range / Oven
- Dining room
- Exterior material: Brick, Vinyl
- Roof type: Asphalt
- Structure type: Ranch
- Unit count: 1
- Floor size: 1,076 sqft
- Heating: Gas
- Laundry: In Unit
- Parcel #: 0933176001
- Pets: Dogs
- Zillow Home ID: 4661146
The Value Range is the high and low estimate market value for which Zillow values a home. The more information, the smaller the range, and the more accurate the Zestimate. See data coverage and accuracy table
Don't agree with your home's Zestimate? Owners can edit their home facts to make the Zestimate more accurate. Plus, you can leave an opinion on your Zestimate value below. Just click "Owner Estimate".
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Popularity on Zillow
Homes like this sold for $169-210K.
Market guideZillow predicts 60174 home values will decrease 1% next year, compared to a 0.6% fall for Saint Charles as a whole. Among 60174 homes, this home is valued 16.3% less than the midpoint (median) home, but is valued 39.4% more per square foot.
Foreclosures will be a factor impacting home values in the next several years. In 60174, the number of foreclosures waiting to be sold is 16.2% greater than in Saint Charles, and 888.6% higher than the national average. This higher local number may prevent 60174 home values from rising as quickly as other regions in Saint Charles.
Learn more about forecast calculations or 60174 home values.
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Data by GreatSchools.org | s3://commoncrawl/crawl-data/CC-MAIN-2015-22/segments/1432207928078.25/warc/CC-MAIN-20150521113208-00091-ip-10-180-206-219.ec2.internal.warc.gz | CC-MAIN-2015-22 | 5,737 | 40 |
https://stjamescsf.org/and-pdf/419-analysis-manifolds-and-physics-pdf-447-490.php | math | Analysis manifolds and physics pdf
File Name: analysis manifolds and physics .zip
- Simons Collaboration on Special Holonomy in Geometry, Analysis and Physics First Annual Meeting
- Analysis, Manifolds and Physics, Part II - Revised and Enlarged Edition
- Analysis, manifolds, and physics
- Physics on Manifolds
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Simons Collaboration on Special Holonomy in Geometry, Analysis and Physics First Annual Meeting
So do feel welcome to drop by at any time, any day, until 18h. If I am in my office and not otherwise busy with other people, you will have my undivided attention. You can also schedule an appointment by email. Note: email links are not activated in a perhaps futile attempt to defeat address-collection software. Self-contained Lecture Notes will be posted further down on this web page; they should be viewed as the primary source for this course. Please be aware that these notes are subject to modification at any time!
Analysis, Manifolds and Physics, Part II - Revised and Enlarged Edition
Chapters: I. Review of fundamental notions of analysis. Differential calculus on Banach spaces. Differentiable manifolds, finite dimensional case. Integration on manifolds. Riemannian manifolds. V bis.
Simons Collaboration on Special Holonomy in Geometry, Analysis and Physics Home Page Spaces with special holonomy are of intrinsic interest in both mathematics and mathematical physics; they appear in many contexts in Riemannian geometry, particularly Ricci-flat and Einstein geometry, minimal submanifold theory and the theory of calibrations, and gauge theory. The exceptional cases, which occur in dimensions 7 and 8, remain the most challenging and the least understood. Nevertheless, they share important features with the better-known case of SU n holonomy, where the three types of structures are known as Calabi-Yau spaces, Hermitian Yang—Mills connections, and special Lagrangian and complex submanifolds. The exceptional holonomy spaces play key roles in the study of fundamental physical theories such as M-theory and F-theory generalizing the role that Calabi-Yau 3-folds play in string theory , and progress in these theories depends crucially on a better understanding of spaces especially singular ones with exceptional holonomy. Four of its principal investigators and four of its postdoctoral fellows presented reports on the most recent developments in various aspects of the field of special holonomy, including the study of adiabatic limits, moduli problems, collapse, gluing constructions using methods from algebraic geometry, and connections with physics. They discussed their research progress during the first year of the collaboration and the current directions of research.
Download Analysis, Manifolds and Physics: Set free book PDF Author: Yvonne Choquet-Bruhat, -Morette DeWitt. Pages: ISBN:
Analysis, manifolds, and physics
In the big scheme of things both have their place but, as this book no doubt demonstrates, my personal preference is to view mathematical physics as a branch of mathematics. The classical texts on mathematical physics which I was originally brought up on, such as Morse and Feshbach , Courant and Hilbert , and Jeffreys and Jeffreys are es- sentially books on differential equations and linear algebra. It follows much more the lines of Choquet-Bruhat, de Witt-Morette and Dillard-Bleick andGeroch , in whichmathematical structures rather thanmathemat- ical analysis is the main thrust. How well I have succeeded must be left to the reader to judge.
Skip to search form Skip to main content You are currently offline. Some features of the site may not work correctly. DOI: Bishop and S.
Twelve problems have been added to the first edition; four of them are supplements to problems in the first edition. The others deal with issues that have become important, since the first edition of Volume II, in recent developments of various areas of physics. All the problems have their foundations in volume 1 of the 2-Volume set Analysis, Manifolds and Physics. It would have been prohibitively expensive to insert the new problems at their respective places. They are grouped together at the end of this volume, their logical place is indicated by a number of parenthesis following the title.
Physics on Manifolds
It seems that you're in Germany. We have a dedicated site for Germany. Editors: Flato , M. This volume contains the proceedings of the Colloquium "Analysis, Manifolds and Physics" organized in honour of Yvonne Choquet-Bruhat by her friends, collaborators and former students, on June 3, 4 and 5, in Paris.
Purchase Analysis, Manifolds and Physics, Part II - Revised and Enlarged Edition - 1st Edition. Print Book & E-Book DRM-free (Mobi, PDF, EPub). × DRM-Free. | s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964363510.40/warc/CC-MAIN-20211208114112-20211208144112-00135.warc.gz | CC-MAIN-2021-49 | 4,936 | 21 |
https://sns.breakers.cyberstep.com/topic/210/why-do-i-keep-getting-equipment | math | why do I keep getting equipment
campbcay000 last edited by campbcay000
out of at least 50 draws on the event most resently I got 8-10 SR pieces of eqipment and only 1 SR hero. so why the hell have I only gotten 3 SR heros and 18 Sr eqipment. do they just have an increased drop chance or am I just the words unluckiest video game player?
Evan last edited by
SR heroes have a 4% chance of dropping and other has a 30% chance of dropping. The information given doesn't go further than that for the prize rates, but I would assume it then does a roll with 50% chance of equipment and 50% chance of gemstone (I'm assuming that gemstones are in the other category.)
For the newest capsule there are only the two SR equipments, so based on my previous guesses you would have something like a 15% chance of one of those vs a 4% chance of a SR character. | s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141193856.40/warc/CC-MAIN-20201127161801-20201127191801-00120.warc.gz | CC-MAIN-2020-50 | 846 | 6 |
https://jacobelyacharjournalist.com/9781848000049/linear-functional-analysis.html | math | Book Title: Linear Functional Analysis
Author: Erwin Kreyszig
Format: Paperback | 324 pages
Publication Date: 21 Dec 2007
This introduction to the ideas and methods of linear functional analysis shows how familiar and useful concepts from finite-dimensional linear algebra can be extended or generalized to infinite-dimensional spaces. Aimed at advanced undergraduates in mathematics and physics, the book assumes a standard background of linear algebra, real analysis (including the theory of metric spaces), and Lebesgue integration, although an introductory chapter summarizes the requisite material. A highlight of the second edition is a new chapter on the Hahn-Banach theorem and its applications to the theory of duality. | s3://commoncrawl/crawl-data/CC-MAIN-2019-39/segments/1568514573053.13/warc/CC-MAIN-20190917061226-20190917083226-00177.warc.gz | CC-MAIN-2019-39 | 728 | 5 |
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An algebraic equation depicts a scale, what is done on one side of the scale with a number is also done to either side of the scale. Formula Sheet for College Algebra Final Exam. Properties of Exponents. | s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570986675316.51/warc/CC-MAIN-20191017122657-20191017150157-00374.warc.gz | CC-MAIN-2019-43 | 4,565 | 8 |
https://demonstrations.wolfram.com/ShortestPathForTheDubinsCar/ | math | Shortest Path for the Dubins Car
Requires a Wolfram Notebook System
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In 1957, Lester Eli Dubins proved that the shortest path between two coordinates for a forward-moving vehicle with a minimum turning radius is composed entirely of no more than three circular arcs of radius or straight lines.[more]
In this Demonstration, the starting position of the blue car is green and its end position (the goal) is red. You can drag two locators, one for the red car's position and the other for the red car's orientation . The sliders let you vary the minimum turning radius or move the blue car from the start to the goal.[less]
Contributed by: Aaron T. Becker and Shiva Shahrokhi (December 2017)
Open content licensed under CC BY-NC-SA
The Dubins car is a simplified mathematical model of a car that moves in the - plane . The car's location is specified by the location of the center of the car's rear axle and the orientation of the car. The car cannot move sideways because the rear wheels would have to slide instead of roll. The Dubins car model stipulates that the car moves forward at a constant speed and has a maximum steering angle that translates into a minimum turning radius . The minimum turning radius circles are drawn tangent to the starting and ending positions with dashed gray circles.
If the car has forward velocity of 1 unit per second, the system equations are
where . The task is to minimize the length of the curve traced out by the center of the rear axle as it moves from the start to the goal. That path is the bounded-curvature shortest path. Dubins proved that the shortest path consists of no more than three segments, where in each segment is either , or . Denote these steering commands by R, S, L for turning right, going straight or turning left. A path is then coded with a three-letter word.
If , then the shortest path is a straight line. For nonzero , the shortest paths are of the form LRL, RLR, LSL, LSR, RSL, RSR. In this Demonstration, each path type is given a different color: LRL is brown, RLR is dark green, LSL is pink, LSR is blue, RSL is orange, and RSR is dark yellow.
LSR (blue) and RSL (orange) are potentially valid only if the distance from start to goal is greater than . The two paths composed entirely of curves, LRL (brown) and RLR (dark green), are potentially valid only if the distance from start to goal is less than .
This Demonstration determines the shortest path by computing the paths using all of the valid words, and then picks the one with shortest length.
All paths are drawn in their respective colors, but the shortest path is drawn with a thicker line. Techniques in show how to determine the regions where each path is optimal. If the car is allowed to move backward as well as forward, there are 46 possible words, and this mathematical model is called the Reeds–Shepp car .
L. E. Dubins, "On Curves of Minimal Length with a Constraint on Average Curvature, and with Prescribed Initial and Terminal Positions and Tangents," American Journal of Mathematics, 79(3), 1957 pp. 497–516. doi:10.2307/2372560.
J. A. Reeds and L. A. Shepp, "Optimal Paths for a Car That Goes both Forwards and Backwards," Pacific Journal of Mathematics, 145(2), 1990 pp. 367–393. projecteuclid.org/euclid.pjm/1102645450.
S. Lavalle, Planning Algorithms, Cambridge University Press, 2006. http://planning.cs.uiuc.edu/node821.html.
X.-N. Bui, P. Souères, J.-D. Boissonnat and J.-P. Laumond, "The Shortest Path Synthesis for Non-holonomic Robots Moving Forwards," Research Report RR-2153, INRIA, France, 1994. hal.inria.fr/inria-00074519. | s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296943562.70/warc/CC-MAIN-20230320211022-20230321001022-00313.warc.gz | CC-MAIN-2023-14 | 3,696 | 18 |
https://www.cbc.ca/news/canada/newfoundland-labrador/math-learning-centre-closing-mun-st-johns-1.3693203?cmp=rss | math | MUN shutting down Math Learning Centre in fall
Centre provided foundation math courses to help prepare students for university math
When the fall semester begins at Memorial University, the Math Learning Centre will be no more.
CBC News has learned that Memorial University, under pressure to find cost savings and make cuts, has decided to shut down the centre come September.
The Math Learning Centre, which is led by associate professor Sherry Mantyka, provides foundation level math courses to university students looking to brush up on basic math skills before taking Math 1090 — a required mathematics course for many degree programs at the school.
"The role of the Math Learning Centre is really to provide foundational mathematical skills for students who are not ready to take a for-credit mathematics course," said Mark Abrahams, MUN's Dean of Science.
When first year students arrive at MUN, the school determines whether or not they require a foundation math course by looking at their high school math grade or through a math placement test.
If the students fail the test, then they are required to complete three foundation math courses before enrolling in Math 1090.
According to Abrahams, the decision to close the Math Learning Centre came down to the bottom line.
"The Mathematics Learning Centre is one area where we felt we could realize some considerable cost savings while minimizing our impact on students," he said.
"What we're doing then is we're providing a different approach to hopefully getting students through Math 1090 as opposed to offering the foundation courses that we have been doing for many years."
Instead of the foundation courses, Abrahams said the school will be offering Math 1090 as a 26 week course over two semesters for students who need more time to process the material.
"We're going to use that additional time to provide students with more examples, more opportunities for interactions with instructors and basically increase the length of time that they're working on that course."
With the financial pressures facing the MUN Science department, Abrahams said it's likely there will be more cuts in the future. | s3://commoncrawl/crawl-data/CC-MAIN-2023-23/segments/1685224656963.83/warc/CC-MAIN-20230610030340-20230610060340-00644.warc.gz | CC-MAIN-2023-23 | 2,165 | 14 |
https://www.arxiv-vanity.com/papers/cond-mat/9902198/ | math | Directed Paths on Hierarchical Lattices with Random Sign Weights
We study sums of directed paths on a hierarchical lattice where each bond has either a positive or negative sign with a probability . Such path sums have been used to model interference effects by hopping electrons in the strongly localized regime. The advantage of hierarchical lattices is that they include path crossings, ignored by mean field approaches, while still permitting analytical treatment. Here, we perform a scaling analysis of the controversial “sign transition” using Monte Carlo sampling, and conclude that the transition exists and is second order. Furthermore, we make use of exact moment recursion relations to find that the moments always determine, uniquely, the probability distribution . We also derive, exactly, the moment behavior as a function of in the thermodynamic limit. Extrapolations () to obtain for odd and even moments yield a new signal for the transition that coincides with Monte Carlo simulations. Analysis of high moments yield interesting “solitonic” structures that propagate as a function of . Finally, we derive the exact probability distribution for path sums up to length for all sign probabilities.
Sums of directed paths are present in numerous models of disordered systems. Polymer configurations in a disordered matrix, dynamics of interfaces grown by deposition and Feynman path sums for electron hopping between impurities[2, 3] are only a few of the relevant examples. In this paper, we focus on the latter example involving a model first introduced by Nguyen, Spivak and Shklovskii (NSS), for interference effects in the strongly localized regime.
In the directed path sign model one studies the sum of all possible directed paths between two sites on a lattice. On each lattice bond, one places a random sign with probability . Each directed path evolved is then computed by multiplying the values of the bonds it crosses. Finally the sum of all paths is obtained. The proponents of the model obtained, numerically for small systems, that a second order transition occurred at between a phase with preferential sign (for the path sum ), and a phase with no preferential sign. NSS also offered appealing arguments based on the behavior of . Presumably, such a parameter grows exponentially above the transition while it goes to zero below . The physical relevance of this transition lies in the fact that it may signal the change between Aharonov-Bohm oscillations of period and those of in the context of hopping conduction.
The NSS argument was later contended by Shapir and Wang arguing that correlations between paths implied that does not necessarily go to zero for any . Subsequently, Wang et al used an exact enumeration scheme to probe the transition for small lattices of maximum size . The work found no evidence of a transition above negative sign probability . Such conclusions were supported by Zhao et al on the basis of numerics, for large square lattices, where it was assured that the transition did not exist above in two dimensions. Nevertheless, the decay of the order parameter as a function of system size was found to be anomalously slow for finite (see also ). Therefrom, more recently Spivak, Feng and Zeng discussed numerical results that suggest a finite jump in the order parameter indicating a first order transition for the sign problem. The authors also imply that the moments increase faster than as indicating there is no unique relation between and the probability distribution . This is an important point since the moments, in such a case, may not contain information about the transition. Finally, in a recent paper by Nguyen and Gamietea, a renewed extensive study of the parameter proves that, at least according to such a parameter, no transition exists; only a strong crossover from logarithmic to exponential behavior is observed.
Besides the numerical approaches, mean field type approximations by Obukhov point to a second order transition for dimensions . Furthermore, Derrida and Cook also took up the problem, analytically, using a sparse matrix approach. They generalized the model to random phases, which includes random signs as a special case. Their approach is mean field in nature and results in a phase diagram where the sign transition is of second order (see also). Nevertheless, mean field results may not apply to low dimension due to the importance of path crossings.
Here we address the following issues: i) What is the order of the sign transition through scaling analysis of the order parameter proposed, ii) do moments of the path sums determine the probability distribution uniquely? and iii) what is the exact behavior of the parameter above and below the transition?. A new perspective will be gained by using hierarchical lattice: Such lattices, while still amenable to analytical manipulation, include crucial path correlation effects absent in mean field.
The paper is organized as follows: Section II discusses the sign model and describes hierarchical lattices. In section III we perform detailed Monte Carlo simulations, close to the transition, for systems of up to size . A scaling analysis is performed for the order parameter to distinguish between first and second order transitions. In section IV we study the moments exactly, using moment recursion relations. We find that moments determine the distribution uniquely according to Carlemans theorem, and find possible indications of a phase transition from odd and even moment extrapolations to . In this section we also discuss the high moment behavior, unveiling interesting structures as a function of the sign probability . Subsequently, we probe the parameter exactly showing, for the first time, its unambiguous crossover between exponential and logarithmic behavior. In section V we obtain the exact probability distribution for lattice sizes and sample the distribution for up to as a function of . We end with the conclusions and a discussion of the mapping of the moments to an -body partition function in one dimension as a continuum model that might aid in explaining the curious high moment behavior.
Ii The sign model
Imagine two reference points on a lattice between which one would like to evolve all possible directed paths and compute a “partition function”
where represents each individual contributing path. By directed it is meant that paths always propagate in the forward direction without loops or overhangs. The random medium in which these paths evolve can be represented by assigning local weights on the bonds or sites that are picked up by the paths as they wander to their final destination. Such a model has been used as a paradigm simulating, for example, a coarse-grained polymer or interface wandering in a random matrix with locally favorable energy minima. The model is interesting because it yields anomalous lateral wandering and energy exponents for the interface/polymer as compared to those generated by simple diffusion, signaling a new disorder induced universality class in dimensions.
Another application, in an entirely different field, is in the context of Variable Range Hopping, a mechanism for conduction in insulators. In this context, one also needs to sum over Feynman paths to compute the transition probability, between impurities, of current bearing electrons. The Feynman paths, in this case, are directed because they are tunneling paths. Any elongation of the latter, in the form of loops or overhangs, is exponentially less probable. For further justification of the model we refer the reader to the review in reference. NSS studied such tunneling processes proposing a directed path model where the local weights are random signs. In such a model, the path is a product of the signs it picks up en route to the final site. Writing eq.(1) more explicitly
where is a random sign according to the distribution . The probability in the NSS model emulates the relative abundance of levels above and below the Fermi energy. This model has been very successful in explaining qualitative and quantitative features of conduction in the strongly localized regime. In particular, intriguing interference effects producing a characteristic periodicity of magnetic field oscillations and changes in the localization length due to non-local effects[3, 17]. In spite of the seemingly different nature of disorder in the NSS model, replica arguments and numerics have shown that it belongs to the same universality class of directed polymers with positive weights[3, 18], at least for close to .
We have taken up the sign model on hierarchical lattices as mentioned in the introduction. A hierarchical lattice is a recursive structure built by repeating a chosen motif. Depending on the latter motif, one can build integer dimensional objects emulating an Euclidean lattice. For this work we chose the Berker lattice or diamond. Such motif (see Fig. 1) has the parameter corresponding to the number of branches between the initial and final points. The lattice size is related to the recursion order as i.e. the number of bonds on any directed path between and . The number of bonds on the lattice (or mass) is given by , so that the effective dimension of the lattice is . In this work we will use except if otherwise stated. Qualitative features of critical behavior of many statistical models are correctly reproduced on such structures with no unphysical effects. In fact, mapping to hierarchical lattices is the basis of the Migdal-Kadanoff renormalization procedure, of frequent use in critical phenomena. As noted before, an important feature of hierarchical lattices over either Bethe lattices/mean field approaches is that path intersections are taken into account. Thus, we expect that the resulting simulations will be more faithful to low dimensional behavior. In fact, we will present, in section IV, further evidence of the adequacy of hierarchical lattices making contact with known recent results on the sign transition.
Iii Sign phase transition in two dimensions
In this section, we have undertaken Monte Carlo simulations on hierarchical lattices to check for scaling properties. Paradoxically, scaling has only been discussed once before in connection with the transition and it is a primary tool to assess its nature. It will be especially useful to clearly distinguish between first order and second order transitions.
Hierarchical lattices were generated to or order ten. Averages were taken over twenty thousand realizations of disorder for a series of values between and . As the size of the system increases more detailed data was collected close to the transition regime . Figure 2 shows Monte Carlo data for the order parameter as a function of . A definite plateau at develops as increases for low , signaling a definite change in the order parameter (positively signed paths dominate).
For the proposed order parameter we should expect the scaling form . Figure 3 shows a good collapse for the same data as the previous figure. As the order parameter is always between zero and one, we only need to find and the correlation length exponent . For the hypothetical transition we find the values and (). The latter exponent is very different from that of percolation on these lattices (; so the role of percolation if any, is not apparent. If the transition were first order the exponent would be the dimensionality of the system . The non trivial scaling found can also be seen by taking the derivative of the order parameter and plotting its maximum as a function of the system size. These criteria rule out a first order transition.
We have also monitored the evolution of with size. The specific value of was found from the peak values of the derivative of the order parameter . The resulting values are plotted in Fig. 4 where, within error bars, the values of and are confirmed. Summarizing, scaling is very good around and does not correspond to the scaling of a first order transition. Furthermore, there is no sign of a discontinuity in the order parameter as suggested in ref.. We thus conclude that, on hierarchical lattices, the transition exists and is second order as mean field predicts. These conclusions are in agreement with work by Roux and Coniglio on hierarchical lattices. There, they analyzed the variable where is the fraction of positive (negative) paths arriving at site , and they suggest a clear positive phase. The order of the transition for hierarchical lattices is not analyzed in detail in their paper. Nevertheless, they noted undue emphasis of hierarchical lattices on the result, and the possible impact of this on the scaling properties of various quantities. We will come back to such observations, briefly, in section V.
Iv Moment recursion relations
A statistic we can probe exactly on hierarchical lattices are the moments of the probability distribution. This is possible because of recursion relations derived by Cook and Derrida and generalized to arbitrary moment and hierarchical order (system size) by Medina and Kardar. The recursion relation for is the following
where is the moment number and is the hierarchical lattice order. This expression is readily generalized to other integer by changing the binomial factor to a multinomial and including the additional branches. Hence, one can emulate higher dimensional networks. The simple form of this recursion permits, given the local moments at order one, to compute moments to any given lattice size. Appropriate programming of the recursion relations, with arbitrary precision computations, is linear in time with lattice order.
The behavior of the moments for the sign model is extremely rich as we shall see in the following. As found in ref. , after a few hierarchical orders, the values converge rapidly to a limiting form as a function of . Such limiting form is important because it also signals the convergence to a unique limiting distribution, at least, if moments do not grow faster than . The asymptotic form of the moments can be obtained for [13, 21],
that is, moments grow exponentially with for . Nevertheless, for , lower moments grow slightly faster than exponential ( with ), gradually converging to exponential growth for larger moments. The latter implies, according to the condition
that the moments determine the distribution uniquely. There are various forms of such a theorem, but the above is the strongest version due to Carleman. If one substitutes above, , -our asymptotic result- the criterion is satisfied. Even if grows slightly faster i.e. the above sum diverges because . Any faster growth would violate eq.(5), factorial growth being the borderline case. That the moments satisfy eq.(5) is one of our central results. In Fig. 5 we show a sequence of moments as a function of the moment number . The different curves, starting from below, represent hierarchical orders one thru nine (sizes thru ). One readily notes convergence to a definite law. The inset shows a comparison between the growth of and that of moments for the particular case of . The asymptotic behavior is already reached at , larger sizes falling on the same curve.
For values close to , the moment sequence has a characteristic sawtooth shape, where even moments are at the crests and the odd at the troughs. Such structure is not a finite size effect. We have checked this for up to on the hierarchical lattice. As all the odd moments go to zero while the even remain finite as expected. On the other hand, as is reduced the sawtooth disappears, first for the higher moments and then for the lower. In this respect there appears to be a phase transition for each moment at different values of , in a way reminiscent of that discussed by Cook and Derrida (in their case as a function of ‘temperature’). The transition for the first two moments occurs close to which is close to that found from Monte Carlo simulations in the previous section. On this basis it is plausible that the disappearance of sawtooth shape is related to the transition.
Figure 6 shows a set of curves for , and various values of , and up to . The last six orders of the hierarchical lattice collapse on the same curve indicating we have achieved asymptotics. For the highest value of one notes the sawtooth behavior, while it disappears for all moments below . Nevertheless, additional structure is observed at moments beyond for and , where a shoulder develops and moves towards larger values as increases, undeformed, in a solitonic manner. Although the analysis of these structures is out of the scope of this paper, it is interesting to analyze it in the light of a mapping to a one dimensional many body problem. In such a mapping the moment number corresponds to the number of particles interacting like charges on contact. Thus we speculate that the shoulders could be related to sudden changes in the character of the ground state as the particle number (moment number) increases. We will discuss this in more detail in the final section.
For even smaller values the curve starts to resemble the well known limit given by eq.(4), and depicted as a flat line at in Fig. 6. From the figure one can graphically identify the value of as a function of using the relation . The quantity is a “free energy” that may reflect the sign transition. We have followed the value at intercept mentioned before as a function of below . When the moments “zigzag” there are two possible extrapolations, while below the assumed transition the moments lead to a single prediction of the free energy. The results are depicted in Fig. 7, where the curves merge around within the error of the extrapolation procedure. Such a value coincides with our Monte Carlo prediction.
One can validate the relevance of hierarchical lattices by checking the exact computation of the variable with . Such a quantity has been discussed extensively in previous work[2, 4, 8, 24]. As mentioned before, was initially suggested as a candidate for a kind of order parameter that diverged exponentially above the transition and went to zero below. Observations by Shapir and Wang showed, nevertheless, that path correlations (crossings) invalidated the vanishing of the parameter for any value of . It has been argued that for small there is a crossover from exponential growth (for ) to logarithmic growth (for )[8, 24]. Shapir and Wang, on the other hand found a change from for to for . Yet, they observe that the former result is incorrect because partial overlaps of pairs of walks should be accounted for.
Simulations on regular lattices to date can only do very poorly in proving the surmised logarithmic behavior below . Here we have computed to sizes for various values in a few CPU minutes. We have found a clear confirmation of logarithmic to exponential crossover as increases. Figures 8 and 9 show and its derivative as a function of respectively. The scales used permit rapid identification of the corresponding behavior. It should be noted that, on euclidean lattices, it is reported the behavior reported is , where but depends weakly on .
On hierarchical lattices we can also demonstrate analytically that there is no transition in the variable . Following Cook and Derrida, eq.(3), for the first two moments, can be written for general as
Now, after defining one can write a recursion relation for as
It is simple to determine that has in general three fixed points, . For () a critical fixed point arises and exhibits a phase transition as NSS proposed. On the other hand, for there are only two trivial fixed points; is unstable and is stable, indicating that always diverges as found above. Values of close to one correspond to , while close to zero correspond to . Analyzing the behavior of the recursion for near the fixed point one can derive from Eq.IV that . The behavior close to , which should be logarithmic, is also verified (numerically) although we have not arrived at a simple closed expression. In summary, hierarchical lattices provide similar results to those expected on euclidean lattices thus seeming a good testing ground for the sign transition.
As a final word; we have computed higher order cummulants of finding no features of special interest related to the transition. The only result worth mentioning is that for , where is the th cummulant of . In what follows we will take advantage of the special structure of hierarchical lattices to compute the full probability distribution for .
V Probability distribution for
Monte Carlo sampling of the distribution of is handicapped by the models distribution broadness. For such reasons Wang et al undertook an exact enumeration study to probe the NSS order parameter . Because of the high computer demand of exact enumeration, they could only access sizes of for all . Here we use a scheme, on hierarchical lattices, permitting access to exactly for all and sampling of the distribution for . The procedure is as follows: As a hierarchical lattice is built recursively following a chosen motif, one can write the following recursion relation for the probability distribution.
where and denote contiguous elements on separate branches of the hierarchical lattice. , where is the sign probability discussed in previous sections. The number of possible outcomes for or number of different paths goes as ( for , and for ). This growth is extremely fast, although many values will be degenerate for any particular disorder realization. Note that while is easily accessible, going an order further, puts the calculation out of reach, no intermediate sizes being available on hierarchical lattices. For we have resorted to a coarse-graining procedure in the following manner: the exact results for involve terms which we cannot evolve exactly to the next order. Nevertheless, we can make a coarse-grained distribution by averaging occurrences in groups of to obtain different values. One can then go to up to by repeating this procedure. Beyond such a size, the coarse graining procedure does not incorporate sufficient detail to see anymore changes in the distribution, so within our resolution we have achieved its limit form.
Fig. 10a shows the probability distribution for for significant values of . The probability distribution is astonishingly complex, even for small sizes, revealing rich interferences in the paths sums . Note that it would be hopeless to sample the distribution using Monte Carlo as there are sixty to one hundred and thirty orders of magnitude of probability. Fig. 10b shows different values for a sample as a function of using the coarse-graining procedure described above. As expected the distribution is symmetric for and gains asymmetry () as moves towards zero. Note that falls slower than exponential, on average, about the peak value. It is notable the speed with which the distribution appears symmetric beyond . This feature is understood in the ‘zigzag’ behavior of the moments, where odd moments are much smaller than even moments and their separation increases exponentially as is increased.
Having the information of the exact distribution one is also able to obtain the exact order parameter introduced in section III. No qualitative differences were found with curves reported in figures 1 and 2 at least to sizes , so sampling of , involved in Monte Carlo, seems to be good enough to draw the conclusions about the transition (see section III).
In Fig. 11 we have depicted the distribution for and without joining the points for the probability amplitude (as was done in Fig. 10). A fractal structure is apparent; The whole distribution, in the shape of an approximate triangle, is built from, scaled, identical triangular structures up to the resolution achieved by the coarse-graining procedure. Similar complexity is expected for the sign problem on Euclidean lattices.
An interesting final point to make in this section is that, in view of the unique relation between distribution and moments (see section IV), it is possible to use known inversion formulas. In this way one could derive the limiting distribution exactly to any order desired.
Vi Summary and Discussion
We have provided evidence for the existence of a phase transition for the directed path sign model on hierarchical lattices. Nontrivial finite size scaling of the order parameter close to the transition, points to a second order phase transition as found from mean field type approaches. From numerical computations, the threshold on diamond hierarchical lattices is and the correlation length exponent is . The latter exponent is very different from that of percolation on the same lattice .
The study of exact moment recursion relations for led us to the definitive conclusion that the moments uniquely determine the probability distribution, according to Carleman’s theorem. Using extrapolations of the derivative of integer moments () to , we were able to find a “free energy” . Such a free energy splits into two possible extrapolations (from even and odd moments) as one goes through the transition point by increasing . The latter transition point coincides with that found in Monte Carlo simulations of the sign transition. We have not completely interpreted this connection in the present paper. Furthermore, we studied the high moments of the partition function below the transition, and found a very interesting non-monotonic behavior including step structures that propagate on the moment number axis, as changes.
Using the fact that moments can be computed exactly we studied the celebrated ratio proposed by NSS. We have shown, analytically that indeed in the ratio does not show a transition as suspected numerically[4, 8, 24] on regular lattices. Furthermore, we have shown that hierarchical lattices exhibit the same logarithmic to exponential crossover for surmised in references and .
Finally, we studied a recursion relation for the full probability distribution for , finding an extremely complex structure even for systems as small as . Previous remarks by Roux and Coniglio of anomalous accumulation of probability at are confirmed. Nevertheless, their claim that the hierarchical lattice becomes essentially one dimensional for large , and thus, the probability distribution should approach a Gaussian is not borne out from our results. One obvious difference is that for a Gaussian all cumulants, larger than two, should be zero which is in disagreement with exact results of section IV. No evident signal of the transition, beyond that already inferred from the order parameter , is found from the full probability distribution.
Medina and Kardar have studied the moments for the sign problem interpreting them as partition functions for -body one dimensional Hamiltonians with contact interactions. Most of the focus, however, has been on the low behavior that yields cummulants of . Nevertheless, it would be interesting to interpret the findings of this paper, regarding high moments, in the light of a many body-theory. A previous effort by Zhang focused on the Hartree-Fock approximation valid only for a large number of particles (higher moments). In Zhang’s approach the sign model was equivalent to finding the ground state of the many body Hamiltonian
where is a charge that acts via contact interaction of the particle: for and for . Zhang’s approach yields . Our findings predict, from the relation , for large (see also ), where increases as . For lower the behavior is non-trivial and is certainly not represented a simple powerlaw of . Therefore, Zhangs results represent some kind of intermediate regime. A more detailed solution of eq. (9) might yield the ‘solitonic’ patterns reported here (see section IV) which are not well understood. As speculated in section IV, the ground state formed by particles with attractive and repulsive interactions might change, suddenly, at critical particle numbers generating discontinuities in the derivative of . More work is needed in this direction.
The highly non-monotonic behavior displayed by the moments calls for caution regarding the regime of validity of moments dependencies on the moment number reported in the literature[3, 23]. Claims of a non-unique relation between moments and the probability distribution were based on expressions only valid in the limit, which is clearly unrelated to the constraints of Carlemans theorem. Obviously, the conclusions of this paper are only valid in the measure to which hierarchical lattices agree with continuum results. For a discussion of the latter point see reference.
Acknowledgements.EM thanks G. Urbina and A. Hasmy for careful reading of the manuscript and R. Paredes for a valuable suggestion. EGA thanks R. Rangel for useful discussions. This work was supported by CONICIT through grant S1-97000368, a grant from the Research Fund of UNEXPO and the POLAR Foundation.
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Practice: What is the mean and standard deviation for the following distribution for the number of drinks you have during a night on the weekend?
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Now we explain the mechanism of the periodic bursting based on nonsmooth bifurcation theory
Finally, part 4 addresses singularity theory in more detail, discussing bifurcation theory
and the close-to-integrable case.
has been widely used to investigate dynamic behaviours of nonlinear components, and to make analytical answers on formation of synchronous resonance, dynamical behaviour of induction machines, chaotic oscillations and Ferro resonance oscillations phenomenon in electrical engineering.
NONLINEAR SOLID MECHANICS: BIFURCATION THEORY
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Pardavi-Horvath, "Mathematical modeling of nonlinear waves and oscillations in gyromagnetic structures by bifurcation theory
methods," Journal of Electromagnetic Waves and Applications, Vol.
Hale, Methods of Bifurcation Theory
, Springer, New York, 1982.
In classical bifurcation theory
, a standard assumption made is that there is a trivial solution from which bifurcation is to occur.
The research interests of George Isac also embrace a wide range of topics, with main contributions in Nonlinear Analysis, Convexity, Optimization, Complementarity Theory, Bifurcation Theory
, Optimal Control, Dynamical systems, Numerical Methods, Nonlinear Analyses in Cones, Stochastic Processes and other.
By using the bifurcation theory
of discrete system in , we obtain that the Hopf bifurcation can be preserved under discretization by Euler method.
basic bifurcation theory
, linear transform theory (Fourier and Laplace transforms), linear systems theory, complex variable techniques .
Topics include complex variables and potential theory (featuring integral representations in a range of analyses methods and nonlinear potential theory in metric spaces), differential equations and nonlinear analysis (mean curvature flow, bifurcation theory
, a nonlinear eigenvalue problem, nonlinear elliptic equations with critical and supercritical Sobolev exponents, eigenvalue analysis of elliptical operators and the theory of nonlinear semigroups), and harmonic analysis (integral geometry and spectral analysis, Fourier analysis and geometric combinatories, eigenfunctions of the Laplacian, fractal analysis via function spaces and five reviews of harmonic analysis techniques). | s3://commoncrawl/crawl-data/CC-MAIN-2019-35/segments/1566027316150.53/warc/CC-MAIN-20190821174152-20190821200152-00055.warc.gz | CC-MAIN-2019-35 | 2,292 | 21 |
https://www.jiskha.com/display.cgi?id=1284422323 | math | posted by Sarah .
Scores on a certain test are normally distributed with a variance of 14. A researcher wishes to estimate the mean score achieved by all adults on the test. Find the sample size needed to assure with 95% confidence that the sample mean will not differ from the population mean by more than 2 units
n = [(z-value * sd)/E]^2
...where n = sample size, z-value will be 1.96 using a z-table to represent the 95% confidence interval, sd = square root of 14 (standard deviation is equal to the square root of the variance), E = 2, ^2 means squared, and * means to multiply.
Plug the values into the formula and finish the calculation. Round your answer to the next highest whole number.
So the answer would be 13.4459 ?
Looks OK! Round up to the next highest whole number, which would be 14.
Thanks MathGuru, the formula helped with a relevant math problem. | s3://commoncrawl/crawl-data/CC-MAIN-2017-30/segments/1500549426639.7/warc/CC-MAIN-20170726222036-20170727002036-00212.warc.gz | CC-MAIN-2017-30 | 867 | 8 |
https://friv-friv2.info/37303.php | math | Jul 30, · Free Download Gps Coordinate Converter 1. Coordinate conversion free download.
Co- ordinate Converter A web- based tool for conversions between projected co- ordinate systems commonly in use in Great Britain and Ireland. 0 - An interactive map that allows users to easily convert various geographical coordinates into different.
Graph Individual ( x, y) Points - powered by WebMath. Find the Equation of a Line Given That You Know Two Points it Passes Through - powered by WebMath. FastGEO, A computational geometry library written in the object pascal language. All about chemical equilibrium Part 2 of 5.
This topic is part of the TCS FREE high school mathematics ' How- to Library'. Home & Hobby software downloads - UTM Coordinate Converter by Ewert Technologies many more programs are available for instant free download.
Download coordinate converter software for free. State Plane coordinate system for the United States is supported.
FastGEO, A computational geometry library written in the object pascal language. All about chemical equilibrium Part 2 of 5.UTM Coordinate Converter allowing you to convert between various Latitude/ Longitudes systems , converts between various geographic coordinate systems the. Free GPS receiver unit software phone, bluetooth, maps for tracking, auto portable handheld GPS devices.
In mathematics the polar coordinate system is a two- dimensional coordinate system in which each point on a plane is determined by a distance from a reference point an angle from a reference direction. In mathematics its polar angle measured from a fixed zenith direction the azimuth angle of its orthogonal projection on a reference plane that.
It contains more than 1000 units of measurement commonly encountered while solving engineering or everyday conversion problems. This Coordinate Converter converts between various geographic coordinate systems, allowing you to convert between various Latitude/ Longitudes systems the Universal Transverse Mercator ( UTM) system.
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TWCC, The World Coordinate Converter is a tool to convert geodetic coordinates in a wide rangeof reference systems. Download Free Geodetic Software Developed.
This page will help you to do that. Superseded replaced by the NGS Coordinate Conversion .Convert Coordinates. In this lesson you' ll learn what a coordinate plane is some coordinate plane terminology.
The most basic plotting skill it to be able to plot x, y points. User account is not.
To see how this works ( you must do so, as this is of such fundamental importance that you simply cannot do any meaningful chemistry without a thorough working understanding of this principle) look again at the hydrogen iodide dissociation reaction. You' ll also see a few examples of coordinate planes in action. | s3://commoncrawl/crawl-data/CC-MAIN-2019-04/segments/1547583662863.53/warc/CC-MAIN-20190119074836-20190119100836-00436.warc.gz | CC-MAIN-2019-04 | 2,858 | 13 |
http://www.appszoom.com/android_applications/math+education/by_matching?status=1 | math | Alert added. Remember that you can edit your alerts from your Settings
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https://www.gradesaver.com/textbooks/math/precalculus/precalculus-6th-edition-blitzer/chapter-p-review-exercises-page-145/158 | math | Work Step by Step
Step 1. Graph the intervals on a number line as shown in the figure. Step 2. Find the union of the two intervals as $(-2,1]\cup [-1,3)=(-2,3)$
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http://tour.penghu.gov.tw/en/tripcontent.aspx?forewordID=8229 | math | How to tour Penghu at the minimum expense and number of days! Special note：The estimated tour fee excludes steamer or air tickets!Suggest season：Spring, Summer
1 day(s)：Letting your heart soar North sea Tour (A paradise for water activities) Gupoyu (A touching love story across time, the feeling of staying on the island alone) (water activity zone) General Island(Wangan) Tiejhanyu (Natural air-conditioning given by nature) (Patrol) Tiejhanyu(Baisha) Sianjiauyu (Jump into the clear water to cleanse the dust on the body and heart together with the blue ocean, golden sand and white waves)( water activity zone) Chipei islet (the pearl of North sea) Staying at the resting place for the first day, let’s unveil slowly the mysterious culture of Fisherman Island (water activity zone) (Starlit barbeque) (Squid fishing at night) The sightseeing wharf in the North Sea Mutou Island 2 day(s)：Filling your memory with the love of Penghu Penghu Reclamation Hall (Walking through the past to understand Penghu) Penghu Reclamation Hall(Magong) The Four-eyes well (The special appearance, the social norm and the ancestral culture have together created the source of Penghu’s life.)。 The Four-eyes well(Magong) Tianhougong (Temple of Goddess) (It was the first Matsu Temple in Taiwan and a first-class cultural heritage. It imitates the traditional architectural style of Chinese palaces and temples. Visit the temple and Matsu will bless you for the rest of your life) Tianhougong(Magong) Shuncheng gate (The most special historic city gate left!) Shuncheng gate(Magong) Guanyinting (Bathing in the remaining light of the sunset, listening to the evening drum and Buddhist music, one can enjoy the beauty of the sunset) Guanyinting(Magong) Fisherman’s Wharf (Walking leisurely along the seaside wooden trestle to enjoy the night view of the seaside and the red light wharf zone) Fisherman’s Wharf(Magong) Magong Airport →(Bring along the love and care of Penghu to engage in another splendid tour in your life) People say goodbye because there will be another encounter. We look forward to the next encounter! Magong Airport (Husi) Makung Airport(Husi)
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https://www.showme.com/sh/?h=FE83YCe | math | Proof that exterior angle of a triangle is greater than either of the non-adjacent angles of a triangle.
11 years ago
Proof of theorem: the measure of an exterior angle of a triangle is greater than the measure of either of the non-adjacent interior angles of the triangle.
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https://en.m.wikisource.org/wiki/Collier%27s_New_Encyclopedia_(1921)/Integral_Calculus | math | Collier's New Encyclopedia (1921)/Integral Calculus
INTEGRAL CALCULUS, a branch of mathematics, the converse of the differential calculus. Having a given or known differential, the integral calculus has for its object to find a function such that, being differentiated, it will produce the given differential. Such expression is called the integral of the differential. The operation of finding the primitive function or integral is called integration. Besides the method of finding the integrals of given differentials, the integral calculus is also applied to various branches of mathematics, as well as to almost every branch of natural philosophy and engineering. | s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575540514893.41/warc/CC-MAIN-20191208202454-20191208230454-00309.warc.gz | CC-MAIN-2019-51 | 667 | 2 |
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Journal Wizard Geometry Midpoint Formula Distance Coordinate.
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https://community.rachio.com/t/wiring-question/3153 | math | Sorry if this is a stupid question but, I know where the wires go, how the heck to I push/plug them into the Rachel 2nd gen?!
Never mind figured this part out.
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https://studysoup.com/tsg/822870/college-physics-volume-1-10-edition-chapter-2-7-problem-46 | math | Step 1 of 3
Linear Momentum - Product if mass and velocity of an object - ⃗ = ⃗ - SI unit: kg*m/s - A vector - The total momentum of a system of objects is the vector sum of the momenta of all the objects - ⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗ +⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗ + ⋯ 1 2 3 Momentum and Newton’s Second Law ⃗ - Ʃ = ⃗ - The net...
Textbook: College Physics, Volume 1
Author: Raymond A. Serway, Chris Vuille
This full solution covers the following key subjects: . This expansive textbook survival guide covers 119 chapters, and 7349 solutions. Since the solution to 46 from 2.7 chapter was answered, more than 215 students have viewed the full step-by-step answer. The answer to “h(x) = x - 3” is broken down into a number of easy to follow steps, and 5 words. This textbook survival guide was created for the textbook: College Physics, Volume 1 , edition: 10. The full step-by-step solution to problem: 46 from chapter: 2.7 was answered by , our top Physics solution expert on 03/09/18, 06:36PM. College Physics, Volume 1 was written by and is associated to the ISBN: 9781285737034. | s3://commoncrawl/crawl-data/CC-MAIN-2020-34/segments/1596439735963.64/warc/CC-MAIN-20200805153603-20200805183603-00582.warc.gz | CC-MAIN-2020-34 | 1,116 | 5 |
https://jgaa.info/getPaper?id=388 | math | Journal of Graph Algorithms and Applications
|Home||Issues||About JGAA||Instructions for Authors|
Special Issue on Selected Papers from the Ninth International Workshop on Algorithms and Computation (WALCOM 2015)
Simultaneous Drawing of Planar Graphs with Right-Angle Crossings and Few Bends
Michael A. Bekos, Thomas C. van Dijk, Philipp Kindermann, and Alexander Wolff
Vol. 20, no. 1, pp. 133-158, 2016. Regular paper.
Abstract Given two planar graphs that are defined on the same set of vertices, a RAC simultaneous drawing is a drawing of the two graphs where each graph is drawn planar, no two edges overlap, and edges of one graph can cross edges of the other graph only at right angles. In the geometric version of the problem, vertices are drawn as points and edges as straight-line segments. It is known, however, that even pairs of very simple classes of planar graphs (such as wheels and matchings) do not always admit a geometric RAC simultaneous drawing. In order to enlarge the class of graphs that admit RAC simultaneous drawings, we allow edges to have bends. We prove that any pair of planar graphs admits a RAC simultaneous drawing with at most six bends per edge. For more restricted classes of planar graphs (e.g., matchings, paths, cycles, outerplanar graphs, and subhamiltonian graphs), we significantly reduce the required number of bends per edge. All our drawings use quadratic area.
Submitted: March 2015.
Reviewed: June 2015.
Revised: July 2015.
Accepted: August 2015.
Final: January 2016.
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