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https://tadalafilmedi.online/94721-notch.html | math | How far the amount they grew more than the bottom part of class if a painting class to ratios worksheet and plot equivalent.
Ratios WordPresscom. Ratio Worksheets Math Worksheets 4 Kids. Ratio Worksheets Printable Math Activities. On this page you will find worksheets on writing ratios using different. Module 1 lesson 1 grade 7.
Finding Ratios Finding Rate k 1 2 3 4 5 6 7 No Filter Finding Ratios link Drag to Scroll Click to Open Example Hover to Enlarge Description Download.
Equivalent ratios A ratio obtained by multiplying or dividing the numerator and denominator of a given ratio by the.
Ratios Math Art Collaborations Teachers and Artists.
Practice on trig ratios worksheet answers. Eureka Math Grade 7 Module 1 HubSpot. 7th Grade Summer Math Packet SAU 39. The lesson contains a power point presentation as well as a worksheet.
Ratio Relations. Ratios and proportional relationships. Using equivalent ratios worksheet answers. Denominator 3 This will create a denominator of a single unit means 1 4. A ratio table shows pairs of corresponding values with an equivalent. Equivalent Ratios Worksheets.
29 Equivalent Ratios Worksheet Pdf Ratio And Proportion Printable Worksheets Easy Tes F Simplifying Grade 5.
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Ratio Relationships. Ch 1 Day 11 Equivalent Ratios 2015-16pdf. Equivalent Ratios Worksheet Educationcom. And worksheets but also in the classroom within artwork and in daily. Learn Multiplication Times Tables 1-10 NO PREP Activity Worksheets Robot.
Ask How is finding equivalent ratios for the table like finding equivalent fractions You are multiplying both parts of the ratio by the same number use visual.
About tables of equivalent ratios tape diagrams double number line.Use Finding Equivalent Unit Fraction with Fractions Find the equivalent.
Walthamstow Hall News
Grade 6 Mathematics. Creating Equivalent Ratios Worksheet Free. Grade 6 Fractions Ratios Rates EduGAINS. Two ratios that have the same value are equivalent ratios Determine. Lesson 2 Using Fractions to Describe Area Lesson 3 Creating Equivalent. Make tables of equivalent ratios relating quantities with whole-number.
Directions Use the digits 1-9 to create 3 equivalent ratios Each digit can only be used once Source Graham.
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Lessons 3 Notes Equivalent Ratios Lesson 4 Notes Equivalent Ratios Lessons 5 Solving Problems by Finding Equivalent Ratios Lesson 6 Solving Problems. | s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446708046.99/warc/CC-MAIN-20221126180719-20221126210719-00216.warc.gz | CC-MAIN-2022-49 | 2,685 | 17 |
https://www.bloodraynebetrayal.com/suzanna-escobar/trending/how-do-you-find-frequency-response-from-impulse-response/ | math | How do you find frequency response from impulse response?
As an equation: X[f] × H[f] = Y[f]. In other words, convolution in the time domain corresponds to multiplication in the frequency domain. Figure 9-7 shows an example of using the DFT to convert a system’s impulse response into its frequency response. Figure (a) is the impulse response of the system.
Is impulse response same as convolution?
Actually, the output signal function Y(t) is considered as the convolution of two functions: the input signal function X(t), and the impulse response function h(t) of the unit, the latter being dependent on its constructional details (e.g. of the input capacitance).
What is frequency response in DSP?
The frequency response of an LTI filter may be defined as the spectrum of the output signal divided by the spectrum of the input signal.
What is the frequency of impulse signal?
The true impulse has a much different magnitude spectrum. It is a constant value across all frequencies between 0 and fs/2 Hz. Its phase spectrum is also a constant. As shown in one of the problems, the phase angle is 0.0 degree over the frequency range of 0 to fs/2 Hz.
What is frequency response of a control system?
– Frequency response is the steady-state response of a system to a sinusoidal input. In frequency-response methods, we vary the frequency of the input signal over a certain range and study the resulting response.
What is impulse response convolution?
Convolution is a very powerful technique that can be used to calculate the zero state response (i.e., the response to an input when the system has zero initial conditions) of a system to an arbitrary input by using the impulse response of a system. It uses the power of linearity and superposition.
What is the best frequency response?
The preferred frequency response for speakers is 20 Hz to 20 kHz. The human audio spectrum ranges from 20 Hz to 20 kHz. Speakers should be able to produce sounds in this range.
What is impulse response of a function?
In signal processing, the impulse response, or impulse response function (IRF), of a dynamic system is its output when presented with a brief input signal, called an impulse. More generally, an impulse response is the reaction of any dynamic system in response to some external change.
Is it possible to calculate the frequency response from impulse response?
Given one, you can calculate the other. The relationship between the impulse response and the frequency response is one of the foundations of signal processing: A system’s frequency response is the Fourier Transform of its impulse response.
What is the equation for convolution in frequency domain?
In the frequency domain, the input spectrum is multiplied by the frequency response, resulting in the output spectrum. As an equation: X [ f] × H [ f] = Y [ f ]. In other words, convolution in the time domain corresponds to multiplication in the frequency domain.
What is impulse response function H(T)?
In the time domain, a system is described by its Impulse Response Function h(t). This function literally describes the response of system at time tto an unit impulse or -function input administered at time t= 0. Suppose that now” is time t, and you administered an impulse to the system at time ˝in the past.
What is the frequency response of a signal?
Remember what the frequency response represents: amplitude and phase changes experienced by cosine waves as they pass through the system. Since the input signal can contain any frequency between 0 and 0.5, the system’s frequency response must be a continuous curve over this range. | s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446711111.35/warc/CC-MAIN-20221206161009-20221206191009-00408.warc.gz | CC-MAIN-2022-49 | 3,613 | 24 |
https://forums.sherdog.com/threads/questions-on-two-day-split.756928/ | math | Alright guys, after reading the FAQ I decided I'm going to start the two day split that's in there. For those that don't know, it's: Day one: Deadlift Overhead press Weighted pullup/chinup Day two: Squat Benchpress Bent over row So I have two questions. 1) What set/rep scheme should I use for all exercises? I was thinking 5x5 for Squat and deadlift, then 3x5 for the rest. Would this work? 2) How would I incorporate cleans into my routine? What rep/set schemes would I use for those? Thank you all in advance for any replies. | s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446711114.3/warc/CC-MAIN-20221206192947-20221206222947-00600.warc.gz | CC-MAIN-2022-49 | 528 | 1 |
https://aetsrhs.org/2015/08/ | math | From Lines To Angles, and Particles To Rigid Bodies
We dove straight into circular motion with the 2nd year students this past week. The primary focus of last year was linear dynamics and although we did study objects that moved along curved paths (projectiles), we were still looking at two-dimensional motion as being composed of two component motions along straight lines.
In the second year program, a good part of the first semester is dedicated to looking at objects that rotate around a central axis. There are two major shifts that will be introduced. The first is the introduction of an entirely new coordinate system – polar coordinates. The students spent most of last year learning about two dimensional vectors in Euclidean space, but this year, we will see that for objects traveling in various curved paths, a polar coordinate space can actually be much easier work with. The other shift will introduce students to collections of particles composed into continuous rigid bodies. This requires some significant changes in how the students view an object’s orientation in space and how an object’s mass is distributed. No longer can we assume that the object’s mass is located at a single point in space. In both cases, we are adding to the complexity of our conception of the universe by adding new representations of both space and the objects that inhabit that space.
Observing Circular Motion
In the modeling pedagogy, a new concept or collection of concepts is introduced using a paradigm lab. These labs are meant to introduce students to a new phenomenon and to be the launching off point of the actual building of a conceptual model.
Using the video analysis and vector visualization tools of LoggerPro, I had the students track the motion of a Styrofoam “puck” that was placed on our air hockey table (yes, we actually have an air hockey table that was donated to the school!) but was also attached to a thin thread to a fixed point on the table. The students used the video to track the motion of the puck as it essentially traveled in a circular path.
Although the lab is a bit tricky to set up, the ability to not only track the position of the object in two dimensions, but also the ability to attach velocity and acceleration vectors to the object is really helpful in engaging students in a great conversation around why the acceleration vector points to the inside of the circle. It also allows us to discover a whole new set of mathematical functions for describing motion. After tracking the position of the puck, we are ready for a class white board discussion.
The Graph Matching Mistake Game
I ask the students to draw the motion map of the puck’s motion in two dimensions including the velocity and acceleration vectors. I then ask them to include the graphs created by LoggerPro. LoggerPro produces a really interesting position vs. time graph in both the x and y dimensions. At this point the class knows the drill, and they use the mathematical function matching tool in LoggerPro to match the graph. I ask the students to include on their whiteboards the function that they think best fits the plotted data. This is where it gets really interesting.
Notice in the above photo that the students used a polynomial function. I then ask the students to use Desmos to plot their graphs. Then I ask them to zoom out on the graph.
This is where they discover how this function can’t explain the position vs time data for an object that continually repeats the same path. Some of the students in the class recognize that the data is better explained using a sine function. Because not all the students have been introduced to this function, it presents an opportunity for some students to teach the other students about how these functions work.
I allow the students to explore the sine function in Desmos, asking them to change the coefficients of the function in order to discover how these coefficients affect the graph.
The next step is to investigate more thoroughly the relationship between the acceleration and the velocity, as well as introduce the benefits of using polar coordinates to describe how an object’s position changes when you are dealing with an object that is traveling in a circular path. Desmos has the ability to change the graph type from the x,y coordinate plate to a polar representation. We discuss the difficulty of representing an object’s circular path using x(t) and y(t) functions as opposed to r(t) and theta(t) because r(t) is just a constant.
Next up, trying to answer the question: “If it’s accelerating inward, then why isn’t it speeding up towards the inside of the circle?!” Once again, the difficult concept of inertia… | s3://commoncrawl/crawl-data/CC-MAIN-2023-23/segments/1685224645810.57/warc/CC-MAIN-20230530131531-20230530161531-00521.warc.gz | CC-MAIN-2023-23 | 4,722 | 14 |
https://www.clickoncare.com/nash-problem-on-spaces-of-arcs | math | The jet schemes and the arc scheme of an algebraic variety give important information about its singularities, in particular about their invariants. A major problem in the area was proposed by J. Nash in 1968. The main goal of this article is to review the results obtained about Nash problem, and some of its modifications. The first three chapters contain an introduction to the subject, including the Nash theorem and a counter-example in dimension 4. The remaining chapters contain results about toric and stable toric varieties, algebraic surfaces, and the higher dimensional case. Also, the embedded Nash problem, the Nash problem for pairs and the local Nash problem are introduced, with some results discussed. | s3://commoncrawl/crawl-data/CC-MAIN-2017-17/segments/1492917127681.50/warc/CC-MAIN-20170423031207-00449-ip-10-145-167-34.ec2.internal.warc.gz | CC-MAIN-2017-17 | 718 | 1 |
http://openstudy.com/updates/51bac9c0e4b0012787fade38 | math | A boy has 3 library tickets and 8 books of his interest in the library. Of
these 8, he does not want to borrow Mathematics Part II, unless Mathematics Part I is
also borrowed. In how many ways can he choose the three books to be borrowed?
Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
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I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
Various cases possible are:
(i) When Maths part-I is borrowed: Here, the boy may borrow maths part-II. So, he has to select 2 books out of the remaining 7 books, which can be done in ways.
(ii) When maths part-I is not borrowed: Here, the boy will not borrow maths part-II. So, he has to select 3 books from the remaining 6 books, which can be done in ways.
∴Total number of ways = +
= 21 + 20 | s3://commoncrawl/crawl-data/CC-MAIN-2017-51/segments/1512948618633.95/warc/CC-MAIN-20171218161254-20171218183254-00180.warc.gz | CC-MAIN-2017-51 | 1,548 | 14 |
https://community.qlik.com/t5/QlikView-Scripting/How-num-function-works-for-date-format/td-p/555995 | math | Discussion Board for collaboration on QlikView Scripting.
if we add num function with current date then it will display some random amount..
Is there anyone to help me regarding the logic implemented in QlikView to calculate the amount.
Thank You In advance.
if you use this function today i.e 03-08-2013, you will get an integer say x. then for the same function combination tomorrow (04-08-2013) you will get x+1 and for day after tomorrow x+2 and so on.
Thats the question...
from where it takes values x ...
How it will calculate value of x
QV Stores dates as serial numbers similar to the case of Excel.
I hope the below link helps you understand better :
This is 1900 Date system:
Hope this helps | s3://commoncrawl/crawl-data/CC-MAIN-2019-13/segments/1552912202704.58/warc/CC-MAIN-20190323000443-20190323022443-00514.warc.gz | CC-MAIN-2019-13 | 702 | 12 |
https://www.stampcommunity.org/topic.asp?TOPIC_ID=80851&whichpage=1򳱮 | math | First of all, I will show the postmark in question:
It is on this cover:
I think it is not a machine cancel because the four bars on the stamp are not horizontally in line with the postmark. At least that is how I see it.
The letters "R.F.D." in the first row are new to me and I do not know what they mean.
I hope someone here can give some information about this postmark. Also to literature, in which I could find something about it.
Oh yes: still the back of the letter:
Have a nice weekend! | s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656104375714.75/warc/CC-MAIN-20220704111005-20220704141005-00070.warc.gz | CC-MAIN-2022-27 | 495 | 7 |
https://www.teachme2.co.za/mathematics-tutors-la-montagne-pretoria | math | These are the Highest Quality Mathematics Tutors in La Montagne, Pretoria. Get Mathematics Lessons in your home with Teach Me 2 – the Best in Tutoring
Mathematics has always been one of my best subjects. I very much enjoyed it and I also did AP Maths at school.
I helped most of my friends at school with Maths and I am keen on stimulating young minds. I only want to tutor Grade 10's because I find them easy to work with.
I'm a final year Applied Mathematics student. Apart from the fact that I do Applied Mathematics as a degree, I believe I am able to explain concepts in a very simplified manner. I have a great knowledge of Mathematics. I am passionate about Maths.
I found it an easy and fun subject to learn. I have a great understanding of the Subject and I can explain it in a way that the learner understands.
I did Maths at school, receiving an 'A' in my final Matric IEB exam. In 2012 I tutored Grade 12 Maths and enjoyed the challenge. | s3://commoncrawl/crawl-data/CC-MAIN-2017-47/segments/1510934806422.29/warc/CC-MAIN-20171121185236-20171121205236-00077.warc.gz | CC-MAIN-2017-47 | 951 | 6 |
http://www.hmsg.co.uk/en/MathematicsClubs | math | Junior Maths Club takes place one lunchtime a week in room 201. It is open to girls in years 7, 8 and 9.
Activities include: taking The Smartie Challenge, a maths quiz along the lines of Who wants to be a millionaire?, where the contestant wins a number of Smarties which doubles with each correct answer; treasure hunts; team puzzles; mathematical who dunnits; code breaking; making models of polyhedra, playing mathematical board games and much more! One of our favourite websites for puzzles is www.nrich.maths.org.uk.
A senior maths club, open to girls in year 10 and above, takes place one lunchtime per week in room 201. We discuss problems from the UKMT follow-on rounds and the Cardiff Senior Mathematics Club.
Girls enter the Junior, Intermediate and Senior Maths Challenge Competitions run by the United Kingdom Mathematics Trust. Teams are entered for the UKMT team maths challenges. In November 2011 our senior team was placed 3rd in the regional final in Cardiff.
Girls in Years 12 and 13 attend meetings of The Senior Mathematics Club which meets about 8 times a year at Cardiff University.
The Mathematics department run maths surgeries every lunchtime for girls who are having difficulty with any aspect of mathematics or who have missed work in mathematics owing to absence.
At the end of year 7 there is a joint geography and maths trip to Cardiff Bay, organised by the geography department. Here are some photographs of the current year 8s enjoying their mathematical discoveries at Techniquest. | s3://commoncrawl/crawl-data/CC-MAIN-2014-42/segments/1414119648146.28/warc/CC-MAIN-20141024030048-00273-ip-10-16-133-185.ec2.internal.warc.gz | CC-MAIN-2014-42 | 1,514 | 7 |
https://www.univerkov.com/a-galvanic-cell-with-an-emf-of-1-5v-and-an-internal-resistance-of-1-0m-is-closed-to-an-external-resistance-of-4-ohm/ | math | A galvanic cell with an EMF of 1.5V and an internal resistance of 1 0m is closed to an external resistance of 4 Ohm. Find the current in the circuit, the voltage drop in the internal part of the circuit, and the voltage at the terminals of the element.
To determine the current in the circuit, we use Ohm’s law for a complete electrical circuit:
I = E / (R + r),
where E is the electromotive force, R is the external resistance of the circuit, r is the internal resistance of the EMF source, I is the current;.
Let’s calculate the current:
I = E / (R + r) = 1.5 / (4 + 1) = 1.5 / 5 = 0.3 (A).
The voltage drop in the inner part of the circuit is determined from the formula:
Ur = I * r.
Substituting the numerical values of the current strength and internal resistance, we get:
Ur = I * r = 0.3 * 1 = 0.3 (B).
The voltage drop across the terminals is determined from the formula:
UR = I * R.
Substituting the numerical values of the current strength and external resistance, we get:
UR = I * R = 0.3 * 4 = 1, 2 (B).
Answer: I = 0.5 (A), Ur = 0.3 (B), UR = 1.2 (B). | s3://commoncrawl/crawl-data/CC-MAIN-2023-50/segments/1700679100745.32/warc/CC-MAIN-20231208112926-20231208142926-00423.warc.gz | CC-MAIN-2023-50 | 1,068 | 15 |
http://mathhelpforum.com/algebra/80767-mechanics-collisions-help.html | math | Hi, not been online in some time but back again now with some more probably simple questions
I can't get my head around this question involving collisions, it's a bit wordy to please bear with me.
Obviously the final velocity of B needs to be greater than 2, but I'm having trouble making this into an equation?3 smooth identical spheres each of mas 1kg move on a straight line on a smooth horizontal floor. B lies between A and C.
Spheres A and B are projected towards each other with speeds 3 m/s and 2 m/s respectivly, and C is projected away from sphere A at a speed of 2m/s.
The coefficient of restitution between any two spheres is e, show that sphere B will only collide with C if e >
Thanks in advance | s3://commoncrawl/crawl-data/CC-MAIN-2017-17/segments/1492917123590.89/warc/CC-MAIN-20170423031203-00064-ip-10-145-167-34.ec2.internal.warc.gz | CC-MAIN-2017-17 | 709 | 6 |
http://www.chiefsplanet.com/BB/showpost.php?p=9314859&postcount=118 | math | Originally Posted by BossChief
I'd like to see the top 10 offensive tackles in the NFL ranked by one metric.
The total amount of sacks allowed all year divided into the total amount of sacks the opposing defenders had that he faced.
That would give a good metric to gauge how well the player actually performs.
Except that you are relying on uninformed people like GoChiefs to decide when a sack is given up by a particular player. that is impossible to determine if you don't know the responsibilities on each and every play. Sounds great in theory, impossible to accurately measure. | s3://commoncrawl/crawl-data/CC-MAIN-2017-13/segments/1490218203515.32/warc/CC-MAIN-20170322213003-00528-ip-10-233-31-227.ec2.internal.warc.gz | CC-MAIN-2017-13 | 584 | 5 |
https://www.booktopia.com.au/applied-reliability-david-c-trindade/prod9781584884668.html | math | Since the publication of the second edition of Applied Reliability in 1995, the ready availability of inexpensive, powerful statistical software has changed the way statisticians and engineers look at and analyze all kinds of data. Problems in reliability that were once difficult and time consuming even for experts can now be solved with a few well-chosen clicks of a mouse. However, software documentation has had difficulty keeping up with the enhanced functionality added to new releases, especially in specialized areas such as reliability analysis.
Using analysis capabilities in spreadsheet software and two well-maintained, supported, and frequently updated, popular software packages-Minitab and SAS JMP-the third edition of Applied Reliability is an easy-to-use guide to basic descriptive statistics, reliability concepts, and the properties of lifetime distributions such as the exponential, Weibull, and lognormal. The material covers reliability data plotting, acceleration models, life test data analysis, systems models, and much more. The third edition includes a new chapter on Bayesian reliability analysis and expanded, updated coverage of repairable system modeling.
Taking a practical and example-oriented approach to reliability analysis, this book provides detailed illustrations of software implementation throughout and more than 150 worked-out examples done with JMP, Minitab, and several spreadsheet programs. In addition, there are nearly 300 figures, hundreds of exercises, and additional problems at the end of each chapter, and new material throughout.
Software and other files are available for download online
"I have used the second edition of this book for an Introduction to Reliability course for over 15 years. ... The third edition ... retains the features I liked about the second edition. In addition, it includes improved graphics ... [and] examples of popular software used in industry ... There is a new chapter on Bayesian reliability and additional material on reliability data plotting, and repairable systems' analysis. ... The book does a good and comprehensive job of explaining the basic reliability concepts; types of data encountered in practice and how to treat this data; reliability data plotting; and the common probability distributions used in reliability work, including motivations for their use and practical areas of application. ... an excellent choice for a first course in reliability. The book also does a good job of explaining more advanced topics ... the book will continue to be a popular desk reference in industry and a textbook for advanced undergraduate or first-year graduate students."
-Journal of the American Statistical Association, June 2014
Basic Descriptive Statistics Populations and Samples Histograms and Frequency Functions Cumulative Frequency Function The Cumulative Distribution Function and the Probability Density Function Probability Concepts Random Variables Sample Estimates of Population Parameters How to Use Descriptive Statistics Data Simulation Reliability Concepts Reliability Function Some Important Probabilities Hazard Function or Failure Rate Cumulative Hazard Function Average Failure Rate Units Bathtub Curve for Failure Rates Recurrence and Renewal Rates Mean Time to Failure and Residual Lifetime Types of Data Failure Mode Separation Exponential Distribution Exponential Distribution Basics The Mean Time to Fail for the Exponential The Exponential Lack of Memory Property Areas of Application for the Exponential Exponential Models with Duty Cycles and Failure on Demand Estimation of the Exponential Failure Rate I" Exponential Distribution Closure Property Testing Goodness of Fit--the Chi-Square Test Testing Goodness of Fit--Empirical Distribution Function Tests Confidence Bounds for I" and the MTTF The Case of Zero Failures Planning Experiments Using the Exponential Distribution Simulating Exponential Random Variables The Two-Parameter Exponential Distribution Test Planning Via Spreadsheet Functions Determining the Sample Size EDF Goodness-of-Fits Tests Using Spreadsheets KS Test Weibull Distribution Empirical Derivation of the Weibull Distribution Properties of the Weibull Distribution Extreme Value Distribution Relationship. Areas of Application Weibull Parameter Estimation: Maximum Likelihood Estimation Method Weibull Parameter Estimation: Linear Rectification Simulating Weibull Random Variables The Three-Parameter Weibull Distribution Goodness of Fit for the Weibull Using a Spreadsheet to Obtain Weibull MLES Using a Spreadsheet to Obtain Weibull MLES for Truncated Data Spreadsheet Likelihood Profile Confidence Intervals for Weibull Parameters The Normal and Lognormal Distributions Normal Distribution Basics Applications of the Normal Distribution The Central Limit Theorem Normal Distribution Parameter Estimation Simulating Normal Random Variables The Lognormal Life Distribution Properties of the Lognormal Distribution Lognormal Distribution Areas of Application Lognormal Parameter Estimation Some Useful Lognormal Equations Simulating Lognormal Random Variables Using a Spreadsheet to Obtain Lognormal MLEs Using a Spreadsheet to Obtain Lognormal MLEs for Interval Data Reliability Data Plotting Properties of Straight Lines Least Squares Fit (Regression Analysis) Rectification Probability Plotting for the Exponential Distribution Probability Plotting for the Weibull Distribution Probability Plotting for the Normal and Lognormal Distributions Simultaneous Confidence Bands Order Statistics and Median Ranks Analysis of Multicensored Data Multicensored Data Analysis of Interval (Readout) Data Life Table Data Left-Truncated and Right-Censored Data Left-Censored Data Other Sampling Schemes (Arbitrary Censoring: Double and Overlapping Interval Censoring)--Peto--Turnbull Estimator Simultaneous Confidence Bands for the Failure Distribution (or Survival) Function Cumulative Hazard Estimation for Exact Failure Times Johnson Estimator Obtaining Bootstrap Confidence Bands Using a Spreadsheet Physical Acceleration Models Accelerated Testing Theory Exponential Distribution Acceleration Acceleration Factors for the Weibull Distribution Likelihood Ratio Tests of Models Confidence Intervals Using the LR Method Lognormal Distribution Acceleration Acceleration Models The Arrhenius Model Estimating I"H with More Than Two Temperatures Eyring Model Other Acceleration Models Acceleration and Burn-In Life Test Experimental Design An Alternative JMP Input for Weibull Analysis of High-Stress Failure Data Using a Spreadsheet for Weibull Analysis of High-Stress Failure Data Using A Spreadsheet for MLE Confidence Bounds for Weibull Shape Parameter Using a Spreadsheet for Lognormal Analysis of the High-Stress Failure Data Shown in Table 8.5 Using a Spreadsheet for MLE Confidence Bounds for the Lognormal Shape Parameter Using a Spreadsheet for Arrhenius--Weibull Model Using a Spreadsheet for MLEs for Arrhenius--Power Relationship Lognormal Model Spreadsheet Templates for Weibull or Lognormal MLE Analysis Alternative Reliability Models Step Stress Experiments Degradation Models Lifetime Regression Models The Proportional Hazards Model Defect Subpopulation Models Summary JMP Solution for Step Stress Data in Example 9.1 Lifetime Regression Solution Using Excel JMP Likelihood Formula for the Defect Model JMP Likelihood Formulas for Multistress Defect Model Example System Failure Modeling: Bottom-Up Approach Series System Models The Competing Risk Model (Independent Case) Parallel or Redundant System Models Standby Models and the Gamma Distribution Complex Systems System Modeling: Minimal Paths and Minimal Cuts General Reliability Algorithms Burn-In Models The "Black Box" Approach--An Alternative to Bottom-Up Methods Quality Control in Reliability: Applications of Discrete Distributions Sampling Plan Distributions Nonparametric Estimates Used with the Binomial Distribution Confidence Limits for the Binomial Distribution Normal Approximation for Binomial Distribution Confidence Intervals Based on Binomial Hypothesis Tests Simulating Binomial Random Variables Geometric Distribution Negative Binomial Distribution Hypergeometric Distribution and Fisher's Exact Test Poisson Distribution Types of Sampling Generating a Sampling Plan Minimum Sample Size Plans Nearly Minimum Sampling Plans Relating an OC Curve to Lot Failure Rates Statistical Process Control Charting for Reliability Repairable Systems Part I: Nonparametric Analysis and Renewal Processes Repairable versus Nonrepairable Systems Graphical Analysis of a Renewal Process Analysis of a Sample of Repairable Systems Confidence Limits for the Mean Cumulative Function (Exact Age Data) Nonparametric Comparison of Two MCF Curves Renewal Processes. Homogeneous Poisson Process MTBF and MTTF for a Renewal Process MTTF and MTBF Two-Sample Comparisons Availability Renewal Rates Simulation of Renewal Processes Superposition of Renewal Processes CDF Estimation from Renewal Data (Unidentified Replacement) True Confidence Limits for the MCF Cox F-Test for Comparing Two Exponential Means Alternative Approach for Estimating CDF Using the Fundamental Renewal Equation Repairable Systems Part II: Nonrenewal Processes Graphical Analysis of Nonrenewal Processes Two Models for a Nonrenewal Process Testing for Trends and Randomness Laplace Test for Trend Reverse Arrangement Test Combining Data from Several Tests Nonhomogeneous Poisson Processes Models for the Intensity Function of an NHPP Rate of Occurrence of Failures Reliability Growth Models Simulation of Stochastic Processes Bayesian Reliability Evaluation Classical versus Bayesian Analysis Classical versus Bayes System Reliability Bayesian System MTBF Evaluations Bayesian Estimation of the Binomial p The Normal/Normal Conjugate Prior Informative and Noninformative Priors A Survey of More Advanced Bayesian Methods Gamma and Chi-Square Distribution Relationships Problems Answers to Selected Exercises References Index
Number Of Pages: 600
Published: 26th August 2011
Publisher: Taylor & Francis Inc
Country of Publication: US
Dimensions (cm): 24.8 x 17.1
Weight (kg): 1.23
Edition Number: 3
Edition Type: New edition | s3://commoncrawl/crawl-data/CC-MAIN-2018-39/segments/1537267156376.8/warc/CC-MAIN-20180920020606-20180920040606-00157.warc.gz | CC-MAIN-2018-39 | 10,199 | 15 |
https://www.guitaretab.com/p/peter-and-gordon/256088.html | math | Help us to improve GuitareTab.comTake our survey!
Peter And Gordon – Woman chords
"Woman" (capo: 2nd. fret) Intro: A ____Verse: 1A D6/A Woman, do you love meD6/A A C#m/G# Woman, if you need me thenF#m B7 E Believe me I need youEaug.5 A Asus4---A7 To be my___woman (Repeat 1st. Verse)____Chorus: 1D And should you ask me how I'm doingE7 A C#m/E F#m What shall I say? Things are OKB7 But I know that they're notG E And I still may have lost you____Verse: 1 (Repeated)A D6/A Woman, do you love meD6/A A C#m/G# Woman, if you need me thenF#m B7 E Believe me I need youEaug.5 A Asus4---A7 To be my___woman____Chorus: 2D I hope you'll take your time and tell meE7 A C#m/E F#m When we're alone, love will come homeB7 I would give up my worldG E If you'll say that my girl is my woman____Music: A---D6/A D6/A---A---C#m/G# F#m---B7---E Eaug.5---A---A7 ____Bridge:A F#m7/A I've got plenty of time(I've got plenty of time)Dmaj7 E7/6 E7 Plenty just to get through itA F#m7/A Once again you'll be mine(Once again you'll be mine)Dmaj7 E7/6 E7 I still think we can do____itE7/6 Bm7 E7 And you know how much I love you____Verse: 2A D6/A Woman, don't forsake meD6/A A C#m/G# Woman, if you take me thenF#m B7 E Believe me I'll take youEaug.5 A C#m/G#---F#m---C#m/E To be my woman________________________Ending Ritardando: D---Bm7---E7---A | s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446711394.73/warc/CC-MAIN-20221209080025-20221209110025-00119.warc.gz | CC-MAIN-2022-49 | 1,321 | 3 |
https://lists.gnu.org/archive/html/guile-user/2002-06/msg00118.html | math | [Date Prev][Date Next][Thread Prev][Thread Next][Date Index][Thread Index]
Re: C++ STL
Re: C++ STL
Mon, 24 Jun 2002 17:50:01 -0300
Yes, I think you are right. However, I think there are some ideas that
could be interesting to use. For instance, it would be nice if we could do
things like this:
(for_each_c++ (i (iota 1 10)) (line (file_lines "file_name.txt)) (in
(some_function i line in))
meaning that some_function would be executed with i going from 1 to 9, line
would be consecutive lines from a file and in would be lines got from user
input (and the "loop" would finish when i or line became #f). In this
example, for_each_c++ itself could be a generator that would return the
consecutive values of some_function, and so it could be used inside another
for_each_c++ (or other iterator-aware algorithm).
"Eric E Moore" <address@hidden> wrote in message
>Not the whole STL, but good chunks of it. For example we already have
a generic singly linked list type, with sort (sort), merge (merge),
copy (list-copy), transform (map) etc. operations defined on it.
Similarly we have some functions for operating on tree structures
(built as lists of lists). We have a (non-resizing) vector type,
which is less supported than the others, but at least can be sorted,
and supports a transform operation (of sorts).
>The way that variable access works in scheme means that iterators and
much of the rest of the STL aren't especially needed.
>It might be worth generalizing some of the functions, but most
schemers tend to use the list-based ones most of the time, which are | s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178369523.73/warc/CC-MAIN-20210304205238-20210304235238-00094.warc.gz | CC-MAIN-2021-10 | 1,567 | 27 |
http://www.solutioninn.com/currently-a-call-contract-with-an-exercise-price-of-10 | math | Question: Currently a call contract with an exercise price of 10
Currently a call contract with an exercise price of $10 on a share of List Aerospace’s common stock is selling for (that is, its premium is) $2. What would the profit or loss graph (similar to that in figure) look like for this option? In drawing this graph, assume that the option is being evaluated on its expiration date. What are the maximum profits, maximum losses, and the break-even point? How would this graph change if the exercise price was $12 and the price (or premium) of the option was $4?
Relevant QuestionsSales for J. P. Hulett Inc. during the past year amounted to $4 million. Gross profits totaled $1 million, and operating and depreciation expenses were $500,000 and $350,000, respectively. Dividend income for the year was ...Kabutell, Inc. had net income of $750,000, cash flow from financing activities of $50,000, depreciation expenses of $50,000, and cash flow from operating activities of $575,000. Calculate the quality of earnings ratio. What ...The liabilities and owners’ equity for Campbell Industries is as follows:Accounts payable ........ $ 500,000Notes payable ........ 250,000Current liabilities ......... $ 750,000Long-term debt ...Draw a profit or loss graph (similar to figure) for a put contract with an exercise price of $45 for which a $5 premium is paid. You may assume that the option is being evaluated on its expiration date. Identify the ...Marx and Winter, Inc. operate a chain of retail clothing stores throughout the U.S. Midwest. The firm recently entered into a loan agreement for $20 million that carries a floating rate of interest equal to LIBOR plus 50 ...
Post your question | s3://commoncrawl/crawl-data/CC-MAIN-2017-39/segments/1505818687484.46/warc/CC-MAIN-20170920213425-20170920233425-00104.warc.gz | CC-MAIN-2017-39 | 1,700 | 4 |
https://www.slideshare.net/abhishekgunasekaran/causes-of-change | math | OBJECTIVESDefine enthalpyDistinguish between heat and temperaturePerform calculations using molar heat capacity
Key termsEnergy (E): - the ability to do work or produce heat.Thermodynamics: - the study of the inter action of heat andother kinds of energy.Heat (q): - the transfer of energy between two objects (internalversus surroundings) due to the difference in temperature.Work (w): - when force is applied over a displacement in thesame direction or a change in volume under the same pressure(w = F × d = −P ΔV).-Work performed can be equated to energy if no heat isproduced (E = w). This is known as the Work Energy Theorem.
Key termsInternal Energy (E): - total energy from work andheat within a system.Temperature: - the average kinetic energy of all theparticles in a substance. - Temperature is NOT Heat.A massive substance with a low temperature canhave a lot of internal heat. This is because there are alot of particles and even though their kinetic energyis low, their TOTAL energy is large.
EnthalpyEnthalpy (H): - the amount of internal energy at aspecific pressure and volume (when there is no workdone).ΔE=q+w (if w=0,thenΔE=q=H)ΔE = q + w ΔE = Change in System’s Internal Energy q= heat w = work
Heat unitHeat Unit: - the measuring units to measure heat orenergy.Specific Heat (cP): - the amount of heat needed toraise one gram of substance by one degree Celsius orone Kelvin.- the higher the specific heat, the more each gram ofsubstance can “hold” the heat. - units are in J/(g • °C)or kJ/(kg • °C) ; J/(g • K) or kJ/(kg • K)
Heat unit Molar Heat Capacity (C): - the amount of heat needed to raise one mole of substance by one degree Celsius or one Kelvin.- the higher the molar heat capacity, the more heat each mole or each particle of a substance can “hold”. - units are in J/(mol • °C) or kJ/(kmol • °C) ; J/(mol • K) or kJ/(kmol • K) Joules: - the metric unit to measure heat or energy named after English physicist James Prescott Joule.
Formulas and termsq = mcPΔT q = nCΔTq = Change in Heat (J or kJ) ΔT = Change inTemperature (in °C or K) m = mass (g or kg) cP =Specific Heat [J/(g • °C or K) or kJ/(kg • °C or K)] n =moles (mol or kmol) C = Molar Heat Capacity [J/(mol• °C or K) or kJ/(kmol • °C or K)]
Substance Specific Heat J/(g • °C or K)Ice H2O(s) 2.01 Water H2O(l) 4.18 Steam H2O(g) 2.00 Ammonia NH3 (g) 2.06 Methanol CH3OH (l) 2.53 Ethanol C2H5OH (l) 2.44 Aluminum Al (s) 0.897
Substance Specific Heat J/(g • °C or K)Carbon (graphite) C (s) 0.709 Copper Cu (s) 0.385 Iron Fe (s) 0.449 Silver Ag (s) 0.235 Gold Au (s) 0.129 Aluminum Chloride, AlCl3 (s) 0.690
Forces Relationship between Molar Heat Capacity and Specific Heat (Molar Mass) × (Specific Heat) = (Molar Heat Capacity) mol× g•K = mol•K Example : How much energy in kJ, is needed to heat 25.0 mol of water from 30.0°C to 75.0°C? Cwater = 75.3 J/(mol • °C) n = 25.0 mol H2O ΔT = 75.0°C − 30.0°C = 45.0°C q=? q = nCΔT q = (25.0 mol)(75.3 J/(mol • °C))(45.0 °C) = 84712.5 J q = 84.7 kJ
OBJECTIVESDefine thermodynamicsCalculate the enthalpy change for a given amount ofsubstance for a given change of temperature
Key termsSystem: - a part of the entire universe as defined bythe problem.Surrounding: - the part of the universe outside thedefined system.Open System: - a system where mass and energy caninterchange freely with its surrounding.Closed System: - a system where only energy caninterchange freely with its surrounding but mass notallowed to enter or escaped the system.
Key termsIsolated System: - a system mass and energy cannotinterchange freely with its surrounding. ExothermicProcess (ΔE < 0): - when energy flows “out” of thesystem into the surrounding.Endothermic Process (ΔE > 0): - when energy flowsinto the system from the surrounding. (Surroundinggets Colder.)Molar Enthalpy Change (∆H): - the amount of changein energy per mole of substance (J/mol or kJ/mol).
Molar Enthalpy Change for Kinetic (Temperature) ChangeExample: Calculate the change in temperature and the molarenthalpy change of iron when it cools from 243.7°C to 18.2°C.Comment on the nature of this thermodynamic process.∆H=CΔT∆H = Molar Enthalpy Change (J/mol kJ/mol)ΔT = Change in Temperature (in °C or K)∆T=Tf −Ti∆H > 0 (endothermic) ∆H < 0 (exothermic)C = Molar Heat Capacity [J/(mol • °C or K)
OBJECTIVESExplain the principles of calorimetryUse Hess’s law and standard enthalpies of formationto calculate ΔH
Key termsStandard State: - standard conditions of 1 atm and25°C. It is denote by a superscript “o”.Standard Molar Enthalpy of Formation (ΔHof): - theamount of heat required / given off to make 1 mole ofcompound from its elemental components understandard conditions.- the Molar Heat of Formation of ALL ELEMENTS is 0kJ. - the state of the compound affects the magnitudeof Hf.
Key terms Molar Heat of Reaction (ΔHrxn): - the amount of heat released when one mole of reactant undergoes various chemical or physical changes.- examples are ΔHcomb, ΔHneut (neutralization), ΔHsol (solution). Standard Molar Enthalpy of Reaction (ΔHorxn): - the amount of heat involved when 1 mol of a particular.
Formulas and termsΔH = nΔHrxnΔH = Change in Enthalpy ΔHrxn = Molar Heat of Reaction(kJ/mol)ΔH = nΔHcombn = moles ΔHcomb = Molar Heat of Combustion (kJ/mol)Product is produced or 1 mol of a particular reactant isconsumed under standard conditions of 1 atm and 25°C.
Hess’s Law Hess’s Law: the indirect method of obtaining overall ΔH°rxn of a net reaction by the addition of ΔH°rxn of a series of reactions.- when adding reactions, compare the reactants and products of theoverall net reaction with the intermediate (step) reactions given.Decide on the intermediate reactions that need to be reversed and /or multiply by a coefficient, such that when added, the intermediateproducts will cancel out perfectly yielding the overall net reaction.- if a particular reaction needs to be reversed (flipped), the sign ofthe ΔH for that reaction will also need to be reversed.- if a coefficient is used to multiply a particular reaction, the ΔH forthat reaction will also have to multiply by that same coefficient.
ExampleExample: Determine the ΔH°rxn for the reaction S (s) + O2(g) → SO2 (g), given the following reactions. S(s) + 32 O2(g) → SO3 (g) ΔH°rxn = −395.2 kJ2SO2(g) +O2(g)→2SO3(g) ΔH°rxn =−198.2kJSO2 in the net reaction is on the product side, whereas 2SO2 in the second reaction is on the reactant side. Hence,we need to reverse the second reaction and its sign of theΔH°rxn.There is only 1 SO2 in the net reaction, whereas there are 2SO2 in the second reaction. Therefore the second reactionand its ΔH°rxn need to be multiply by the coefficient of 1⁄2.
Standard Enthalpy of Reaction Direct Method to determine Standard Enthalpy of Reaction ΔHorxn = ΣHoproducts − ΣHoreactants ΔHorxn = Change in Enthalpy of Reaction ΣHoproducts = Sum of Heat of Products (from all nΔHof of products) ΣHoreactants = Sum of Heat of Reactants (from all nΔHof of reactants)
OBJECTIVESDefine enthalpy, discuss the factors that influencethe sign and magnitude of ΔS for a chemical reactionDescribe Gibbs energy, and discuss the factors thatinfluence the sign and magnitude of ΔGIndicate whether ΔG values describe spontaneous ornonspontaneous reactions
Key termsFirst Law of Thermodynamics: - states that energy cannot becreated or destroyed. It can only be converted from one form toanother. Therefore, energy in the universe is a constant- also known as the Law of Conservation of Energy (ΣEinitial =ΣEfinal).Calorimetry: - uses the conservation of energy (Heat Gained =Heat Lost) to measure calories (old unit of heat: 1 cal = 4.184 J).- physical calorimetry involves the mixing of two systems (onehotter than the other) to reach some final temperature.- the key to do these problems is to identify which system isgaining heat and which one is losing heat.
A Simple Styrofoam CalorimeterConstant-Pressure Calorimeter (or StyrofoamCalorimeter) - commonly used to determineΔHneut, ΔHion, ΔHfus, ΔHvap, ΔHrxn of non-combustion reaction. First, the sample’s mass ismeasured. Water is commonly used to absorb orprovide the heat for the necessary change. The initialand final temperatures of the water arerecorded, allowing us to find the amount of heatchange. By applying the law of conservation ofenergy, we can then calculate the necessary molarenthalpy of change.
Molar Heat of CombustionMolar Heat of Combustion (ΔHcomb): - the amountof heat released when one mole of reactant is burnedwith excess oxygen.
Enthalpy of Combustion ΔH = nΔHcomb ΔH = Change in Enthalpy n = moles ΔHcomb = Molar Heat of Combustion (kJ/mol)
Chemical Combustion CalorimetryHeat Lost = Heat Gained (Combustion Reaction)(water, kinetic)nsampleΔHcomb = CcalΔT (if bomb calorimeter isused) ornsampleΔHcomb = mwcP,wΔT (if the heat absorbedby the calorimeter itself is ignored)
Schematic of a Bomb CalorimeterThe reaction is often exothermic and thereforeΔHcomb < 0.We often use a constant-volume calorimeter (or bombcalorimeter) to determine ΔHcomb due to its well-insulated design. It is calibrated for the heat capacity ofthe calorimeter, Ccal, before being use for to calculateΔHcomb of other substances. The sample is measured andburned using an electrical ignition device. Water iscommonly used to absorb the heat generated by thereaction. The temperature of the water increases,allowing us to find the amount of heat generated. Byapplying the law of conservation of energy, we can thencalculate the ΔHcomb of the sample.
The world is made up of chemical reactions, it’s theway how you look at it and take it to your stride | s3://commoncrawl/crawl-data/CC-MAIN-2017-30/segments/1500549424148.78/warc/CC-MAIN-20170722202635-20170722222635-00020.warc.gz | CC-MAIN-2017-30 | 9,766 | 29 |
https://www.cssd.ab.ca/schools/stfrancis/Programs/mathematics/Pages/default.aspx | math | Co-ordinating Teacher (CT)
Mr. Marco Filipetto
Math Tips for Students and Parents: Math – Study Skills
Course Progression Map
Who should take the Mathematics-1 course sequence?
Mathematics-1 is designed for students who plan to apply for post-secondary programs that require calculus skills.
If you want to enter a post-secondary program such as engineering, mathematics, sciences, some business studies, or other programs that require advanced math skills, you should take Mathematics-1.
Mathematics-1 includes topics such as permutations and combinations, relations and functions, sequences and series, and trigonometry.
Mathematics 30-1 is a co-requisite for Mathematics 31 and may be required for post-secondary calculus courses.
Who should take the Mathematics-2 course sequence?
Mathematics-2 is designed for students who want to attend a university, college, or technical institute after high school, but do not need calculus skills.
If you want to study at the post-secondary level in fields such as arts programs, civil engineering technology, medical technologies, or some apprenticeship programs, you should take Mathematics-2. This sequence will fulfill most high-school students’ needs.
Mathematics-2 includes topics such as relations, functions and equations, probability, statistics, and trigonometry.
Who should take the Mathematics-3 course sequence?
Mathematics-3 is designed for students who want to learn the mathematics needed to enter most trades or want to enter the workforce after high school.
Mathematics-3 includes topics such as finance, geometry, measurement, and trigonometry.
Most apprenticeship training programs in Alberta will recommend students successfully complete Mathematics 30-3. However, a small number of apprenticeship training programs may require students to complete the -2 course sequence in order to meet the mathematics entrance level competencies for those trades. Further information regarding apprenticeships can be found at http://www.albertacanada.com/opportunity/work/credentials-regulated-trades.aspx
NOTE: No matter the course sequence you choose you should always check the most up-to-date information on post-secondary mathematics entrance requirements, which is available on the Alberta Learning Information Service (ALIS) website and directly from the institutions themselves.
For more in depth information and FAQs; visit the Alberta Learning website at: http://education.alberta.ca/teachers/program/math/... | s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600400192887.19/warc/CC-MAIN-20200919204805-20200919234805-00597.warc.gz | CC-MAIN-2020-40 | 2,474 | 19 |
https://www.openfile.me/bibtex | math | How to open BibTeX document .bibtex files
Have you had trouble opening the bibtex file on your computer? What are bibtex files? We explain what they are and recommend software that we know will open them.
What is bibtex file?
Files with bibtex extension can be most typically found as bibliographic databases from BibTeX reference management software.
BibTeX document description
File extension bibtex is used for a native BIBTEX doctype class is for BibTeX bibliographic databases as used by the LaTeX package for the TeX-typesetting program.
A .bibtex doctype supports TeX macro encodings of European characters, string substitution and hypertext links to "crossref" entries.
Suggested software to open bibtex file
A reference handling program for LaTeX documents
A sophisticated source code editor for programmers | s3://commoncrawl/crawl-data/CC-MAIN-2023-40/segments/1695233510501.83/warc/CC-MAIN-20230929090526-20230929120526-00750.warc.gz | CC-MAIN-2023-40 | 816 | 10 |
http://en.wnrcn.com/news.asp?id=74 | math | |Obliquity sensor, just as its name implies is Angle size and transmission Angle perception. If it is only measuring Angle? The answer is more than that. When an object has a tilt, we can use Newton's laws of basic mechanics, through the analysis of the concrete stress distribution of the object, get the acceleration of the object, the integral in time be able to get speed, acceleration and speed in time for integral can get displacement. Through the obliquity sensor, therefore, we can get is acceleration, velocity and position information. | s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780057417.92/warc/CC-MAIN-20210923074537-20210923104537-00573.warc.gz | CC-MAIN-2021-39 | 546 | 1 |
https://www.coursehero.com/tutors-problems/Finance/535008-Problem-3-A-Treasury-bond-futures-contract-settles-at-105-8-/ | math | a. What is the present value of the futures contract?
b. If the contract settles at 105-8, are current market interest rates higher or lower than the standardized rate on a futures contract? Explain.
c. What is the implied annual interest rate on the futures contract?
d. Calculate the new value of the futures contract if interest rates increase by 1 percentage point annually.
e. Calculate your profit or loss if you sold a futures contract at 105-8 and purchased an offsetting contract when rates increased by 1 percentage point annually.
See attached file for full problem description.
Recently Asked Questions
- Please refer to the attachment to answer this question. This question was created from test 2.docx.
- Suppose X is a normal with zero mean and standard deviation of $10 million. a) Find the value at risk for X for the risk tolerances h=0.01, 0.02, 0.05, 0.10,
- What are typical roles and rules that one might see in a chemical dependent family? can you elaborate | s3://commoncrawl/crawl-data/CC-MAIN-2018-30/segments/1531676589404.50/warc/CC-MAIN-20180716154548-20180716174548-00332.warc.gz | CC-MAIN-2018-30 | 980 | 10 |
http://oilf.blogspot.com/2015/04/math-problems-of-week-common-core_17.html | math | A sample high school math problem from PARCC (The Partnership for Assessment and Readiness for College and Careers, a consortium of 23 states involved in developing Common Core tests):
PARCC's discussion of how this problem aligns with Common Core Standard MP.7:
A more challenging set of "seeing quadratic structure" problems from over a century ago (Wentworth's New School Algebra):
1. Are there other useful structures one could recognize the PARCC problem as having other than Q2 + 2Q = 0? For example, might recognizing it as having the form a*a = b*a be an alternative, non-brute-force way of seeing its solutions?
2. If "seeing structure in a quadratic equation" warrants a special Common Core standard (MP.7), why aren't students getting more challenging quadratic structure problems like those in Wentworth above?
3. Was "seeing structure in a quadratic equation" even more important a century ago, before we needed the Common Core authors to remind us of how important it is? | s3://commoncrawl/crawl-data/CC-MAIN-2017-13/segments/1490218189903.83/warc/CC-MAIN-20170322212949-00281-ip-10-233-31-227.ec2.internal.warc.gz | CC-MAIN-2017-13 | 985 | 6 |
https://www.kaysonseducation.co.in/questions/p-span-sty_4499 | math | If A bar of given length moves with its extremities on two fixed straight lines at right angles, then the locus of any point on the bar describes a/an
Let the fixed straight lines be along the coordinate axes and ABbe the bar of length l such that its extremities A(a, 0) and B(0, b) are on the coordinate axes. Then,
Let P(h, k) be a point marked on the bar such that it divides the bar AB in the ratio λ : 1. Then,
Substituting these values in (i), we get
Hence, the locus of P(h, k) is
which represents an ellipse.
The locus of the point of intersection of tangents to the ellipse , which make complementary angles with x-axis, is
The locus of the foot of the perpendicular drawn from the centre of the ellipse on any tangent is
, be the end points of the latusrectum of the ellipse x2 + 4y2 = 4. The equations of parabolas with latusrectum PQ are
The locus of the point of intersection of perpendicular tangents to.
S(3, 4) and S’(9, 12) are two foci of an ellipse. If the foot of the perpendicular from S on a tangent to the ellipse has the coordinates (1, –4), then the eccentricity of the ellipse is
The tangent at a point P(θ) to the ellipse cuts the auxiliary circle at points Q and R. If QR subtends a right angle at the centre C of the ellipse, then the eccentricity of the ellipse is
Let d1 and d2 be the lengths of the perpendiculars drawn from fociS and S’ of the ellipse to the tangent at any point P on the ellipse. Then, SP : SP’ =
The eccentricity of an ellipse with centre at the origin and axes along the coordinate axes, is 1/2. If one of the directrices is x = 4, then the equation of the ellipse is
If the tangents are drawn to the ellipse x2 + 2y2 = 2, then the locus of the mid-point of the intercept made by the tangents between the coordinate axes is
The normal at a point P on the ellipse x2 + 4y2 = 16 meets the x-axis at Q. If M is the mid-point of the line segment PQ then the locus of M intersects the latusrectums of the given ellipse at the points | s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964358480.10/warc/CC-MAIN-20211128073830-20211128103830-00608.warc.gz | CC-MAIN-2021-49 | 1,991 | 16 |
https://www.christies.com/lotfinder/lot/crown-1662-by-john-roettier-first-3812809-details.aspx?intObjectID=3812809 | math | This coin has many characteristics of a proof. The obverse die in particular has been very carefully prepared and polished. The flan is very full, the edges a little higher than normal and the teeth carefully cut. In fact the teeth actually protect the edge by projecting slightly. On the reverse the eleven harp strings are weak as is the crown over the Irish shield. All these characteristics are shared by the example in the Lingford sale, lot 281, which was described as 'struck like a proof', and by the example in the Inveruglas collection (Noble auction 48, lot 4461), which was described as a proof.
Of these coins Linecar and Stone state '...the dividing line between them and what may constitute a proof is often a matter of opinion; furthermore they command prices close to those realised by actual proofs.' In his recent pamphlet 'J Roettier, Patterns and Proofs of Charles II, Crowns, Notes', Roddy Richardson goes one stage further. 'There is a very good case for the so called "struck like a proof" pieces...I am of the opinion that these are in fact proofs and should be listed as such.' | s3://commoncrawl/crawl-data/CC-MAIN-2018-26/segments/1529267864303.32/warc/CC-MAIN-20180621231116-20180622011116-00121.warc.gz | CC-MAIN-2018-26 | 1,103 | 2 |
https://neocities.org/site/yobun?event_id=1304740 | math | added many yume nikki buttons, and two misc! i forgot how much i loved doing buttons! ^__^
A tag can only be a single word, and can only contain letters and numbers.
Select the tags you would like to remove:
You are going to block this site. This will do the following:
Are you sure you want to do this? | s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141711306.69/warc/CC-MAIN-20201202144450-20201202174450-00362.warc.gz | CC-MAIN-2020-50 | 303 | 5 |
https://www.physicsforums.com/threads/centre-of-mass-collision-momentum.685864/ | math | Two blocks m1 and m2 are connected by an ideal spring of force constant k. The blocks are placed on smooth horizontal surface. A horizontal force F acts on the block m1. Initially spring is relaxed, both the blocks are at rest. What is maximum elongation of spring? i think it would be when both the objects are moving with same velocity, so i applied law of conservation of energy but the equation has too many variables. | s3://commoncrawl/crawl-data/CC-MAIN-2018-26/segments/1529267864337.41/warc/CC-MAIN-20180622010629-20180622030629-00246.warc.gz | CC-MAIN-2018-26 | 422 | 1 |
https://casmusings.wordpress.com/2011/07/ | math | Kudos to Dave Gale and chris maths for their great posts about introductory lessons that inspired the questions I pose below. At this point, I don’t have an answer to the query, but I welcome any insights and particularly any other spin-off ideas you may have.
If you have a standard sheet of square grid paper whose dots are exactly 1 unit apart and I ask you to draw a square of area 1, a square of area 4, and a square of area 9, you would probably quickly respond with the following.
Then I ask you to draw a square of area … [deliberate pause] … many immediately begin to think of continuing the pattern to area 16, but instead I ask for a square of area 10. Whether you know the Pythagorean Theorem or just how to compute the areas of squares and triangles, some experimentation hopefully will lead you to some form of the following figure which shows a square with area 10. The real twist for students here is that they need to adjust their point of view from what I’ll call horizontal squares (above) to tilted squares (below).
So, here are my questions:
1) What square areas can be created using square grid paper?
2) What areas of squares can be created more than one way?
3) Is there a largest square area that can NOT be created using square grid paper?
STOP! STOP! STOP!
Do not read any further if you want to work on these questions yourself.
What follows are my musings on these questions and some definite spoilers are included.
Perfect squares (1, 4, 9, 16, 25, 36, …) obviously can be found using increasingly larger horizontal squares. Dave’s ‘blog post gives a great start at the non-perfect, tilted squares.
Image source here.
The information he gives in the image above leads to areas of 2, 5, 8, 10, 13, 17, 18, 20, 25, 26, 29, 32, 34, 37, …
Merging the “tilted” list with the “horizontal list gives 1, 2, 4, 5, 8, 9, 10, 13, 16, 17, 18, 20, 25, 26, 29, 32, 34, 36, 37, …
The missing square areas are 3, 6, 7, 11, 12, 14, 15, 19, 21, 22, 23, 24, …
Whether this list ends depends on the solution to posed question #3.
Comparing the horizontal and tilted lists, the first area that can be found both ways is 25. I briefly thought that was an amazing find until I remembered that the smallest integral Pythagorean Triple is 3-4-5. So a tilted square whose vector position (using Dave’s language) can be expressed as [3,4] can also be created using a horizontal side of 5–the Pythagorean Theorem arises!
There may be other ways to get equivalent square areas (I’d love to hear any if you know some!), but any integral Pythagorean Triple represents a square area that can be represented at least two ways on square grid paper. There are an infinite number of such equivalences.
I don’t know the answer to this, but I think I’m close. I’ll post the problem before I finish it for the fun of letting others into the enjoyment of solving what I think is a cool pre-collegiate level math problem.
I did notice that the missing areas at the end of my discussion of question 1 seems to include a large number of multiples of 3, excluding of course, the horizontal squares with sides that have lengths that are multiples of 3. So is it possible to prove that any area that is
– a multiple of 3, but
– not a perfect square
can not be drawn on square grids?
If so, then there is no maximum area of a square that cannot be drawn using square grid paper.
If not, then the solution to this question may lie in a direction I have not conceived.
Again, I don’t know the answers to questions 1 or 3. Discussion is welcome and encouraged. | s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320304686.15/warc/CC-MAIN-20220124220008-20220125010008-00241.warc.gz | CC-MAIN-2022-05 | 3,584 | 26 |
https://www.mathnasium.com/labordayspn | math | News from Mathnasium of St. Peter's North
Labor Day Weekend Word Problems
Aug 30, 2018
Lower Elementary: Question: Kylie sold books at a yard sale for 10¢ each and toys for 50¢ each. If she sells 6 books and 3 toys, how much does Kylie earn altogether?
Solution: Kylie earned 10¢, 6 times for the books. That’s 10, 20, 30, 40, 50, 60¢. She earned 50¢, 3 times for the toys. That’s 50, 100, 150¢, or $1.50. So, altogether, Kylie earned $1.50 + $0.60 = $2.10.
Question: Eight groups of children are performing skits at their summer camp comedy show. Each skit is 5 minutes long. If each group performs once and the campers must be done with the comedy show by 9:15 pm, then what is the latest time they can start the show?
Answer: 8:35 pm
Solution: The amount of time is takes for all of the groups to finish their skits is 8 × 5 = 40 minutes. Since they have to finish the show by 9:15 pm, we count back 40 minutes before 9:15 pm to 8:35 pm.
Question: A 9-foot tree casts a 6-foot shadow. Cameron’s dog casts a 2-foot shadow. Cameron is twice as tall as the dog. How tall is Cameron?
Answer: 6 feet
Solution: The tree’s shadow’s length is two-thirds the height of the tree. So, the length of the dog’s shadow is two-thirds its height; 2 feet is two-thirds of 3 feet, so the dog must be 3 feet tall. That means that Cameron is 6 feet tall because he’s twice as tall as the dog.
Algebra and Up:
Question: The profit earned by a coffee company, measured in thousands of dollars, is modeled by the function f(t) = t2 – 8t + 16, wherein t is measured in months and t = 1 is January 2012. What month does the coffee company earn the least amount of money? How much do they earn?
Answer: The coffee company earned $0 in April.
Solution: This function is a parabola that opens upward, so the lowest value is at the vertex. To find the month, we find –b/2a = –8/–2 = 4. So, the vertex is at t = 4, which represents the month of April. To find how much they earned, we set t = 4 and solve: 42 – 8(4) + 16 = 16 – 32 + 16 = 0. So, they earned $0 in April.
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https://myhomeworkwriters.com/continuous-functions-assignment-assignment-help-services-2/ | math | Continuous Functions Assignment | Assignment Help Services
Let f, g : R → R be continuous functions. (a) Prove that if f(r) = 0 for all r ∈ Q, then f(x) = 0 for all x ∈ R. (b) Prove that if f(r) = g(r) for all r ∈ Q, then f(x) = g(x) for all x ∈ R.
How should I go about this problem using sequences? For example, can I form a sequence r-sub-n —-> x and somehow use that show f(x) = 0?
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https://community.appsheet.com/t/set-a-limit-of-how-many-digits-can-be-inputted-in-a-cell/38567 | math | Hi community =)
I’m trying to make a simple app for member registration and facing a problem with data validation. desperately need help.
I need an formula/expression that sets limit of digits can be inputted in a cell based on the value of other column.
say i have 2 columns, BANK and ACCOUNT NUMBER
i need to limit digits in ACCOUNT NUMBER to 10 if value in BANK is CENTRAL BANK, and limit 15 digits in ACCOUNT NUMBER if value in BANK is LOCAL BANK.
Any help is much appreciated | s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178358798.23/warc/CC-MAIN-20210227084805-20210227114805-00514.warc.gz | CC-MAIN-2021-10 | 482 | 6 |
https://www.prep4usmle.com/forum/thread/84185/ | math | |Prep for USMLE|
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Hi... need some clarification and advice here!
Read some where there we could schedule the step 3 exam on a weekend.... either a friday n monday or a saturday n monday.
Is that true...? and if it is so, then is it advisable to do it this way...? also what are the odds of getting such combination days?
Would really appreciate if someone could solve this dilemma... thanks in advance!
It is really tough to get such dates,especially at this time as everyone needs their step 3 for the visa processing.But if you can take a Sat/Mon that would be great.This exam is all about your performance on the day and it helps to have a day in between to rest and freshen up.
But if you can't get a date like that don't worry.it's doable on 2 consecutive days too.
hey... thanks a ton for your prompt reply!
However was wondering if there could be any cons to it....?
I'm still to receive my scheduling permit... lets see what's in store once I get it... till then, hoping for the best... always
Thanks again and good luck with everything'
If the center is not open sun... then sat/mon counts
as consecutive days. I did it this way thinking it would be
good for the rest.
In actual fact the second day is much shorter and less tiring than
first day. ccs usually done in half the time so it is a short day
and the blocks are shorter as well.
So did not feel that it was a great advantage , just another day
to add to the anxiety. Depends on your personality if you feel
you need the rest after day one.
Hey gray... thats really helpful and positive considering your amazing score!
Thanks for your input... really appreciate it!
Good luck for the match
This thread is closed, so you cannot post a reply.
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https://peoplepill.com/people/alfred-tauber | math | Alfred Tauber (5 November 1866 – 26 July 1942) was a Hungarian-born Austrian mathematician, known for his contribution to mathematical analysis and to the theory of functions of a complex variable: he is the eponym of an important class of theorems with applications ranging from mathematical and harmonic analysis to number theory. He was murdered in the Theresienstadt concentration camp.
Life and academic career
Born in Pressburg, Kingdom of Hungary, Austrian Empire (now Bratislava, Slovakia), he began studying mathematics at Vienna University in 1884, obtained his Ph.D. in 1889, and his habilitation in 1891. Starting from 1892, he worked as chief mathematician at the Phönix insurance company until 1908, when he became an a.o. professor at Vienna University, though, already from 1901, he had been honorary professor at TH Vienna and director of its insurance mathematics chair. In 1933, he was awarded the Grand Decoration of Honour in Silver for Services to the Republic of Austria, and retired as emeritus extraordinary professor. However, he continued lecturing as a privatdozent until 1938, when he was forced to resign as a consequence of the "Anschluss". On 28–29 June 1942, he was deported with transport IV/2, č. 621 to Theresienstadt, where he was murdered on 26 July 1942.
Pinl & Dick (1974, p. 202) list 35 publications in the bibliography appended to his obituary, and also a search performed on the "Jahrbuch über die Fortschritte der Mathematik" database results in a list 35 mathematical works authored by him, spanning a period of time from 1891 to 1940. However, Hlawka (2007) cites two papers on actuarial mathematics which do not appear in these two bibliographical lists and Binder's bibliography of Tauber's works (1984, pp. 163–166), while listing 71 entries including the ones in the bibliography of Pinl & Dick (1974, p. 202) and the two cited by Hlawka, does not includes the short note (Tauber 1895) so the exact number of his works is not known. According to Hlawka (2007), his scientific research can be divided into three areas: the first one comprises his work on the theory of functions of a complex variable and on potential theory, the second one includes works on linear differential equations and on the Gamma function, while the last one includes his contributions to actuarial science. Pinl & Dick (1974, p. 202) give a more detailed list of research topics Tauber worked on, though it is restricted to mathematical analysis and geometric topics: some of them are infinite series, Fourier series, spherical harmonics, the theory of quaternions, analytic and descriptive geometry. Tauber's most important scientific contributions belong to the first of his research areas, even if his work on potential theory has been overshadowed by the one of Aleksandr Lyapunov.
His most important article is (Tauber 1897). In this paper, he succeeded in proving a converse to Abel's theorem for the first time: this result was the starting point of numerous investigations, leading to the proof and to applications of several theorems of such kind for various summability methods. The statement of these theorems has a standard structure: if a series ∑ an is summable according to a given summability method and satisfies an additional condition, called "Tauberian condition", then it is a convergent series. Starting from 1913 onward, G. H. Hardy and J. E. Littlewood used the term Tauberian to identify this class of theorems. Describing with a little more detail Tauber's 1897 work, it can be said that his main achievements are the following two theorems:
- Tauber's first theorem. If the series ∑ an is Abel summable to sum s, i.e. limx→ 1 ∑+∞
n=0 an x = s, and if an = ο(n), then ∑ ak converges to s.
This theorem is, according to Korevaar (2004, p. 10), the forerunner of all Tauberian theory: the condition an = ο(n) is the first Tauberian condition, which later had many profound generalizations. In the remaining part of his paper, by using the theorem above, Tauber proved the following, more general result:
- Tauber's second theorem. The series ∑ an converges to sum s if and only if the two following conditions are satisfied:
- ∑ an is Abel summable and
k=1 k ak = ο(n).
This result is not a trivial consequence of Tauber's first theorem. The greater generality of this result with respect to the former one is due to the fact it proves the exact equivalence between ordinary convergence on one side and Abel summability (condition 1) jointly with Tauberian condition (condition 2) on the other. Chatterji (1984, pp. 169–170) claims that this latter result must have appeared to Tauber much more complete and satisfying respect to the former one as it states a necessary and sufficient condition for the convergence of a series while the former one was simply a stepping stone to it: the only reason why Tauber's second theorem is not mentioned very often seems to be that it has no profound generalization as the first one has, though it has its rightful place in all detailed developments of summability of series.
Contributions to the theory of Hilbert transform
Frederick W. King (2009, p. 3) writes that Tauber contributed at an early stage to theory of the now called "Hilbert transform", anticipating with his contribution the works of Hilbert and Hardy in such a way that the transform should perhaps bear their three names. Precisely, Tauber (1891) considers the real part φ and imaginary part ψ of a power series f,
- z = r with r = | z | being the absolute value of the given complex variable,
- ck r = ak + ibk for every natural number k,
- φ(θ) = ∑+∞
k=1 akcos(kθ) − bksin(kθ) and ψ(θ) = ∑+∞
k=1 aksin(kθ) + bkcos(kθ) are trigonometric series and therefore periodic functions, expressing the real and imaginary part of the given power series.
Under the hypothesis that r is less than the convergence radius Rf of the power series f, Tauber proves that φ and ψ satisfy the two following equations:
Assuming then r = Rf, he is also able to prove that the above equations still hold if φ and ψ are only absolutely integrable: this result is equivalent to defining the Hilbert transform on the circle since, after some calculations exploiting the periodicity of the functions involved, it can be proved that (1) and (2) are equivalent to the following pair of Hilbert transforms:
- the complex valued continuous function φ(θ) + iψ(θ) defined on a given circle is the boundary value of a holomorphic function defined in its open disk if and only if the two following conditions are satisfied
- the function [φ(θ − α) − φ(θ + α)]/α is uniformly integrable in every neighborhood of the point α = 0, and
- the function ψ(θ) satisfies (2).
- Tauber, Alfred (1891), "Über den Zusammenhang des reellen und imaginären Theiles einer Potenzreihe" [On the relation between real and imaginary part of a power series], Monatshefte für Mathematik und Physik, II: 79–118, doi:10.1007/bf01691828, JFM 23.0251.01.
- Tauber, Alfred (1895), "Ueber die Werte einer analytischen Function längs einer Kreislinie" [On the values of an analytic function along a circular perimeter], Jahresbericht der Deutschen Mathematiker-Vereinigung, 4: 115, archived from the original on 2015-07-01, retrieved 2014-07-16.
- Tauber, Alfred (1897), "Ein Satz aus der Theorie der unendlichen Reihen" [A theorem about infinite series], Monatshefte für Mathematik und Physik, VIII: 273–277, doi:10.1007/BF01696278, JFM 28.0221.02.
- Tauber, Alfred (1898), "Über einige Sätze der Potentialtheorie" [Some theorems of potential theory], Monatshefte für Mathematik und Physik, IX: 79–118, doi:10.1007/BF01707858, JFM 29.0654.02.
- Tauber, Alfred (1920), "Über konvergente und asymptotische Darstellung des Integrallogarithmus" [On convergent and asymptotic representation of the logarithmic integral function], Mathematische Zeitschrift, 8: 52–62, doi:10.1007/bf01212858, JFM 47.0329.01.
- Tauber, Alfred (1922), "Über die Umwandlung von Potenzreihen in Kettenbrüche" [On the conversion of power series into continued fractions], Mathematische Zeitschrift, 15: 66–80, doi:10.1007/bf01494383, JFM 48.0236.01. | s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446711336.41/warc/CC-MAIN-20221208114402-20221208144402-00834.warc.gz | CC-MAIN-2022-49 | 8,213 | 30 |
http://nrich.maths.org/2668 | math | Imagine you have six different colours of paint. You paint a cube
using a different colour for each of the six faces. How many
different cubes can be painted using the same set of six colours?
Take the numbers 1, 2, 3, 4 and 5 and imagine them written down in
every possible order to give 5 digit numbers. Find the sum of the
How many tricolour flags are possible with 5 available colours such
that two adjacent stripes must NOT be the same colour. What about | s3://commoncrawl/crawl-data/CC-MAIN-2017-22/segments/1495463607649.26/warc/CC-MAIN-20170523183134-20170523203134-00259.warc.gz | CC-MAIN-2017-22 | 459 | 7 |
https://xexatifo.tk/the-method-of-fractional-steps.php | math | Splitting schemes of a high degree of accuracy have now attained a very advanced stage. One modification of this method is the so-called "particles-in-cells" method: The splitting is carried out according to physical processes and is independent of the reduction in the dimension of the operators.
Splitting methods like local one-dimensional methods and hopscotch methods are often used in Western literature. Their applicability is somewhat limited, as fairly regular domains like squares are needed. Log in. Namespaces Page Discussion. Views View View source History. Jump to: navigation , search. For the system of differential equations 1 where is a differential operator, , , the absolutely stable implicit schemes of simple approximation 2 become ineffective in the case of multi-dimensional problems.
For obtaining economical stable difference schemes methods are proposed based on the following ideas: 1 splitting of the difference schemes; 2 approximate factorization; 3 splitting weak approximation of the differential equations. In the case of equation 1 the respective difference schemes have the following form for the sake of simplicity, two fractional steps have been taken and the periodic Cauchy problem is considered : the splitting scheme: 3 the approximate factorization scheme: 4 the weak approximation scheme: 5 In the case of the schemes 3 and 4 inversion of the operator is replaced by inversion of the operator , i.
It is applicable especially to potential problems, problems of elasticity and problems of fluid dynamics. The method offers a powerful means of solving the Navier-Stokes equations and the results produced so far cover a range of Reynolds numbers far greater than that attained in earlier methods. Further development of the method should lead to complete numerical solutions of many of the boundary layer and wake problems which at present defy satisfactory treatment. As noted by the author very few applications of the method have yet been made to problems in solid mechanics and prospects for answers both in this field and other areas such as heat transfer are encouraging.
As the method is perfected it is likely to supplant traditional relaxation methods and finite element methods, especially with the increase in capability of large scale computers.
The literal translation was carried out by T. Cheron with financial support of the Northrop Corporation.
The editing of the translation was undertaken in collaboration with N. Later these results were extended by different authors to the equations of elasticity and plasticity and to multiply connected domains.
AMS :: Mathematics of Computation
Zav'yalov and Dr. Valeri L. This book is a comprehensive survey of different efficient algorithms for computing 1-D and 2-D splines. Our own main results relate to a new technique which we developed to obtain optimal error bounds for polynomial spline interpolation. This method is based on an integral representation of the error estimate. In many cases it gives minimal values of constants in error bounds for interpolation splines.
The same approach is also used to find optimal error bounds for local spline approximation methods. This book has become a standard textbook for students, researchers and engineers in Russia and over eleven thousands copies were sold. Shape-Preserving Spline Interpolation: Standard methods of spline functions do not preserve shape properties of the data.
By introducing shape control parameters into the spline structure, one can preserve various characteristics of the initial data including positivity, monotonicity, convexity, linear and planar sections. Based on interpolating splines, methods with shape control are usually called methods of shape-preserving spline interpolation. Here the main challenge is to develop algorithms that choose shape control parameters automatically. The majority of such algorithms solve the problem only for some special data.
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To solve the problem in a general setting, I gave a classification of the initial data and reduced the problem of shape-preserving interpolation to the problem of Hermite interpolation with constraints of inequality type. The solution is a C2 local generalized tension spline with additional knots. This allows for development of a local algorithm of shape-preserving spline interpolation where shape control parameters are selected automatically to meet the monotonicity and convexity constraints for the data.
Dr. Boris I. Kvasov
Its application makes it possible to give a complete solution to the shape-preserving interpolation problem for arbitrary data and isolate the sections of linearity, the angles, etc. Tension GB-Splines: In my opinion, my most significant contribution to the theory of splines, involves the development of " direct methods " for constructing explicit formulae for tension generalized basis splines GB-splines for short and finding recursive algorithms for the calculation of GB-splines.
This approach has yielded new local bases for various tension splines including among others rational, exponential, hyperbolic, variable order splines, and splines with additional knots. | s3://commoncrawl/crawl-data/CC-MAIN-2020-16/segments/1585370524043.56/warc/CC-MAIN-20200404134723-20200404164723-00453.warc.gz | CC-MAIN-2020-16 | 5,390 | 21 |
https://www.brainkart.com/article/Inductance-of-a-Single-Phase-Two-Wire-Line_12357/ | math | ![if !IE]> <![endif]>
INDUCTANCE OF A SINGLE PHASE TWO-WIRE LINE
A single phase line consists of two parallel conductors which form a rectangular loop of one turn.
When an alternating current flows through such a loop, a changing magnetic flux is set up. The changing flux links the loop and hence the loop (or single phase line) possesses inductance. It may appear that inductance of a single phase line is negligible because it consists of a loop of one turn and the flux path is through air of high reluctance. But as the X –sectional area of the loop is very **large, even for a small flux density, the total flux linking the loop is quite large and hence the line has appreciable inductance.
Consider a single phase overhead line consisting of two parallel conductors A and B spaced d metres apart as shown in Fig. 9.7. Conductors A and B carry the same amount of current ( i.e. IA = IB ), but in the opposite direction because one forms the return circuit of the other.
IA+IB = 0
In order to find the inductance of conductor A (or conductor B), we shall have to consider the flux linkages with it. There will be flux linkages with conductor A due to its own current IA and also A due to the mutual inductance effect of current IB in the conductor B Flux linkages with conductor A due to its own current
Flux linkages with conductor A due to current IB
Total flux linkages with conductor A is
Note that eq. ( ii) is the inductance of the two-wire line and is sometimes called loop inductance. However, inductance given by eq. ( i) is the inductance per conductor and is equal to half the loop inductance.
Fig. shows the three conductors A, B and C of a 3-phase line carrying currents IA , IB and IC respectively. Let d 1 , d2 and d3 be the spacings between the conductors as shown. Let us further assume that the loads are balanced i.e. IA + IB + IC = 0. Consider the flux linkages with conductor There will be flux linkages with conductor A due to its own current and also due to the mutual inductance effects of IB and IC
If the three conductors A, B and C are placed symmetrically at the corners of an equilateral triangle of side d, then, d1 = d2 = d3 = d. Under such conditions, the flux Derived in a similar way, the expressions for inductance are the same for conductors B and C.
When 3-phase line conductors are not equidistant from each other, the conductor spacing is said to be unsymmetrical. Under such conditions, the flux linkages and inductance of each phase are not the same. A different inductance in each phase results in unequal voltage drops in the three phases even if the currents in the conductors are balanced. Therefore, the voltage at the receiving end will not be the same for all phases. In order that voltage drops are equal in all conductors, we generally interchange the positions of the conductors at regular intervals along the line so that each conductor occupies the original position of every other conductor over an equal distance. Such an exchange of positions is known as transposition. Fig.shows the transposed line. The phase conductors are designated as A, B and C and the positions occupied are numbered 1, 2 and 3. The effect of transposition is that each conductor has the same average inductance.
Fig. shows a 3-phase transposed line having unsymmetrical spacing. Let us assume that each of the three sections is 1 m in length. Let us further assume balanced conditions i.e.,
IA + IB +IC = 0
Let the line currents be :
As proved above, the total flux linkages per metre length of conductor A is
If we compare the formula of inductance of an un symmetrically spaced transposed line with that of symmetrically spaced line, we find that inductance of each line conductor in the two cases will be equal if
The distance d is known as equivalent equilateral spacing for un symmetrically transposed line
Copyright © 2018-2023 BrainKart.com; All Rights Reserved. Developed by Therithal info, Chennai. | s3://commoncrawl/crawl-data/CC-MAIN-2023-23/segments/1685224646076.50/warc/CC-MAIN-20230530163210-20230530193210-00701.warc.gz | CC-MAIN-2023-23 | 3,946 | 20 |
https://research.monash.edu/en/publications/weak-martingale-solutions-to-the-stochastic-landaulifshitzgilbert | math | We propose an unconditionally convergent linear finite element scheme for the stochastic Landau–Lifshitz–Gilbert (LLG) equation with multi-dimensional noise. By using the Doss–Sussmann technique, we first transform the stochastic LLG equation into a partial differential equation that depends on the solution of the auxiliary equation for the diffusion part. The resulting equation has solutions absolutely continuous with respect to time. We then propose a convergent θ-linear scheme for the numerical solution of the reformulated equation. As a consequence, we are able to show the existence of weak martingale solutions to the stochastic LLG equation.
- Finite element
- Landau–Lifshitz–Gilbert equation
- Stochastic partial differential equation | s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656104668059.88/warc/CC-MAIN-20220706060502-20220706090502-00176.warc.gz | CC-MAIN-2022-27 | 760 | 4 |
http://humanthermodynamics.wikifoundry.com/page/Negative+free+energy+change | math | |Reaction coordinate showing two possible directions of spontaneous reactions; the region in red depicting a reaction quantified by a negative free energy change (ΔG < 0) of products on going to reactants, otherwise referred to as an exergonic reaction. |
For isothermal-isobaric (typical earth-bound) systems, negative free energy change is stated mathematically as:
where the symbol ΔG or free energy change is defined mathematically as:
1. Thims, Libb. (2007). Human Chemistry (Volume One) (graph, pg. 113). Morrisville, NC: LuLu. | s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030337663.75/warc/CC-MAIN-20221005172112-20221005202112-00392.warc.gz | CC-MAIN-2022-40 | 535 | 4 |
https://experts.arizona.edu/en/publications/percolation-thresholds-for-discrete-continuous-models-with-nonuni | math | We introduce a class of discrete-continuous percolation models and an efficient Monte Carlo algorithm for computing their properties. The class is general enough to include well-known discrete and continuous models as special cases. We focus on a particular example of such a model, a nanotube model of disintegration of activated carbon. We calculate its exact critical threshold in two dimensions and obtain a Monte Carlo estimate in three dimensions. Furthermore, we use this example to analyze and characterize the efficiency of our algorithm, by computing critical exponents and properties, finding that it compares favorably to well-known algorithms for simpler systems.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Statistics and Probability
- Condensed Matter Physics | s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662529658.48/warc/CC-MAIN-20220519172853-20220519202853-00449.warc.gz | CC-MAIN-2022-21 | 794 | 5 |
https://brainmass.com/statistics | math | Statistics is the study of the collection, organization, analysis, interpretation and presentation of data. Statistics looks at all aspects of data. Statistics is mostly application based due to its numerical roots. It is usually considered a distinct mathematical science rather than a branch of mathematics. People who study statistics are called statisticians.
Statisticians will improve data quality by developing specific experiment designs and survey samples. Statistics provides tools for both predictions and forecasting - the most important use of data and statistical models. It is applicable to a wide variety of academic disciplines. The methods can summarize a collection of data. It is useful in communicating the results of experiments and research. This method is called descriptive statistics.
Statistics is closely related to probability theory. Probability starts from the given parameters of a total population to deduce probabilities that pertain to samples. Statistical inference moves in the opposite direction; it inductively infers from samples to the parameter of a total population.
Common concepts include probability distributions, density functions, z-scores, t-tests, regression analysis, hypothesis testing, ANOVA analysis, etc.© BrainMass Inc. brainmass.com May 26, 2020, 1:15 pm ad1c9bdddf | s3://commoncrawl/crawl-data/CC-MAIN-2020-24/segments/1590347391277.13/warc/CC-MAIN-20200526160400-20200526190400-00437.warc.gz | CC-MAIN-2020-24 | 1,324 | 4 |
https://www.moneyland.ch/en/earnings-per-share-definition | math | The term earnings per share (EPS) denotes a measure used to find the value which a public company delivers to its shareholders. EPS indicates the amount of profit which each share making up the company earns over a given time frame.
Earnings per share is found by dividing a company’s profit (net income minus preferred stock dividends) by the number of ordinary shares which form its outstanding stock (stock held by shareholders as opposed to treasury stock).
This measurement provides a good indicator of the intrinsic value of shares and the dividends which shareholders can expect to receive from a company.
Swiss stock broker comparison | s3://commoncrawl/crawl-data/CC-MAIN-2019-22/segments/1558232254889.43/warc/CC-MAIN-20190519141556-20190519163556-00527.warc.gz | CC-MAIN-2019-22 | 644 | 4 |
https://www.watchdepot.com.au/christmas-gifts/for-her | math | Christmas Gifts For Her
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Shop now and pay later with our finance options. We offer humm, Zip, LatitudePay, Latitude Interest Free and Afterpay at Watch Depot. We also have free shipping when you spend over $69. Happy shopping! | s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662578939.73/warc/CC-MAIN-20220525023952-20220525053952-00366.warc.gz | CC-MAIN-2022-21 | 2,657 | 35 |
https://www.analystforum.com/t/confused-w-one-problem/61449 | math | V3 - Corp Finance…Reading 30 Q17 EBIT = 400,000 all equity WACC = 10% tax rate = 30% Garth Co. will issue $1m in debt and buyback equivalent amount of equity. What is the cost of equity after the issuance? (The end-of-chapter solution calculates the unlevered value of the company using EBIT without adjusting for taxes…WHY???..Also, example on pgs.106-107 is identical to this problem yet unlevered value is calculated using earnings after taxes.) Please help…Thanks!
You’re lucky, you’re confused with one problem only… others are confused with many more than that Sorry, I have no help with this one, but good luck.
bro i thought i had mastered corp till u showed up After lookin at this i think ebit(1-t) is clearly a better proxy for cash which is what realy matters I think cfai made a mistake. I found many such mistakes before and i emailed about them. A nice lady named wanda handles such emails. But so far she never admits a mistake and answers with. Its an aproximation. Or its a convention. I say take it to cfai and update us.
Hi, check the CFAI errata. This was incorrect in the book - the one who made up the problem hadn’t accounted for taxes… The right answer (after taking into account taxes) is C.
Could someone demonstrate how you get 1.33 = (r_0-r_D)(1-.30)D/E? The #s I’m using are giving me 1.55% which is wrong. | s3://commoncrawl/crawl-data/CC-MAIN-2020-45/segments/1603107904287.88/warc/CC-MAIN-20201029124628-20201029154628-00422.warc.gz | CC-MAIN-2020-45 | 1,354 | 5 |
http://www.chegg.com/homework-help/questions-and-answers/working-chapter-3-problem-19-physics-giancoli-6th-edition-step-2-got-stuck-gets-sin-2-thet-q929034 | math | 0 pts endedThis question is closed. No points were awarded.
I was working on chapter 3 problem 19 in Physics by Giancoli (6th edition) and on step 2 I got stuck because when it gets to sin 2(theta) = 2.88 I don't know how to get theta. It says that it equals 0.4239 and I don't know how to get that answer. Then it goes right on to getting the answer for the angle and I don't understand how they got 2(theta) = 25. Can you please explain these to me? | s3://commoncrawl/crawl-data/CC-MAIN-2014-15/segments/1397609526102.3/warc/CC-MAIN-20140416005206-00191-ip-10-147-4-33.ec2.internal.warc.gz | CC-MAIN-2014-15 | 451 | 2 |
http://www.researchgate.net/researcher/79420751_Richard_L_Naff | math | [Show abstract][Hide abstract] ABSTRACT: Numerical methods based on unstructured grids, with irregular cells, usually require discrete shape functions to approximate the distribution of quantities across cells. For control-volume mixed finite-element methods, vector shape functions are used to approximate the distribution of velocities across cells and vector test functions are used to minimize the error associated with the numerical approximation scheme. For a logically cubic mesh, the lowest-order shape functions are chosen in a natural way to conserve intercell fluxes that vary linearly in logical space. Vector test functions, while somewhat restricted by the mapping into the logical reference cube, admit a wider class of possibilities. Ideally, an error minimization procedure to select the test function from an acceptable class of candidates would be the best procedure. Lacking such a procedure, we first investigate the effect of possible test functions on the pressure distribution over the control volume; specifically, we look for test functions that allow for the elimination of intermediate pressures on cell faces. From these results, we select three forms for the test function for use in a control-volume mixed method code and subject them to an error analysis for different forms of grid irregularity; errors are reported in terms of the discrete L2 norm of the velocity error. Of these three forms, one appears to produce optimal results for most forms of grid irregularity.
[Show abstract][Hide abstract] ABSTRACT: The mixed finite-element approximation to a second-order elliptic PDE results in a saddle-point problem and leads to an indefinite
linear system of equations. The mixed system of equations can be transformed into coupled symmetric positive-definite matrix
equations, or a Schur complement problem, using block Gauss elimination. A preconditioned conjugate-gradient algorithm is
used for solving the Schur complement problem. The mixed finite-element method is closely related to the cell-centered finite
difference scheme for solving second-order elliptic problems with variable coefficients. For the cell-centered finite difference
scheme, a simple multigrid algorithm can be defined and used as a preconditioner. For distorted grids, an additional iteration
is needed. Nested iteration with a multigrid preconditioned conjugate gradient inner iteration results in an effective numerical
solution technique for the mixed system of linear equations arising from a discretization on distorted grids. Numerical results
show that the preconditioned conjugate-gradient inner iteration is robust with respect to grid size and variability in the
hydraulic conductivity tensor.
[Show abstract][Hide abstract] ABSTRACT: Numerical methods for grids with irregular cells require discrete shape functions to approximate the distribution of quantities across cells. For control-volume mixed finite-element (CVMFE) methods, vector shape functions approximate velocities and vector test functions enforce a discrete form of Darcy''s law. In this paper, a new vector shape function is developed for use with irregular, hexahedral cells (trilinear images of cubes). It interpolates velocities and fluxes quadratically, because as shown here, the usual Piola-transformed shape functions, which interpolate linearly, cannot match uniform flow on general hexahedral cells. Truncation-error estimates for the shape function are demonstrated. CVMFE simulations of uniform and non-uniform flow with irregular meshes show first- and second-order convergence of fluxes in the L
2 norm in the presence and absence of singularities, respectively. | s3://commoncrawl/crawl-data/CC-MAIN-2014-42/segments/1414637900019.55/warc/CC-MAIN-20141030025820-00177-ip-10-16-133-185.ec2.internal.warc.gz | CC-MAIN-2014-42 | 3,664 | 13 |
https://weqyoua.com/quizzes/8459-Mathematics_Quiz | math | Subscribe to our youtube channel for more tests.
Which fraction is the largest?
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Extremely Hard Science Quiz Even Einstein would scratch his head! | s3://commoncrawl/crawl-data/CC-MAIN-2018-34/segments/1534221209040.29/warc/CC-MAIN-20180814131141-20180814151141-00264.warc.gz | CC-MAIN-2018-34 | 778 | 15 |
https://projecteuclid.org/euclid.nmj/1114649297 | math | Nagoya Mathematical Journal
- Nagoya Math. J.
- Volume 167 (2002), 217-233.
On the dimension and multiplicity of local cohomology modules
This paper is concerned with a finitely generated module $M$ over a(commutative Noetherian) local ring $R$. In the case when $R$ is a homomorphic image of a Gorenstein local ring, one can use the well-known associativity formula for multiplicities, together with local duality and Matlis duality, to produce analogous associativity formulae for the local cohomology modules of $M$ with respect to the maximal ideal. The main purpose of this paper is to show that these formulae also hold in the case when $R$ is universally catenary and such that all its formal fibres are Cohen-Macaulay. These formulae involve certain subsets of the spectrum of $R$ called the pseudo-supports of $M$; these pseudo-supports are closed in the Zariski topology when $R$ is universally catenary and has the property that all its formal fibres are Cohen-Macaulay. However, examples are provided to show that, in general, these pseudo-supports need not be closed. We are able to conclude that the above-mentioned associativity formulae for local cohomology modules do not hold over all local rings.
Nagoya Math. J., Volume 167 (2002), 217-233.
First available in Project Euclid: 27 April 2005
Permanent link to this document
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 13D45: Local cohomology [See also 14B15]
Secondary: 13C15: Dimension theory, depth, related rings (catenary, etc.) 13H10: Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) [See also 14M05]
Brodmann, Markus P.; Sharp, Rodney Y. On the dimension and multiplicity of local cohomology modules. Nagoya Math. J. 167 (2002), 217--233. https://projecteuclid.org/euclid.nmj/1114649297 | s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575540482038.36/warc/CC-MAIN-20191205190939-20191205214939-00346.warc.gz | CC-MAIN-2019-51 | 1,806 | 13 |
https://kanalizacjawarszawa.com.pl/34214/formula-for-critical-speed-of-a-rotating-mill.html | math | Critical rotation speed of dry ball-mill was studied by experiments and by numerical simulation using Discrete Element Method (DEM) The results carried out by both methods showed good agreement It has been commonly accepted that the critical rotation speed is a ,
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The critical speed of the mill, &c, is defined as the speed at which a single ball will , rotating 813 Power drawn by ball, semi-autogenous and autogenous mills , In equation 814, D is the diameter inside the mill liners and Le is the effective.
In solid mechanics, in the field of rotordynamics, the critical speed is the theoretical angular velocity that excites the natural frequency of a rotating object, such as a shaft, propeller, leadscrew, or gear
Mill Critical Speed Determination The "Critical Speed" for a grinding mill is defined as the rotational speed where centrifugal forces equal gravitational forces at the mill shell's inside surface
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Mill Speed - Critical Speed Mill Speed No matter how large or small a mill, ball mill, ceramic lined mill, pebble mill, jar mill or laboratory jar rolling mill, its rotational speed is important to proper and efficient mill operation
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Mill capacity can be increased by increasing speed but there is very little increase in efficiency (ie kWht-1) when the mill is operated above about 40-50% of the critical speed Please join and login to participate and leave a comment
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was 38 mm for the larger drum and 225 mm for the smaller one , circuit was used to determine the speed of rotation by monitoring the applied voltage , rotation changed (which we took for passing the `critical speed' at which WWI occurs)
Critical rotation speed of dry ball-mill was studied by experiments and by numerical simulation using Discrete Element Method (DEM) The results carried out by both methods showed good agreement
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The critical speed of a rotating mill is the RPM at which a grinding medium will begin to “centrifuge”, namely will start rotating with the mill and therefore cease to carry out useful work Ball mills have been successfully run at speeds between 60 and 90 percent of critical speed, but most mills operate at speeds between 65 and 79 percent .
The point where the mill becomes a centrifuge is called the "Critical Speed", and ball mills usually operate at 65% to 75% of the critical speed Ball Mills are generally used to grind material 1/4 inch and finer, down to the particle size of 20 to 75 microns
Formula For Critical Speed Of A Rotating Mill - , Feb 15, 2016 Critical Speed Formula For Ball Mill formula for calculating the critical This is the rotational speed where balls will not fall critical speed on a Chat Now; What it is the optimun speed for a ball mill .
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This formula calculates the critical speed of any ball mill Most ball mills operate most eff, and the ball mill stop grinding The ball mill rotating speed is called critical speed when th, critical rotating speed reasonably can realize the effective control on the steel ball consu, the slower the rotation If the peripheral speed of the .
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TECHNICAL NOTES 8 GRINDING R P King 8-2 &ROOLVLRQ , 812 Critical speed of rotation The force balance on a particle against the wall is given by 8-3 Centrifugal force outward Fc mp& 2 Dm 2 (81) , Figure 84 The effect of mill speed on the power drawn by a rotating mill
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By the formula (3) can be seen, the critical rotation speed of steel ball centrifugal, Read more The Influence of Ball Mill Critical Speed on Production Efficiency The ball mill rotating speed is called critical speed when the outmost layer balls , and now only the calculation formula on critical speed in theory is widely used
critical rotating speed of mill This formula calculates the critical speed of any ball mill Most ball mills operate most efficiently between% and% of their critical speed Read More >>Critical Rotating Speed Of A Millhiaimpolymersin | s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623487610196.46/warc/CC-MAIN-20210613161945-20210613191945-00109.warc.gz | CC-MAIN-2021-25 | 7,836 | 30 |
http://miningcoin.top/hackaday-bitcoin-calculator/ | math | Hackaday bitcoin calculator
Posted On 27.01.2016
1970s: it provided fast 4-bit arithmetic and logic functions, and could be combined to handle larger words, making it hackaday bitcoin calculator key part of many CPUs. But if you look at the chip more closely, there are a few mysteries. Schematic of the 74LS181 ALU chip, from the datasheet. The internal structure of the chip is surprisingly complex and difficult to understand at first.
The 74181 chip is important because of its key role in minicomputer history. Before the microprocessor era, minicomputers built their processors from boards of individual chips. Early minicomputers built ALUs out of a large number of simple gates. The datasheet for the 74181 ALU chip shows a strange variety of operations. So how is the 74181 implemented and why does it include such strange operations? Is there any reason behind the 74181’s operations, or did they just randomly throw things in? And why are the logic functions and arithmetic functions in any particular row apparently unrelated?
I investigated the chip to find out. Why are there 16 possible functions? 4 rows in the truth table. Each row can output 0 or 1. Arithmetic functions The 74181’s arithmetic operations are a combination of addition, subtraction, logic operations, and strange combinations such as “A PLUS AB PLUS 1”. It turns out that there is a rational system behind the operation set: they are simply the 16 logic functions added to A along with the carry-in. | s3://commoncrawl/crawl-data/CC-MAIN-2018-47/segments/1542039743184.39/warc/CC-MAIN-20181116194306-20181116215358-00003.warc.gz | CC-MAIN-2018-47 | 1,491 | 5 |
http://math.stackexchange.com/questions/525001/polynomial-third-degree | math | A third degree polynomial $p(x)=0$ when $x=1$ and $x=3$. We also learn that $p(x) \geq 0 $ when $x \geq 1$ and $p(2) =2$. Determine $p(x)$. How should I proceed? I presume no calculus is needed.
Hint: $p(x) = a(x-1)(x-3)(x-b)$ and only for one value of $b$ this polynomial doesn't change its sign around the point $x=3$. | s3://commoncrawl/crawl-data/CC-MAIN-2016-30/segments/1469257830091.67/warc/CC-MAIN-20160723071030-00244-ip-10-185-27-174.ec2.internal.warc.gz | CC-MAIN-2016-30 | 320 | 2 |
https://blender.stackexchange.com/questions/280355/how-do-i-keep-the-noise-in-my-cycles-render-animation | math | Blender automatically reduces noise on Cycles renders now, but I don't want that. Googling this comes up only with ways to reduce noise, but I want to keep the noise you get in cycles.
$\begingroup$ It's the opposite to reduce noise, basically, turn in off denoise, lower render samples $\endgroup$– EmirNov 29, 2022 at 15:56
$\begingroup$ @Emir Thanks, but how do I turn it off? $\endgroup$– litleangleNov 29, 2022 at 15:59
You can turn off the denoising in the render settings. If you want even more noise, reduce the number of samples.
$\begingroup$ Thank you! it was right under my nose the whole time. $\endgroup$ Nov 29, 2022 at 16:01 | s3://commoncrawl/crawl-data/CC-MAIN-2023-23/segments/1685224653930.47/warc/CC-MAIN-20230607143116-20230607173116-00755.warc.gz | CC-MAIN-2023-23 | 644 | 5 |
https://math.meta.stackexchange.com/questions/21841/how-to-type-greater-than-or-equal-to-symbols | math | What are the markups for such symbols?
You can use
$\geq$ (to get $\geq$) or for a variant
(to get $\geqslant$).
For less than or equal to replace the "g" by "l".
For the strict versions, $\gt$ and $\lt$, you can use
or just the symbols
$<$. The symbols did sometimes create issues but I think this is fixed by now.
For a general guide see MathJax basic tutorial and quick reference
2$\begingroup$ Not completely fixed, unfortunately. When
$a<b$is in a title, and another question is closed as a duplicate of it, the automatic comment has
$a<b$which doesn't render: $a<b$. This isn't a reason to avoid strict inequality signs in titles as much as a reason to finally fix this over-escaping bug... $\endgroup$– user147263Nov 1, 2015 at 18:33
$\begingroup$ Thanks, I was not aware of this. What I thought of was an issue that the post got completely cut off as something got misinterpreted. $\endgroup$– quid ModNov 1, 2015 at 18:38
4$\begingroup$ That also happens, when new users post things like
a<b therefore -b>-awithout dollar signs: this renders as
a-aon the site. Some such questions get closed as unclear, unless someone realizes what is going on and edits. $\endgroup$– user147263Nov 1, 2015 at 18:41
¸leqslant) for $\geqslant$ (and $\leqslant$). See this post for general information about MathJax commands. $\endgroup$
\gefor $\ge$ and
\lefor $\le$ $\endgroup$ | s3://commoncrawl/crawl-data/CC-MAIN-2023-23/segments/1685224643585.23/warc/CC-MAIN-20230528051321-20230528081321-00112.warc.gz | CC-MAIN-2023-23 | 1,377 | 19 |
https://www.physicsforums.com/threads/finding-series-solution-for-the-differential-equation.823561/ | math | 1. The problem statement, all variables and given/known data y'' - xy' + xy = 0 around x0=0 Find a solution to the 2nd order differential equation using the series solution method. 2. Relevant equations Assume some function y(x)= ∑an(x-x0)n exists that is a solution to the above differential equation. 3. The attempt at a solution How on earth do I shift the index in each equation to make the xn in each series the same power? I don't see any way to do it. | s3://commoncrawl/crawl-data/CC-MAIN-2018-22/segments/1526794867904.94/warc/CC-MAIN-20180526210057-20180526230057-00182.warc.gz | CC-MAIN-2018-22 | 460 | 1 |
https://www.sarthaks.com/104726/pinki-deepati-and-kaku-are-partners-sharing-profits-in-the-ratio-of-kaku-is-given-guarantee | math | Pinki, Deepati and Kaku are partner’s sharing profits in the ratio of 5:4:1. Kaku is given a guarantee that his share of profits in any given year would not be less than Rs. 5,000. Deficiency, if any, would be borne by Pinki and Deepti equally. Profits for the year amounted to Rs. 40,000. Record necessary journal entries in the books of the firm showing the distribution of profit. | s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323587659.72/warc/CC-MAIN-20211025092203-20211025122203-00047.warc.gz | CC-MAIN-2021-43 | 385 | 1 |
https://collaborate.princeton.edu/en/publications/stability-and-equilibrium-states-of-infinite-classical-systems | math | We prove that any stationary state describing an infinite classical system which is "stable" under local perturbations (and possesses some strong time clustering properties) must satisfy the "classical" KMS condition. (This in turn implies, quite generally, that it is a Gibbs state.) Similar results have been proven previously for quantum systems by Haag et al. and for finite classical systems by Lebowitz et al.
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Mathematical Physics | s3://commoncrawl/crawl-data/CC-MAIN-2024-18/segments/1712296817463.60/warc/CC-MAIN-20240419234422-20240420024422-00720.warc.gz | CC-MAIN-2024-18 | 522 | 4 |
http://www.hispanicbusiness.com/2014/5/22/patent_issued_for_printable_light-emitting_compositions.htm | math | Patent number 8721922 is assigned to
The following quote was obtained by the news editors from the background information supplied by the inventors: "This invention relates to light emitting compositions and light-emitting devices that include the light-emitting compositions. Specifically, this invention relates to light emitting compositions that are printable and light-emitting devices that include iridium-functionalized nanoparticles.
"Organic Light Emitting Diodes (OLEDs) can be composed of small molecule or polymeric fluorescent or phosphorescent compounds. OLEDs comprise a cathode, a hole transporting layer, an emissive layer, an electron transporting layer and an anode. OLED devices emit light as a result of recombination of positive charges (holes) and negative charges (electrons) inside an organic compound (emissive) layer. This organic compound is referred as an electro-fluorescent material or electro-phosphorescent material depending on the nature of the radiative process. As OLED devices have developed to increase luminousity and increased lifetimes, additional layers, such as hole blocking layers and electron blocking layers, have been incorporated into the OLED device. However, introducing more layers of materials has made the OLED structure increasingly complex. This increased complexity makes the fabrication process significantly more difficult. The addition of layers also makes fabrication more difficult because poor control of layer thickness may impair performance. Thus, improving the performance of OLEDs is often tedious, difficult, and expensive.
"There are several methods for manufacturing these above described layers within an OLED device. Primary methodologies include dry processing and wet processing. Dry processing is processing performed without a liquid. Examples of a dry processing operation include dry etching, laser ablation, chemical vapor deposition and vacuum deposition. Dry processing methods have several drawbacks, including difficulty controlling the thickness or composition of a previously deposited layer during serial deposition, high cost of equipment set up and maintenance, slow processing, and difficulty with substrates having a large area. Thus wet production methods may offer significant advantages.
"Solution or wet-processing includes the dissolution or suspension of the precursor materials in a solvent and the application of the solution to the desired substrate. Exemplary methodologies include spin coating and inkjet applications. Spin coating can be undesirable because large quantities of the dissolved solution are spun off of the desired surface during the coating process. Thus, large amounts material is wasted production costs are higher.
In addition to the background information obtained for this patent, VerticalNews journalists also obtained the inventors' summary information for this patent: "The inventors have discovered compositions that are, inter alia, useful as ink compositions that may be used in inkjet printers to fabricate light emitting compositions and devices. Some embodiments described herein relate to compositions comprising an iridium-functionalized nanoparticle that can include a nanoparticle core and an iridium-complex. In other embodiments, the iridium-functionalized nanoparticles described herein are light-emitting, e.g., white light-emitting.
"One embodiment disclosed herein is a composition comprising an electron transport compound, an emissive compound, and an organic solvent, wherein the emissive compound is represented by formula (I):
"##STR00001## wherein core is a nanoparticle core, n is 2, X is a single bond or
"##STR00003## is independently a first optionally substituted bidentate ligand;
"##STR00004## is a second optionally substituted bidentate ligand selected from:
"##STR00005## wherein m is an integer in the range of 1 to 9, p is an integer in the range or 1 to 20, z is 0, 1 or 2, R.sup.1 is selected from alkyl, substituted alkyl, aryl and substituted aryl, R.sup.2 is selected from: alkyl, substituted alkyl, aryl and substituted aryl, and * indicates a point of attachment of the second optionally substituted bidentate ligand to the core or X.
"One embodiment also disclosed herein is a composition comprising an electron transport compound, an emissive compound, and an organic solvent, wherein the emissive compound is represented by one of the following formulas:
"##STR00006## wherein R' is represented by
"##STR00008## and R'' is represented by
"##STR00009## wherein each
"##STR00010## is independently a first optionally substituted bidentate ligand, and
"##STR00011## is a second optionally substituted bidentate ligand; R.sup.3 is
"##STR00012## wherein k is 0 or an integer selected from 1 to 20, and R.sup.5 is independently selected from the following:
"##STR00013## ##STR00014## ##STR00015##
"wherein R is independently selected from H or alkyl, and * indicates a point of attachment in R.sup.3.
"Another embodiment provides a method of fabricating a light-emitting device comprising depositing any composition disclosed herein upon an electrically conductive substrate via an inkjet printer.
"Another embodiment provides a composition (IV) comprising: an emissive compound represented by Formula (IV), and an electron transport compound; and an organic solvent.
"With respect to Formula (IV), each R.sup.4 is independently selected from:
"##STR00017## and R.sup.5 is
"Another embodiment is composition (V) comprising: an emissive compound represented by Formula (V), an electron transport compound, and an organic solvent.
"With respect to formula (V), each R.sup.6 is independently selected from the following:
"These and other embodiments are described in greater detail below."
URL and more information on this patent, see:
Keywords for this news article include: Nanoparticle, Nanotechnology, Emerging Technologies,
Our reports deliver fact-based news of research and discoveries from around the world. Copyright 2014, NewsRx LLC
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https://secure.ssa.gov/apps10/poms.nsf/lnx/0500810310 | math | TN 53 (10-11)
SI 00810.310 How to Compute Countable Income
A. Procedure for computing countable income
1. Evaluate income
Evaluate all reported or estimated income for the month.
2. Determine what is not income
Do not consider certain kinds of payments, property, or services as income for Supplemental Security Income (SSI) purposes. For more information on what is not income, see SI 00815.001 through SI 00815.600.
If deeming applies, see items not included in deeming SI 01320.100 through SI 01320.200.
3. Deduct income excluded under other federal statutes
For exclusions not in title XVI of the Social Security Act, see SI 00830.055. Exclude any of this income in determining countable income.
4. Compute countable unearned income
Subtract applicable exclusions from unearned income to determine countable unearned income. For information on unearned income exclusions, see SI 00830.050 through SI 00830.100.
5. Compute countable earned income
Subtract applicable exclusions from earned income to determine countable earned income. For information on earned income exclusions, see SI 00820.500 and SI 00830.060.
6. Compute countable income
Add countable earned income, countable unearned income, and the value of the one-third reduction (if applicable) to arrive at total countable income. | s3://commoncrawl/crawl-data/CC-MAIN-2018-22/segments/1526794872114.89/warc/CC-MAIN-20180528072218-20180528092218-00583.warc.gz | CC-MAIN-2018-22 | 1,295 | 16 |
http://www.avsforum.com/forum/23-screens/1464320-what-s-difference-between-these-two-screens.html | math | I'm looking for a 120-125" 16:9 screen, I found these two on Amazon:
Elite Screens VMAX120UWH2 Electric Projection Screen (120 Inch 16:9 AR) $480
Elite Screens ELECTRIC125H Electric Projection Screen -125-Inch 16:9 AR $230
same brand, what's the difference? first one costs more than double the 2nd one, I'm sure I'm missing something here? | s3://commoncrawl/crawl-data/CC-MAIN-2017-43/segments/1508187823153.58/warc/CC-MAIN-20171018214541-20171018234541-00481.warc.gz | CC-MAIN-2017-43 | 340 | 4 |
https://www.semanticscholar.org/paper/An-Introduction-to-the-%CF%80-Calculus-Parrow/55f491acb0ab76d15be3715db04c61dc6589d50e | math | Context-based process algebras for mobility
- Computer ScienceProceedings. Fourth International Conference on Application of Concurrency to System Design, 2004. ACSD 2004.
Two new formalisations of the finite fragment of the /spl pi/-calculus are provided, defined in a way which exhibits the global state and the execution context of a process without needing to rely heavily on term rewriting techniques.
Introduction to Concurrency Theory
- EconomicsTexts in Theoretical Computer Science. An EATCS Series
This introductory chapter outlines the main motivations for the study of concurrency theory and the differences with respect to the theory of sequential computation. It also reports the structure of…
Petri Net Semantics of the Finite pi-calculus Terms
- Computer ScienceFundam. Informaticae
This construction renders in a compositional way the control flow aspects present in π-calculus process expressions, by adapting the existing graph-theoretic net composition operators.
Expressiveness of the π-Calculus and the $-Calculus
- Computer Science
It is demonstrated that both models are more expressive than Turing Machines, i.e., they belong to superTuring models of computation, and are able to solve the halting problem of the Universal Turing Machine.
Free-Algebra Models for the pi-Calculus
A novel algebraic description for models of the @p-calculus is obtained, and an existing construction is validated as the universal such model, and it is generalised to prove that all free-algebra models are fully abstract.
Controlling Process Modularity in Mobile Computing
- Computer ScienceICTAC
A variant of π-calculus which can flexibly and dynamically control process modularity is presented, and a notion of bisimulation-preorder is proposed to reflect some aspects of mobile distributed computing such as interaction costs.
A Hierarchy of Behavioral Equivalences in the π-calculus with Noisy Channels
- Computer ScienceComput. J.
An early transitional semantics of the ρN-calculus is presented, which is not a directly translated version of the late semantics of πN, and six kinds of behavioral equivalences are extended, which are helpful to verify behavioral equivalence of two agents.
SHOWING 1-10 OF 46 REFERENCES
The Polyadic π-Calculus: a Tutorial
- Computer Science
The π-calculus is a model of concurrent computation based upon the notion of naming that is generalized from monadic to polyadic form and semantics is done in terms of both a reduction system and a version of labelled transitions called commitment.
Objects in the pi-Calculus
- Computer ScienceInf. Comput.
Two semantics for a parallel object-oriented programming language are presented. One is a two-level transitional semantics in which the global behaviour of a system is derived directly from the…
An Object Calculus for Asynchronous Communication
- Computer ScienceECOOP
This paper shows basic construction of the formal system along with several illustrative examples of the communication primitive, which results in a consistent reduction of Milner's calculus, while retaining the same expressive power.
A Symbolic Semantics for the pi-Calculus
- Computer ScienceInf. Comput.
A sound and complete proof system is introduced for symbolic bisimulation, which is more amenable to automatic manipulation and sheds light on the logical differences among different forms of bisimulations over algebras of name-passing processes.
On Encoding p-pi in m-pi
- Computer ScienceFSTTCS
A type system for mπ processes is introduced which captures the interaction regime underlying the encoding of pπ processes respecting a sorting, and a full-abstraction result is shown: two p π processes are typed barbed congruent iff their mπ encodings are monadic-typed barbedCongruent.
The Weak Late pi-Calculus Semantics as Observation Equivalence
- Computer ScienceCONCUR
The Weak Late π-calculus semantics can be characterized as ordinary Observation congruence over a specialized transition system where both the instantiation of input placeholders and the name substitutions are explicitly handled via suitable constructors.
Functions as Processes
- Computer Science, MathematicsMath. Struct. Comput. Sci.
This paper exhibits accurate encodings of the λ-calculus in the π-calculus. The former is canonical for calculation with functions, while the latter is a recent step towards a canonical…
A Calculus of Communicating Systems
- Computer ScienceLecture Notes in Computer Science
A case study in synchronization and proof techniques, and some proofs about data structures in value-communication as a model of CCS 2.0.
Towards a Lambda-Calculus for Concurrent and Communicating Systems
- Computer Science, MathematicsTAPSOFT, Vol.1
This work introduces a calculus for concurrent and communicating processes, which is a direct and simple extension of the λ-calculus, and shows that the ε-abstraction is a particular case of reception (on a port named λ), and application is a specific case of cooperation. | s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656104209449.64/warc/CC-MAIN-20220703013155-20220703043155-00535.warc.gz | CC-MAIN-2022-27 | 5,001 | 48 |
http://www.enotes.com/homework-help/simply-typed-lambda-calculus-question-beta-435526 | math | Simply Typed Lambda Calculus question - Beta Reduction
1. The problem:
Under the assumption that BETA is a closed term show that (λx.α)(β) and α[x→β] are logically equivalent.
2. Relevant equations
I'm sure I have to use β-reduction but I'm not sure how in this case:
0 Answers | Be the first to answer
Join to answer this question
Join a community of thousands of dedicated teachers and students.Join eNotes | s3://commoncrawl/crawl-data/CC-MAIN-2015-27/segments/1435375098808.88/warc/CC-MAIN-20150627031818-00227-ip-10-179-60-89.ec2.internal.warc.gz | CC-MAIN-2015-27 | 416 | 8 |
https://questioncove.com/updates/4f5e4c53e4b0602be438fa86 | math | In circle A shown below, BD is a diameter and the measure of CB is 36°. What is the measure of ∡DBC?
to prove it join AC then angle CAB = 36 angle at the centre subtended by arc CB angle CDB = 18 ( angle at the centre is double the angle at the circumference standing on the same arc CB) Angle BCD = 90 ( angle in a semi circle) therefore angle DBC = 72 ( angle sum of a triangle)
Oh, I was using the wrong equation. I kept getting 36. Thank you!
Join our real-time social learning platform and learn together with your friends! | s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964363405.77/warc/CC-MAIN-20211207170825-20211207200825-00371.warc.gz | CC-MAIN-2021-49 | 531 | 4 |
http://www.thefreedictionary.com/Saturnicentric | math | 1) With a bright core (located at the following end of what became a long, complex, bright region with several secondary spots) at saturnicentric
latitude +34[degrees], its positive drift in System III longitude of +2.
I have defined b as the square root of the absolute value of the product of the Saturnicentric latitude of the Earth and of the Sun; b is a latitude that is always within about 27[degrees] of Saturn's equator.
During this study, the value of B', the Saturnicentric latitude of the Sun referred to the plane of the rings, went from 0[degrees] in 1995 to 27[degrees] in 2002 and back down to 0[degrees] in 2009.
The quantity b ("a type of geometric average of Saturnicentric latitude of Sun and Earth from Saturn's ring plane") is computed from equation (1):
In this equation B is the Saturnicentric latitude of the Earth referred to the plane of the rings and B' is the Saturnicentric latitude of the Sun referred to the plane of the rings.
Four different methods were used in measuring the Saturnicentric latitudes which are: visual, reticle, photograph and video measurements.
Summary of Saturnicentric latitudes of various features on Saturn.
The Saturnicentric latitude of the Earth (B)= the Saturnicentric latitude of the Sun (B').
The Saturnicentric right ascensions of the Sun and Earth should be equal.
An average value, along with the standard deviation of the measurements, was used in computing Saturnicentric latitudes (Alexander, 1980).
These data have been used to produce a map of Saturn and define the approximate Saturnicentric latitudes of the two principal belts on that planet.
declinations of Earth and Sun, and hence the tilts of the ring as seen from the Earth and the Sun would be different even if the plane of Saturn's orbit did coincide with the ecliptic. | s3://commoncrawl/crawl-data/CC-MAIN-2018-47/segments/1542039743854.48/warc/CC-MAIN-20181117205946-20181117231946-00071.warc.gz | CC-MAIN-2018-47 | 1,800 | 13 |
https://www.termpaperwarehouse.com/essay-on/Shdujgk/204700 | math | Submitted By shekinah
Name: _____________________________________Date: ____/_____/_____ Course/Session: ___________
PreLab Composition and Resolution of Forces: Force Table
Instructions: Prepare for this lab activity by answering the questions below. Note that this is a PreLab. It must be turned in at the start of the lab period. Time cannot be given in lab to perform PreLab activities. After the start of lab activities, PreLabs cannot be accepted.
Q1. What is the basic difference between scalars and vectors?
Q2. Do the plus and minus signs that signify positive and negative temperatures imply that temperature is a vector quantity? Explain.
Q3. Which of the following statements, if any, involves a vector? (a) My bank account shows a negative balance of –15 dollars. (b) I walked two miles due north along the beach. (c) I walked two miles along the beach. (d) I jumped off a cliff and hit the water traveling straight down at 17 miles per hour. (e) I jumped of a cliff and hit the water traveling at 17 miles per hour.
Q4. Two vectors, A and B, are added by means of vector addition to give a resultant vector R: R = A + B. The magnitudes of A and B are 2 m and 7 m, respectively, and they can have any orientation. What are the maximum and minimum possible values for the magnitude of R?
Q5. Top of Form
Q5. During a relay race, runner A runs a certain distance and then hands off the baton to runner B, who runs a certain distance and hands off the baton to runner C, who runs a certain distance. In the four cases below, graphically add the three displacement vectors A, B and C together and draw the resultant vector R. A (a) (b) (c) B (d)... | s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323588526.57/warc/CC-MAIN-20211028193601-20211028223601-00038.warc.gz | CC-MAIN-2021-43 | 1,658 | 10 |
http://ucmensoctetfan.weebly.com/top-10-n-stuff.html | math | The Original UC Men's Octet Fan Page
Octet Fans Share!
Jason Mabie Interview
Octet Album Information
Top 10 'n Stuff
View My Stats
Note to Self: Need More "n Stuff".
UC Men's Octet Top Ten
The Top 10 Reasons to love the Octet
#10.) They don't need no stinking instruments!
#9.) They don't need 8 guys!
#8.) Rick Wood is so dorky.
#7.) Kenny Kamrin is even dorkier!
#6.) (Smart + Sexy + Vocal Talent) * 7 = Awesome
#5.) Stayin' Alive proves that they can elicit squees just by taking off their jackets! That's hot.
#4.) "I am Jordante."
#3.) Jason Mabie's soulful voice!
#2.) They Mystery of the Eighth Guy
and the number 1 reason to love the UC Men's Octet -
#1.) Bohemian Rhapsody - need I say more?
Congrats on 1.5 Million + views on Bohemian Rhapsody!
Create your own unique website with customizable templates.
UC Men's Octet, Men's A Cappella, Music, Fan Page | s3://commoncrawl/crawl-data/CC-MAIN-2021-04/segments/1610703519600.31/warc/CC-MAIN-20210119170058-20210119200058-00068.warc.gz | CC-MAIN-2021-04 | 864 | 23 |
http://poetryrl.ga/coved/probability-of-drawing-a-royal-flush-in-poker-206.php | math | The first table is for a partially wild card that can only be used to complete a straight, flush, straight flush, or royal flush, otherwise it must be used as an ace (same usage as in pai gow poker).An explanation of poker odds and poker hands probability. but sans wild cards the highest possible in poker [also called simply a royal flush]). POKER ODDS for.After all there are only 52 cards in a deck and 4 of each card, therefore the odds should be the same for each.The mean is less than the median with a negative skew, and greater with a positive skew.
. Probabilities in Poker Probabilities of drawing. Approximate Hand Exact Probability Probability. Royal Flush. The number of.
What is the probability of drawing a flush (all five cardsProbability and the Flush. The flush is just a bit easier to get than a full house. It is a hand well worth trying for in a poker game. To find out what the chances.How did you determine that this is the number of total possible results.A Holistic Statistical Test for Fairness in Video. Recall that a Royal Flush is a poker hand that consists of. to derive the probability of drawing a royal.The expected frequency of a royal would increase from once every 40388 hands to once every 23081.This machine allows one to play three hands at a time where the cards one holds are carried forward from the first hand to the other two.
To answer your first question, there are 2598960 ways to choose 5 cards out of 52 for the initial hand.I tried the software in question in free-play mode and my results seemed fine.For a near-exact answer to streak questions such as this we need to use matrix algebra.In Jacks or Better, for the most part, you are not going to get a winning session over a few hours if you do not hit a royal.Such a player would not be able to sue the casino because it was his fault for playing so badly.The reason my video poker return tables have almost 20 trillion combinations is you also have to consider what could happen on the draw.
Conditional Probability and Cards - homepages.math.uic.eduIn an earlier column, you said that in full pay Jacks or Better the perfect strategy player will average one royal flush every 40,388 plays.
According to my page on sequential royal video poker, the odds are just about one in four million.What are the probabilities of all poker hands. than a flush. So, we compute the probability. Royal Flush 4,234.
I once hit six royals in single-line video poker within 5,000 hands.Either she is using some kind of worthless progression, or this is second-hand exaggeration.I have noticed in your tables of probabilities and expected returns for video poker, that the probabilities (and corresponding number of hands) for each hand vary for the same type (jacks or better, for example) from one pay out chart to another.Probability and Poker. and the Royal Flush 2. Probability and the. three of a kind from a pair drawing three cards. 8. Probability and Two Pairs There are.Define m as the expected number of four of a kinds to get one that you need.If one is dealt, say, four of a kind on the initial draw of five cards, one will be paid on all three hands.
Could you comment on the variance and covariance in Spin Poker.
Rules of Card Games: Poker Hand Ranking - Pagat.comStep 4: Multiply the initial state after 5,000 hands by T-24,995,500.I assumed that given two plays of equal royal probability the player will choose the play which maximizes the return on the other hands.Things get more complicated with straights and flushes but still manageable.If your strategy were to maximize the number of royals at all costs then you would hit a royal once every 23081 hands.I was wondering if I could get your help on computing the probability distribution table for Jacks or Better.Although I strongly feel poker based games should be played with only one deck, I will submit to the will of my readers and present the following tables.I know as the jackpot increases, so does the payback percentage.
In poker, players construct sets of five playing cards, called hands, according to the rules of the game being played. Each hand has a rank, which is compared.Probabilities of Poker Hands with Variations. Royal Flush – all five cards. Hand Number Probability Straight Flush 2 40 0.00002.straight flush 4-of-a-kind full house flush. Here is a table summarizing the number of 7-card poker hands. The probability is the probability of having the hand.Dear Mr. Wizard, How do minimum payback laws affect video poker machines.
All 10 hands (and thus all 100 lines) failed to bring up a single win.You have developed an excellent website for information concerning gambling, and I have found it very useful.For the benefit of other readers, the coefficient of skewness (skew) for any random variable is a measure of which direction has the longer tail.What are the odds of being dealt a royal flush on a Triple Play video poker machine.A royal flush is an ace, king, queen, jack, and 10, all of one suit. A straight flush is five consecutive cards all of the same suit (but not a royal flush), where an ace may count as either high or low. A full house is three-of-a-kind and a pair. A flush is five cards of the same suit (but not a royal flush or straight flush).Please can you calculate the probability of drawing a blank on 10 hands of 10 line JoB.Culture & Cosmos Card Games: Probability of a Royal Flush The poker hand known as a royal flush consists of an ace, king, queen, jack and ten card and all must be in.On your video poker tables you use the figure of 19,933,230,517,200 possible results.I was wondering why there are so many more than 52 choose 5, and how to compute them.
Probability Of Royal Flush casino hotels las vegas free poker chart play pai gow poker with fortune bonus.
Probablity of Royal Flush | Physics Forums - The Fusion ofOn the draw there are 1, 47, 1081, 16215, 178365, or 1533939 ways to draw the replacement cards, depending on how many card the player holds.It can also happen if a hand 5,000 games ago was a royal, but the new hand is also a royal.How many hands to reduce the probability of no royal flush in n. The probability of a royal flush in a poker hand is. Probability of drawing a flush from a.
It is interesting to note that skew is greatest for Jacks or Better.However, if you limit me to games that are easy to find, my nomination is Triple Double Bonus, with a standard deviation of 9.91. Here is that pay table.Thank you for your valuable time in reading and hopefully responding.It makes sense to have four aces as the premium four of a kind, because aces are the highest card in regular poker.For example with any pair and 3 singletons the probability of improving the hand to a two pair is always the same. | s3://commoncrawl/crawl-data/CC-MAIN-2018-47/segments/1542039745800.94/warc/CC-MAIN-20181119150816-20181119172816-00513.warc.gz | CC-MAIN-2018-47 | 6,752 | 14 |
https://www.wyzant.com/resources/answers/56191/do_i_use_an_arc_length_formula_how_do_i_go_about_solving_this_problem | math | The first step to solving this problem is understanding what it is really asking.
The distance that the pulley rotates through, will be the height that the object is lifted to. Therefore, the problem is really asking you to determine how far the outside edge of the pulley will travel as it rotates 810 degrees.
In order to determine that, you will need to multiply the number of revolutions that the pulley passes through, by the distance traveled per revolution - that is, the circumference. So, there are two, relatively straightforward steps to this problem: determining how many revolutions it has gone through, and determining its circumference.
To determine the number of revolutions, divide 810 degrees by the number of degrees in one complete revolution (360).
To determine the circumference, use the formula C = 2*r*PI.
Once you have both of those parts, simply multiply them together, and you will have your answer. | s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141171126.6/warc/CC-MAIN-20201124053841-20201124083841-00035.warc.gz | CC-MAIN-2020-50 | 926 | 6 |
https://csusonoma.augusoft.net/index.cfm?method=ClassInfo.ClassInformation&int_class_id=371&int_category_id=7&int_sub_category_id=29 | math | Designed to give students an understanding of finite mathematics applied in the modern world to social sciences, economic analysis, statistical analysis, and decision making. Topics may include linear models, linear programming, financial mathematics, sets, combinatorics, probability, and statistics. Recommended for students with interests in the social sciences and management. Satisfies the Area B4 GE requirement (Mathematics/Quantitative Reasoning). C- or better required for GE credit. Prerequisite: Students need to be GE Math ready to register for this course. | s3://commoncrawl/crawl-data/CC-MAIN-2020-16/segments/1585370496227.25/warc/CC-MAIN-20200329201741-20200329231741-00000.warc.gz | CC-MAIN-2020-16 | 569 | 1 |
https://digitalcommons.kennesaw.edu/facpubs/3686/ | math | This paper introduces quasi-maximum likelihood estimator for multivariate diffusions based on discrete observations. A numerical solution to the stochastic differential equation is obtained by higher order Wagner-Platen approximation and it is used to derive the first two conditional moments. Monte Carlo simulation shows that the proposed method has good finite sample property for both normal and non-normal diffusions. In an application of estimating stochastic volatility models, we find evidence of closeness between the CEV model and the GARCH stochastic volatility model. This finding supports the discrete time GARCH modeling of market volatility.
Studies in Nonlinear Dynamics and Econometrics
Digital Object Identifier (DOI) | s3://commoncrawl/crawl-data/CC-MAIN-2024-10/segments/1707947475727.3/warc/CC-MAIN-20240302020802-20240302050802-00630.warc.gz | CC-MAIN-2024-10 | 735 | 3 |
https://unemployed-professor.com/2022/01/24/inter-firm-comparison-is-carried-out-with-the-help-of-ratios-although-they-are-not-exclusive-and/ | math | 1. Write short notes on:
(a) Liquidity test ratio
(b) Acid test ratio
(c) Profitability test ratios
(d) Turnover ratios.
2. “Inter-firm comparison is carried out with the help of ratios although they are not exclusive and conclusive indicators of performance”. Examine.
3. Prepare a proforma income statement for the month of April, May and June for Eastern Ltd. from the following information’s:
(i) Sales are projected at Rs.4,50,000, Rs.4,80,000 and Rs.4,30,000 for April, May and June respectively.
(ii) Cost of goods sold is Rs.1,00,000 plus 30% of selling price per month.
(iii) Selling expenses are 4% of sales.
(iv) Rent Rs.15,000 per month.
(v) Administrative expenses for April are expected to be Rs.1,20,000 but are expected to rise 2% per month over the previous month’s expenses.
(vi) The company has Rs.5,00,000 of 12% loan, interest payable monthly.
(vii) Corporate tax expected is 40%. | s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710808.72/warc/CC-MAIN-20221201085558-20221201115558-00787.warc.gz | CC-MAIN-2022-49 | 909 | 14 |
http://www.chegg.com/homework-help/questions-and-answers/rock-mass-750-kg-lowered-using-rope-rock-starts-rest-descends-downward-acceleration-275-m--q1561291 | math | A rock of mass 7.50 kg is lowered using a rope. The rock starts from rest and descends with a downward acceleration of 2.75 m/s2. When the rock has descended a distance of 4.30 m, what is (a) the work done by gravity on the rock? (b) the work done by the rope on the rock? (c) the kinetic energy of the rock? (d) the speed of the rock? | s3://commoncrawl/crawl-data/CC-MAIN-2015-48/segments/1448398450745.23/warc/CC-MAIN-20151124205410-00165-ip-10-71-132-137.ec2.internal.warc.gz | CC-MAIN-2015-48 | 335 | 1 |
https://cowetaamerican.com/2022/07/23/what-are-the-properties-of-three-dimensional-shape/ | math | What are the properties of three-dimensional shape?
3D shapes have three dimensions – length, width and depth.
What are properties of shapes?
2D shapes have sides and angles (sometimes referred to as vertices). Sides are the individual lines that make up a 2D shape, while the angles (vertices) are the corners where the edges meet. 2D stands for two-dimensional, as 2D shapes only have two dimensions: length (how long it is) and width (how wide it is).
What is the study of the properties of figures of three dimensions?
Unlike 2-D geometry, three-dimensional geometry, or 3-D geometry, deals with objects that have three measurable dimensions: length, width, and height. You can see this if you compare a 2-D shape, like a square, to its 3-D equivalent, a cube.
What is a 3 dimensional shape called?
Three-dimensional figures include prisms and pyramids, as well as figures with curved surfaces. A prism is a three-dimensional figure with two parallel, congruent bases. The bases, which are also two of the faces, can be any polygon. The other faces are rectangles. A prism is named according to the shape of its bases.
What are the properties of 2D and 3D shapes?
2d Shapes and 3d Shapes
|It is a shape surrounded by three or more straight lines in a plane and sometimes with a closed curve.
|If a shape is surrounded by a no. of surfaces or planes then it is a 3D shape.
What is 2D and 3D shapes in maths?
2D (two-dimensional) shapes are flat, while 3D (three-dimensional) shapes are solid objects with length, breadth, and depth.
How many 3 dimensional shapes are there?
What are the different types of three dimensional shapes? The different types of three dimensional shapes are cone, cylinder, cuboid, cube, sphere, rectangular prism, pyramid.
What are our 3 dimensions?
Everything around us, from the houses we live in to the objects we use in everyday life, has three dimensions: height, length, and width.
What is the meaning of 3 dimensional?
1 : relating to or having the three dimensions of length, width, and height A cube is three-dimensional. 2 : giving the appearance of depth or varying distances a three-dimensional movie. | s3://commoncrawl/crawl-data/CC-MAIN-2024-18/segments/1712296818081.81/warc/CC-MAIN-20240422051258-20240422081258-00441.warc.gz | CC-MAIN-2024-18 | 2,145 | 20 |
https://www.polytechforum.com/mech/the-mechanics-of-the-universe-8699-.htm | math | THE MECHANICS OF THE UNIVERSE
Copyright 1984-2006 Allen C. Goodrich
The planets orbit the sun in a special mean orbital radius L to conserve total energy. The modified first law of thermodynamics , which states that the total energy of the universe is a constant, is the fundamental equation of the universe. The sum of kinetic and potential energies is a constant.
m (2 pi L)^2 / t^2 + G m(M-m) /L = A CONSTANT. (if no charges are present)
- Delta m(2 pi L)^2/T^2 = - Delta Gm(M-m)/L
What's so important about this modified first law of thermodynamics? It says that no energy change or force is necessary for orbital motion.
A positive change of kinetic energy is accompanied by a negative change of potential energy relative to the rest of the universe to conserve the total energy. The universe has been found to be expanding at an accelerating rate. The potential energy of the universe is continually decreasing and the kinetic energy is continually increasing. Again, to conserve the total energy relative to the rest of the universe. This is why the modified first law is so important. The conservation of total energy must be maintained relative to the rest of the expanding universe. Kinetic and potential energies must be computed relative to the rest of the expanding universe.
This modified first law leads to the conclusion that the force of gravity and the velocity of light are misleading illusions.
The definition of Kinetic and Potential Energies is most important to an understanding that these energies are relative to the rest of the effective universe, not just relative to any other mass. Kinetic energy is mass m times the square of the velocity relative to the rest of the effective universe. For example the kinetic energy of the earth is effectively relative to the sun plus the rest of the planets of the solar systen. Potential energy is the product of the mass m times the mass of the rest of the effective universe M-m divided by the distance L between their effective centers of mass. M is the mass of the entire effective universe. t is the orbital time for one complete revolution. G is the gravitational constant. Once this is clearly understood, the modified First Law of Thermodynamics becomes the Fundamental Equatiion of the Universe. This equation ,then, defines the photon and the rest of the universe.
The Thomas R. Young two slit defraction pattern, the complete logic of quantum mechanics, the true nature of gravitation, the fact that light does not have a mass or a velocity, all become quite obvious. This is a simple solution to so many of the problems that baffled scientists for hundreds of years. We remember that Sir Isaac Newton proposed the force of gravity F_g = k m_1 m_2 / L^2. Scientists have known that action at a distance without the transfer of energy was not possible. A force of gravity would not be possible without the transfer of energy. The amount of energy required to cause the so called force of gravity to make the planets travel in orbits, other than the equilibrium orbit,about the sun would be tremendous and is not available. Another explanation is necessary. Einstein and other scientists have assuned that masses change the shape of space time. These explanations have their problems.
No problems exist if the modified first law of thermodynamics is used.This is the Fundamental Equation of the Universe.
One night when I was walking on Myrtle Beach in the light of the full moon, the full moon was at its highest point in the sky, and the beach was very wide. The lowest tide was present. This is not what would be expected according to the gravitational theory. The gravitational theory states that the tide should be very high. One can find this explained in most older dictionaries or encyclopedias. The water of the ocean is shown bulging on the side of the earth directly under the full moon. The tides never occur in this way. This discrepancy with the law of gravity is explained by the requirement for the time required for the water to flow due to the force . No one has bothered to explain that the water would have to flow at more than1000 miles per hour to complete this picture. This flow would wash all of the continents away in one day, Here, we have a big problem with the force of gravity .
The NOAA U.S. Coast and Geodetic Survey has monitored the tides at many ocean ports for many years and this data is available. The Jet Propulsion Laboratory has plotted the position and phases of the moon with changes of time. This data is also available. No one has previously published a correlation ot these two sets of data. If they had, it would become very obvious that invariably the lowest tide occurred when the full moon and new moon were exactly directly at their highest point in the sky. It would have been obvious that the lowest tide also occurred on the opposite side of the earth. Not at all consistant with the existing gravitational theory. However, this is predicted by the modified first law of thermodynamics, when the kinetic and potential energies are relative to the rest of the effective universe.
The planets orbit the sun at a special mean radius L, to conserve total energy. If one calculates the kinetic and potential energies of the planets and moons,at orbital distance L, one finds that the two are nearly equal in magnitude but opposite in sign. This is the only mean orbital radius L where no change of total energy is necessary. Nature obays this modified first law.
The assumption of a force of gravity, with its energy transfer, action at a distance, is not necessary to explain orbital motion at equilibrium. Gravitation is explained by the modified first law of thermodynamics. A force must be present and an energy change is necessary at any other radius, such as a body on the surface of the earth.
The Thomas R. Young's two slit defraction pattern is also explained by the modified first law of thermodynamics if one uses the charges e in this fundamental equation for the calculation of kinetic and potential energies.
Delta e_1 (2 pi L)^2 / t^2 = Delta-K e_1 e_2 /4 pi E_o L.
Where e_2 is the charge of the rest of the effective universe and . e_1 is the orbital electron. E_o is the dielectric constant. Here, the masses would have little effect by comparison and can be neglected. The kinetic energy change of the electron would then be a function of a change of potential energy relative to the rest of the effective universe. The energy of the electron of the atom on the defraction pattern screen would be a function of the rest of the effective universe. The electron would sense the fact that one or two of the slits was open and the Thomas R Young defraction pattern is explained.
We now have the basis for a new quantum mechanics. Light , that is observed as a change of the kinetic energy of the electron, which has the correct energy density (time), direction and frequency, in the expanding universe, is not a particle, with mass and velocity ( kinetic energy ), but it is a function of the potential energy change of the rest of the effective universe .+ | s3://commoncrawl/crawl-data/CC-MAIN-2023-23/segments/1685224649105.40/warc/CC-MAIN-20230603032950-20230603062950-00740.warc.gz | CC-MAIN-2023-23 | 7,098 | 19 |
https://books.google.com/books?id=wBIoAQAAMAAJ&source=gbs_book_other_versions_r&hl=en | math | Feedback control of dynamic systems
Addison-Wesley, 1994 - Technology & Engineering - 778 pages
The third edition of this bestselling textbook on undergraduate controls continues to develop students insight into control problems and methods for solving them. Because of the importance of design problems and their motivational effect on students, the authors emphasize design in addition to analysis techniques throughout the text. The book demonstrates the unifying principles behind numerous individual design techniques to assist students in creating their own problem-solving toolbox. The latest edition of Feedback Control of Dynamic Systems reflects many of the recent advances in control system design including balanced coverage of frequency response and state space topics and an introduction to digital control.
What people are saying - Write a review
An Overview and Brief History of Feedback Control
17 other sections not shown
actuator amplifier angle approximation Assume asymptotes bandwidth block diagram Bode plot CACSD Chapter characteristic equation circuit closed-loop poles closed-loop system coefficients complex compute Consider constant corresponding crossover frequency curve damping ratio defined derivative determine differential equations equations of motion estimator feedback control field FIGURE Final Value Theorem find first first-order flow frequency response impulse response integral control KG(s Laplace transform lead compensator linear loop magnitude MATLAB matrix method nonlinear numerical Nyquist plot open-loop output overshoot parameter partial-fraction expansion phase margin PID controller plant pole locations poles and zeros polynomial rad/sec reference input result root locus Routh s-plane sample rate second-order system Section sensitivity function sensor shown in Fig shows signal sinusoidal Sketch Solution specifications speed stability state-space state-variable form steady-state error step response system for Problem system shown system type term torque transfer function transient response unity feedback system variables vector voltage | s3://commoncrawl/crawl-data/CC-MAIN-2015-27/segments/1435375095270.70/warc/CC-MAIN-20150627031815-00198-ip-10-179-60-89.ec2.internal.warc.gz | CC-MAIN-2015-27 | 2,105 | 7 |
https://studopedia.net/13_45246_IV-Answer-the-questions-below-and-then-ask-for-more-information-Work-in-pairs.html | math | IV. Answer the questions below and then ask for more information (Work in pairs).
1. Who didn’t consider 1 to be a number at all?
2. What number associates with negatives? Why?
3. What number is the dimension of the smallest magic square in which every row, column, and diagonal equals fifteen?
4. What numbers are considered to be perfect in Mathematics? Why?
5. What does the number 7 determine in China?
1. In what country is the number 4 considered to be unlucky?
2. Why was the number 5 important to the Maya?
3. Why is a knot tied in the form of the pentagram called a lover’s knot in England?
4. What number leads to a few years of bad luck, if you break a mirror?
5. What did students pursue in medieval education?
DO YOU KNOW THAT…
· The number 8 is generally considered to be an auspicious number by numerologists. The square of any odd number, less one, is always a multiple of 8 (for example, 9 − 1 = 8, 25 − 1 = 8 × 3, 49 − 1 = 8 × 6), a fact that can be proved mathematically.
· The early inhabitants of Wales used nine steps to measure distance in legal contexts; for example, a dog that has bitten someone can be killed if it is nine steps away from its owner’s house, and nine people assaulting one constituted a genuine attack.
· The number 20 has little mystical significance, but it is historically interesting because the Mayan number system used base 20. When counting time the Maya replaced 20 × 20 = 400 by 20 × 18 = 360 to approximate the number of days in the year. Many old units of measurement involve 20 (a score), for example, 20 shillings to the pound in pre-decimal British money system.
V. Find information on the Internet and give a presentation of the number you are interested in (brings you good or bad luck).
Reading and Speaking
NUMBER AND REALITY
Many aspects of the natural world display strong numerical patterns, and these may have been the source of some number mysticism. For example, crystals can have rotational symmetries that are twofold, threefold, fourfold, and sixfold but not fivefold − a curious exception that was recognized empirically by the ancient Greeks and proved mathematically in the 19 th century.
An especially significant number is the golden ratio, usually symbolized by the Greek letter ϕ. It goes back to early Greek mathematics under the name ‘extreme and mean ratio’ and refers to a division of a line segment in such a manner that the ratio of the whole to the larger part is the same as that of the larger part to the smaller. This ratio is precisely (1 + √5)/2, or approximately 1.618034. The popular name golden ratio, or golden number, appears to have been introduced by the German mathematician Martin Ohm in Die reine Elementarmathematik (1835; ‘Pure Elementary Mathematics’). If not, the term is not much older and certainly does not go back to ancient Greece as is often claimed.
In art and architecture the golden number is often said to be associated with elegance of proportion; some claim that it was used by the Greeks in the design of the Parthenon. There is little evidence for these claims. Any building has so many different lengths that some ratios are bound to be close to the golden number or for that matter to any other ratio that is not too large or small. The golden number is also often cited in connection with the shell of the nautilus, but this too is a misunderstanding. The nautilus shell has a beautiful mathematical form, a so-called logarithmic (or equiangular) spiral. In such a spiral each successive turn is magnified in size by a fixed amount. There is a logarithmic spiral associated with the golden number, and in this case the fixed amount is precisely ϕ. However, the spiral of the nautilus does not have the ratio ϕ. Logarithmic spirals exist with any given number as their ratio, and the nautilus ratio has no special significance in mathematics.
The golden number is, however, legitimately associated with plants. This connection involves the Fibonacci numbers (1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144…), in which each number, starting with 2, is the sum of the previous two numbers. These numbers were first discussed in 1202 by the Italian mathematician Leonardo Pisano, who seems to have been given the nickname Fibonacci (son of Bonaccio) in the 19th century. The ratio of successive Fibonacci numbers, such as 34/21 or 55/34, gets closer and closer to ϕ as the size of the numbers increases. As a result, Fibonacci numbers and ϕ enjoy an intimate mathematical connection.
Fibonacci numbers are very common in the plant kingdom. Many flowers have 3, 5, 8, 13, 21, or 34 petals. Other numbers occur less commonly; typically they are twice a Fibonacci number, or they belong to the ‘anomalous series’ 1, 3, 4, 7, 11, 18, 29… with the same rule of formation as the Fibonacci numbers but different initial values. Moreover, Fibonacci numbers occur in the seed heads of sunflowers and daisies. These are arranged as two families of interpenetrating spirals, and they typically contain, say, 55 clockwise spirals and 89 counterclockwise ones or some other pair of Fibonacci numbers.
This numerology is genuine, and it is related to the growth pattern of the plants. As the growing tip sprouts, new primordial − clumps of cells that will become special features such as seeds − arise along a generative spiral at successive multiples of a fixed angle. This angle is the one that produces the closest packing of primordial; and for sound mathematical reasons it is the golden angle: a fraction (1 − 1/ ϕ) of a full circle, or roughly 137.5 degrees.
I. Match the words (1–11) with the definitions/explanations (a– k):
Дата добавления: 2019-02-26; просмотров: 144; Мы поможем в написании вашей работы!
Мы поможем в написании ваших работ! | s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656103556871.29/warc/CC-MAIN-20220628142305-20220628172305-00731.warc.gz | CC-MAIN-2022-27 | 5,889 | 27 |
https://internetoracle.org/digest.cgi?N=371 | math | } Human, Human, mini mite,
} In Urban jungles, out of sight,
} Human, Human, tiny spore,
} I'll answer your question, your faith restore.
} I exist; always have, always will.
} With me there was no spawn to spill.
} I'm the one and only, no Mom or Dad,
} No one to tell me, "Be good, not bad".
} Because of this I have no button,
} No dimple down there, I ain't got nuthin'.
} And thus, no fiber, no fuzz, no lint.
} But finding this out, you'll now pay a mint.
} You see, I hate being buttonless; it makes me mad.
} And it's a sorry human that makes me sad.
} Your question answered, I'll have one yet,
} So now, in payment, it's *your's* I'll get. | s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243989856.11/warc/CC-MAIN-20210511184216-20210511214216-00388.warc.gz | CC-MAIN-2021-21 | 649 | 16 |
https://www.degreeinfo.com/index.php?threads/distance-phd-in-history.38012/#post-386559 | math | I am looking for a distance Ph.D. in History. I would prefer somewhere from the U.K. I am looking into Open University. I am also looking into The University of South Africa, but I am not sure how reputable a degree from UNISA would be. I need a Ph.D. in History. It must be via distance education, and I would prefer dissertation only. Any suggestions are welcome. Thanks! | s3://commoncrawl/crawl-data/CC-MAIN-2024-10/segments/1707947474650.85/warc/CC-MAIN-20240226030734-20240226060734-00878.warc.gz | CC-MAIN-2024-10 | 373 | 1 |
http://gmatclub.com/forum/is-n-2-an-even-integer-162578.html?fl=similar | math | - Statement (1) is sufficient. If n/2 is an odd integer, we can find n by multiplying both sides by 2. n is 2 times an odd integer, which is always an even. If n is an even, then n^2 is an even -- an even times an even is always an even.
Statement (2) is not sufficient. Note that "not an even integer" does not mean "an odd integer." It could also refer to any non-integer, such as 4.5. If n = 3, then n^2 = 9 and n^2/2 = 4.5, which is not an even integer. In that case, the answer is "no." However, if n^2 = 2, then n^2/2 = 1, which is not an even integer. But in this case, n^2 is even, so the answer is "yes." Choice (A) is correct.
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Need motivation? check out this video or this one | "We are what we repeatedly do. Excellence, then, is not an act, but a habit." - Aristotle
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https://www.framingham.k12.ma.us/Domain/1725 | math | To engage in rigorous competition math and prepare for meets in the Greater Boston Math League. Framingham students who participate in the math team view the Greater Boston Math League math meets as an integral part of their high school extracurricular experience. Students are bonded by their desire to practice recreational mathematics and the math team gives them an outlet to pursue their mathematical interests.
Advisor: Brendon Ferullo
Meeting: Every Wednesday unless there is a faculty meeting, then on Thursday. 2:30-5:30
Eligibility: All students
Student Officer: Josh Ginzburg, Jacob Cohen | s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710771.39/warc/CC-MAIN-20221130192708-20221130222708-00526.warc.gz | CC-MAIN-2022-49 | 599 | 5 |
https://princeton.universitypressscholarship.com/view/10.23943/princeton/9780691153131.001.0001/upso-9780691153131-chapter-008?print | math | A fundamental result in Riemannian geometry is the jet isomorphism theorem which asserts that at the origin in geodesic normal coordinates, the full Taylor expansion of the metric may be recovered from the iterated covariant derivatives of curvature. As a consequence, one deduces that any local invariant of Riemannian metrics has a universal expression in terms of the curvature tensor and its covariant derivatives. Geodesic normal coordinates are determined up to the orthogonal group, so problems involving local invariants are reduced to purely algebraic questions concerning invariants of the orthogonal group on tensors. This chapter proves an analogous jet isomorphism theorem for conformal geometry. By making conformal changes, the Taylor expansion of a metric in geodesic normal coordinates can be further simplified, resulting in a “conformal normal form” for metrics about a point.
Princeton Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.
If you think you should have access to this title, please contact your librarian.
To troubleshoot, please check our FAQs , and if you can't find the answer there, please contact us. | s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662534693.28/warc/CC-MAIN-20220520223029-20220521013029-00153.warc.gz | CC-MAIN-2022-21 | 1,310 | 4 |
http://augustabluescompany.com/179-case-study-fluid-mechanics-politeknik.php | math | Friction coefficient f is 0. Calculate the velocity entering the diffuser. The following treatment is limited to incompressible fluids. Discharge and Mass Flowrate 59 Mass Flowrate The mass of fluid passing through a given cross section in unit time is called the mass flow rate.
This occurs in the case of uniform flow and steady flow Continuity Equation 61 Example 4: A meter orifice has a mm diameter rectangular hole in the pipe. If the density of mercury is If the area of cross-section of the stream of fluid is a, then force due to pressure p on cross-section is pa.
The glass are install with the bubble light which can be operation for 6 hours that show the movement of the bubble on the floor. There is a sharp entrance to the pipe and the diameter is 50 mm for the first 15 m from the entrance.
The pressure in a vacuum is called absolute zero, and all pressures referenced with respect to this zero pressure are termed absolute pressures. At the end of this chapter student will able to: Viscosity -A fluid at rest cannot resist shearing forces but once it is in motion, shearing forces are set up between layers of fluid moving at different velocities.
So when people walk along this walking sitethe water fountain will flow up the water for only a few seconds but it will continue to flow up by next water fountain.
A U tube manometer measures the pressure difference between two points A and B in a liquid. This water fountain works when there are people walking case study fluid mechanics politeknik along the fountain side.
The entry from the reservoir to the pipe is sharp and the outlet is 12 m below the surface level in the reservoir. Describe flow rate 3.
Specific volume, v is defined as the reciprocal of mass density. Oil flows through a pipe at a velocity of 1. Although venturi meters can be applied to the measurement of gas, they are most commonly used for liquids.
An inverted U tube as shown in the figure below is used to measure the pressure difference between two points A and B which has water flowing. Take f as 0. Let this pressure be p.
This is because of the weight of the fluid above it. Such a condition can be approached very nearly in a laboratory when a vacuum pump is used to evacuate a bottle.
Example 2: Since these boundaries may be large colleges in california with creative writing major the force may differ from place to place it is convenient to work in terms of pressure, p, which is the force per unit area.
Progress out the construction site.
Two reservoirs are connected by a pipeline which is mm in diameter for the first 6 m and mm in diameter for the remaining 15 m. The diameter of the pipe is 8 cm.
Determine the loss of head due to friction in a pipe 14 m long and 2 m diameter which carries 1. In addition, the application will motivate and attract the student to be interested in studying this course.
The diameter M and N are both 20 cm and 5 cm. Show relationship between pressure and depth 2. After 7 seconds of collecting water the weight of the bucket is 8.
The more dense the fluid above it, the more pressure is exerted on the object that is submerged, due to the weight of the fluid. A simple Barometer consists of a tube of more than 30 inch mm long inserted into an open container of mercury with a closed and evacuated end at the top and open tube end at the bottom and with mercury extending from the container up into the tube. | s3://commoncrawl/crawl-data/CC-MAIN-2019-26/segments/1560628000353.82/warc/CC-MAIN-20190626134339-20190626160339-00409.warc.gz | CC-MAIN-2019-26 | 3,405 | 16 |
https://www.reddit.com/user/tjaymiller | math | Hi. I have the task to make a high-quality picture of these letters.
Does anyone have an idea what the font is called? It's probably free because I can't imagine the person spending a lot of time finding a good font.
Any help is much appreciated. (I've tried the font identifiers online but they didn't gave me good results)
Hi. I'm currently working on the characterization of an absorption
process for packed columns. This is a seperation process in which a
component of a gasphase is removed by the solution in a solvent. I
couldn't find a detailed explenation of what happens on a molecular
level. How do the molecules of the gasphase solve? Do they go through
a phase transition by getting stuck in the liquid Phase and condense
or what happens?
Does anyone have good literature recommenations on this topic?
Thanks a lot!
I've been searching for a while for a P&ID-Diagram Template but I've only come across some electric circuits.
I've recently found a picture that pretty much contains everything that I need as to get started.
Can anyone help me with converting this into Tikz, or give me some references to get started?
Hi. I haven't had an iOS device in a while, but I got myself an iPad. Now I need a cydia tweak or something that makes downloading paid iOS apps on my device as convenient as possible. Any suggestions?
There are like dozen types of densities that I read about, and quiete frankly don't understand the difference of: - Packing density - Tap Density - Bulk Density
Which one is important for partquality (density)?
The question isn't meant as to which metals have a low enough melting point. It is meant as to which metals can be melted with plasma and not evaporate? I guess there are lowmelting metals that evaporate under plasma heat.
Thanks a lot
Would be interesting to know which kind of materials are sold in which quantities. I've searched for something like this but couldn't find it. Anyone else has a good source?
Hi! I've read that in the EBM-Process (Electron Beam Melting), the powder bed is preheated to about 800 °C (1075 K) for sintering and reduction of internal stress. Is it than even possible to manufacture lowmelting metals like Ti-Aloys or Al-Aloys or is there the danger of evaporation?
Would be cool to know.
Thanks for answers
My question relates to the relation between the median and the mode of a logarithmic normal distribution. In a particle size distribution, the median describes the particle size under which 50% of the quantity of particles are. The mode though describes the most occuring particle size. I've read that the mode and the median are the same for the logarithmic normal distribution and found that somewhat confusing.
Is the median and mode the same for a logarithmic normal distribution?
So I've read in a book that metal atomization is limited to metals with Ts<1800°C. No explanation was given and it was a well known powder metallurgy book (75k Downloads), wtf they don't answer this I don't know...
Why are they limited to 1800°C? Does it have to do with the fact that ceramic crucibles isn't stable at these temperatures or something?
Hi. Some might take this as an obvious answer. I've gotten the answer a lot: "so you can release pressure in the turbine". But this answer doesn't quite satisfy my thoughts. So the steam power plant works like this: (1) You put work/power in to increase fluid pressure (Win) (2) You transfer heat to the fluid through e.g. combustion (Qin) (3) You release pressure to gain power/work (Wout) (4) You condense the fluid to release heat (Qout)
Obviously the power that you get out of the plant Wout has to be higher than Win to achieve a lucrative process. So Wout has to be a combination of Qin and Win. My question is from a more thermodynamical viewpoint: Why is it that there is a pump needed? I mean I could just put in the Heat through the combustion and transfer that into Power. | s3://commoncrawl/crawl-data/CC-MAIN-2018-51/segments/1544376826354.54/warc/CC-MAIN-20181214210553-20181214232553-00292.warc.gz | CC-MAIN-2018-51 | 3,905 | 30 |
https://answers.sap.com/questions/5161033/sdsalesdocumentcreate-required-data-to-get-correct.html | math | I need to create sales documents through this function module. I Entered the following data:
SALES_HEADER_IN: All required data
SALES_ITEMS_IN: ITM_NUMBER=000010, MATERIAL=MAT1.
SALES_SCHEDULES_IN: ITM_NUMBER=000010, REQ_QTY=100, REQ_DATE= 02.12.2008 (today).
I expect that the table SCHEDULE_EX throws the following lines:
ITM_NUMBER=000010, REQ_QTY=100,COMMIT_QTY=49, TP_DATE= 02.12.2008
ITM_NUMBER=000010, REQ_QTY=100,COMMIT_QTY=51, TP_DATE= 02.01.2009
These lines are because 49 units are in stock and 51 are not and they can be delivered one month after.
But after I execute the function I check the SCHEDULE_EX table and I have this:
ITM_NUMBER=000010, REQ_QTY=100,COMMIT_QTY=0, TP_DATE= 02.12.2008
ITM_NUMBER=000010, REQ_QTY=0,COMMIT_QTY=0, TP_DATE= 02.01.2009
Do I have to put more data in the function to accomplish the desired result? | s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964363135.71/warc/CC-MAIN-20211205035505-20211205065505-00365.warc.gz | CC-MAIN-2021-49 | 844 | 12 |
https://techgsolution.com/qa/quick-answer-why-does-mc-cross-atc-at-its-minimum.html | math | - What happens when MC ATC?
- Which cost can never become zero?
- When MC is equal to AC the slope of AC is?
- Can average fixed cost be 0?
- Which curve is not affected by fixed cost?
- What is the average cost curve?
- What can we say about MC when AC is minimum?
- At what unique point does marginal cost cross AVC and ATC?
- Can fixed cost be zero?
- What is the shape of AFC curve?
What happens when MC ATC?
When the addition to total cost (the marginal cost) associated with the production of another unit of output is greater than ATC, ATC rises.
Conversely, if the marginal cost of another unit is less than ATC, ATC will fall.
Hence, ATC declines as long as MC is above ATC.
When MC is above ATC, ATC rises..
Which cost can never become zero?
Answer. The fixed costs can never be zero in short period. The fixed costs, whether the firm produces or not, will never be zero and will be always positive. The examples of fixed costs include depreciation, insurance, rent, salaries etc.
When MC is equal to AC the slope of AC is?
(iii) When the slope of AC is equal to zero (i.e., AC is minimum), MC is equal to AC. Therefore, MC cuts AVC and AC from below at their respective minimum points.
Can average fixed cost be 0?
The reason, of course, is that as output increases, a given fixed cost is spread more thinly over a larger quantity. Second, average fixed cost remains positive, it never reaches a zero value and never turns negative.
Which curve is not affected by fixed cost?
Answer: Fixed costs do not affect the marginal cost of production since they do not typically vary with additional units. Variable costs, however, tend to increase with expanded capacity, adding to marginal cost due to the law of diminishing marginal returns. This is your answer.
What is the average cost curve?
Average total cost (ATC) is calculated by dividing total cost by the total quantity produced. The average total cost curve is typically U-shaped. … The marginal cost curve is upward-sloping. Average variable cost obtained when variable cost is divided by quantity of output.
What can we say about MC when AC is minimum?
ADVERTISEMENTS: 1. When MC is less than AC, AC falls with increase in the output, i.e. till 3 units of output. … When MC is equal to AC, i.e. when MC and AC curves intersect each other at point A, AC is constant and at its minimum point.
At what unique point does marginal cost cross AVC and ATC?
There is one point where the marginal cost curve and the average variable cost curve intersect. They intersect at the lowest point of the average variable cost curve. The marginal cost curve represents how much more the next unit costs than the previous unit.
Can fixed cost be zero?
For example, if there are only fixed costs associated with producing goods, the marginal cost of production is zero. If the fixed costs were to double, the marginal cost of production is still zero. The change in the total cost is always equal to zero when there are no variable costs.
What is the shape of AFC curve?
The average fixed costs AFC curve is downward sloping because fixed costs are distributed over a larger volume when the quantity produced increases. AFC is equal to the vertical difference between ATC and AVC. Variable returns to scale explains why the other cost curves are U-shaped. | s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178369721.76/warc/CC-MAIN-20210305030131-20210305060131-00358.warc.gz | CC-MAIN-2021-10 | 3,307 | 33 |
https://sciencegraph.net/app-review/automated-house-flipping-app-review/ | math | # Automated House Flipping App Review: Revolutionizing the Real Estate Industry
Are you tired of the tedious process of manually flipping houses? Do you want to increase your efficiency and maximize your profits in the real estate industry? Look no further than automated house flipping apps. These cutting-edge tools are transforming the way real estate investors buy, renovate, and sell homes. In this blog, we’ll review the benefits and features of automated house flipping apps and answer some of the most frequently asked questions about this innovative technology.
## Benefits of Automated House Flipping Apps
### Increased Efficiency
Manual house flipping can be time-consuming and costly. With an automated house flipping app, you can streamline the process and save time and money. These apps can quickly analyze property data and identify potential deals, reducing the need for manual research and analysis.
### Improved Accuracy
Automated house flipping apps use advanced algorithms and machine learning to analyze large amounts of data. This technology can identify trends and patterns that may be missed by human analysis, resulting in more accurate property evaluations and investment decisions.
### Enhanced Communication
Automated house flipping apps often have built-in communication tools that allow investors to connect with contractors, real estate agents, and other professionals involved in the flipping process. This streamlines communication and ensures that everyone is on the same page throughout the project.
### Increased Profits
By reducing the time and resources required to flip a house, automated house flipping apps can help investors maximize their profits. These apps can help identify potential deals, estimate renovation costs, and accurately predict the selling price, allowing investors to make informed decisions and increase their ROI.
## Features of Automated House Flipping Apps
### Property Analysis
Automated house flipping apps can quickly analyze property data and provide investors with valuable insights about the property, including:
– Estimated property value
– Potential renovation costs
– Projected selling price
– Comparable properties in the area
– Potential ROI
### Project Management
Automated house flipping apps often include tools for project management, including:
– Task lists and timelines
– Budget tracking
– Contractor management
– Communication tools
### Investment Analysis
Automated house flipping apps can help investors evaluate potential deals and determine whether they are worth pursuing. These tools can analyze:
– Purchase price
– Renovation costs
– Expected selling price
– Potential ROI
### Marketing and Sales
Automated house flipping apps can also assist with the marketing and sales process, including:
– Listing creation and management
– Open house scheduling
– Buyer communication
– Closing documents
## Frequently Asked Questions
### What is an automated house flipping app?
An automated house flipping app is a software tool designed to automate and streamline the process of flipping houses. These tools can analyze property data, estimate renovation costs, manage projects, and assist with marketing and sales.
### How do I use an automated house flipping app?
To use an automated house flipping app, simply download the app and create an account. You can then input property data and receive valuable insights and analysis about the property. The app will also provide tools for project management, investment analysis, and marketing and sales.
### How much does an automated house flipping app cost?
The cost of an automated house flipping app varies depending on the provider and the features included. Some apps offer a free trial period, while others charge a monthly or annual subscription fee.
### Are automated house flipping apps reliable?
Automated house flipping apps use advanced algorithms and machine learning to analyze property data and provide investment insights. While no tool can guarantee success in the real estate industry, these apps can help investors make informed decisions and increase their chances of success.
### Can automated house flipping apps replace real estate professionals?
Automated house flipping apps are designed to assist real estate professionals, not replace them. While these tools can provide valuable analysis and insights, they cannot replace the expertise and experience of real estate agents, contractors, and other professionals involved in the flipping process.
In conclusion, automated house flipping apps are revolutionizing the real estate industry by helping investors increase efficiency, accuracy, and profits. By providing valuable property analysis, project management tools, and investment insights, these apps can help investors make informed decisions and maximize their ROI. If you’re looking to streamline your house flipping process and increase your success in the real estate industry, consider using an automated house flipping app today. | s3://commoncrawl/crawl-data/CC-MAIN-2023-40/segments/1695233510942.97/warc/CC-MAIN-20231002001302-20231002031302-00200.warc.gz | CC-MAIN-2023-40 | 5,033 | 49 |
https://rd.springer.com/chapter/10.1007/978-3-662-03338-8_18 | math | Rank over Finite Fields and Codes
Although the bilinear complexity of a bilinear map ϕ over a finite field may not be the minimum number of multiplications and divisions necessary for computing ϕ, the study of such maps gives some insight into the problem of computing a bilinear map over the ring of integers of a global field, such as the ring Z of integers: any bilinear computation defined over Z (that is, whose coefficients belong to Z) gives via reduction of constants modulo a prime p a bilinear computation over the finite field F p . In this chapter we introduce a relationship observed by Brockett and Dobkin between the rank of bilinear maps over a finite field and the theory of linear error-correcting codes. More precisely, we associate to any bilinear computation of length r of a bilinear map over a finite field a linear code of block length r; the dimension and minimum distance of this code depend only on the bilinear map and not on the specific computation. The question about lower bounds for r can then be stated as the question about the minimum block length of a linear code of given dimension and minimum distance. This question has been extensively studied by coding theorists; we use their results to obtain linear lower bounds for different problems, such as polynomial and matrix multiplication. In particular, following Bshouty [85, 86] we show that the rank of n x n-matrix multiplication over F2 is 5/2n2 — o(n2). In the last section of this chapter we discuss an interpolation algorithm on algebraic curves due to Chudnovsky and Chudnovsky . Combined with a result on algebraic curves with many rational points over finite fields, this algorithm yields a linear upper bound for R(F q n/F q )for fixed q.
KeywordsFinite Field Linear Code Prime Power Prime Divisor Block Length
Unable to display preview. Download preview PDF. | s3://commoncrawl/crawl-data/CC-MAIN-2018-30/segments/1531676590069.15/warc/CC-MAIN-20180718060927-20180718080927-00352.warc.gz | CC-MAIN-2018-30 | 1,864 | 4 |
https://answers.yahoo.com/question/index?qid=20110624070517AABiR15 | math | Financial accounting question from Horngren book?
Question - The following data pertain to Franciso Corporation. Total assets at january 1, 20X1 were $110,000 ; at December 31, 20X1, $ 124,000. During 20X1, sales were $354,000 , cash dividends were $5000, and operating expenses (EXCLUSIVE of the cost of goods sold) were 200,000. Total liabilities at December 31,20X1 were $55,000 ; at january 1, 20X1, $50,000. There was no additional capital paid in during 20X1.
Compute the following :
(1)Stockholder's equity, January 1, 20X1 and December 31,20X1
(2)Net Income for 20X1
(3)Cost of the goods sold for 20X1
PS : Introduction to financial accounting by Horngren, Sundem, Elliot book has good theory but it does not give hints or solutions at the end and there is no students manual. The instructor manual is impossible to get. | s3://commoncrawl/crawl-data/CC-MAIN-2019-39/segments/1568514573735.34/warc/CC-MAIN-20190919204548-20190919230548-00133.warc.gz | CC-MAIN-2019-39 | 828 | 7 |
https://data.mendeley.com/datasets/wp7yk8vtg9/1 | math | Data for the paper "Verified simulation of the stationary polymer fluid flows in the channel with elliptical cross-section"
The xlsx files contain the results of numerical simulation of the stationary non-isothermal incompressible viscoelastic polymer fluid flow of Poiseuille type through the channel with elliptical cross-section having an inclusion, which is heating element of elliptical shape. Specifically, the files contain the approximate values of the dimensionless velocity (u) and temperature (Y) of the flow computed in 1 681 data points distributed inside the channel. In the files their coordinates in Cartesian system are denoted by (y,z), and several regimes of flows are considered. To describe the polymer fluid flow, the generalised mesoscopic Pokrovskii — Vinogradov model was used, and the corresponding Poiseuille-type stationary solutions were found using the non-local method without saturation (NMWS). The detailed description of the model with all parameters and the method can be found in the paper by Boris Semisalov et al. "Verified simulation of the stationary polymer fluid flows in the channel with elliptical cross-section''. This paper also contains the comparison of the data from xlsx files with the results of simulation obtained using two other methods, which are the least-squares collocation method (LSCM) and the finite element method (FEM), see this comparison in tables 8 — 11 of the paper. Thus, the given data represent benchmark for the considered flow of polymer fluid. | s3://commoncrawl/crawl-data/CC-MAIN-2023-50/segments/1700679100674.56/warc/CC-MAIN-20231207121942-20231207151942-00331.warc.gz | CC-MAIN-2023-50 | 1,520 | 2 |
https://pals.sri.com/standards/other/nctmsPK-5.html | math | Grades PK-5 National Council of Teachers of Mathematics Principles and
First, select below the National Council of Teachers
of Mathematics (NCTM) Principles and Standards you wish to assess.
Next, click on the "Show Tasks for Selected Standards" button
to view the tasks that are intended to meet the standards you
Understand numbers, ways of representing numbers, relationships
among numbers, and number systems. (eNO1)
Understand meanings of operations and how they relate to
one another. (eNO2)
Compute fluently and make reasonable estimates. (eNO3)
Understand patterns, relations and functions. (eAL1)
Represent and analyze mathematical situations and structures using
algebraic symbols (eAL2)
Use mathematical models to represent and understand quantitative
Analyze change in various contexts. (eAL4)
Analyze characteristics and properties of two- and three-dimensional
geometric shapes and develop mathematical arguments about
geometric relationships. (eGEO1)
Specify locations and describe spatial relationships using
coordinate geometry and other representational systems.
Apply transformation and use symmetry to analyze mathematical
Use visualization, spatial reasoning, and geometric modeling
to solve problems. (eGEO4)
Formulate questions that can be addressed with data
collect, organize, and display relevant data to answer
Select and use appropriate statistical methods to
analyze data. (eDAP2)
Develop and evaluate inferences and predictions that
are based on data. (eDAP3)
Understand and apply basic concepts of probability.
Build new mathematical knowledge through problem solving. (ePS1)
Solve problems that arise in mathematics and in other contexts.
Apply and adapt a variety of appropriate strategies to solve problems.
Monitor and reflect on the process of mathematical problem solving.
Recognize reasoning and proof as fundamental aspects
of mathematics. (eRP1)
Make and investigate mathematical conjectures. (eRP2)
Develop and evaluate mathematical arguments and proofs.
Select and use various types of reasoning and methods
of proof. (eRP4)
Organize and consolidate their mathematical thinking through communication.
Communicate their mathematical thinking coherently and clearly
to peers, teachers, and others. (eCOM2)
Analyze and evaluate the mathematical thinking and strategies
of others. (eCOM3)
Use the language of mathematics to express mathematical ideas
Recognize and use connections among mathematical ideas.
Understand how mathematical ideas interconnect and
build on one another to produce a coherent whole.
Recognize and apply mathematics in contexts outside
of mathematics. (eCNX3)
Create and use representations to organize, record, and communicate
mathematical ideas. (eREP1)
Select, apply, and translate among mathematical representations
to solve problems. (eREP2)
Use representations to model and interpret physical, social, and
mathematical phenomena. (eREP3) | s3://commoncrawl/crawl-data/CC-MAIN-2017-17/segments/1492917121869.65/warc/CC-MAIN-20170423031201-00584-ip-10-145-167-34.ec2.internal.warc.gz | CC-MAIN-2017-17 | 2,905 | 57 |
https://www.hackmath.net/en/example/2082 | math | Find three numbers so that the second number is 4 times greater than the first and the third is lower by 5 than the second number. Their sum is 67.
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At a weather centre, the temperature at midnight was -2 degree Celsius and by noon it had raised 4 degree Celsius. What is the new temperature? | s3://commoncrawl/crawl-data/CC-MAIN-2018-17/segments/1524125948126.97/warc/CC-MAIN-20180426105552-20180426125552-00627.warc.gz | CC-MAIN-2018-17 | 2,977 | 32 |
http://delta.cs.cinvestav.mx/~mcintosh/comun/flexagon/node11.html | math | The flexing operation, we have seen, requires a thumbhole with a hinge. In the case of the proper flexagon, this is the number one thumbhole. This thumbhole splits the left hand pat into two groups, one composed of a single subpat and the other composed of subpats. The complete flexing operation inverts the top-most subpat of the left pat, leaving it on the left side, while it deposits the remaining subpats on the inverted right pat (see figure 8.1). The number one thumbhole has been opened out to display the next side. The two new pats are now joined by what was originally the hinge. When the flexagon is rotated, the hinges must be renumbered. The original hinge will become the new hinge, and each of the other hinges will have values one lower than before the flex and rotation. In the normal flexing operation of a proper flexagon, which has a consecutive subpat hinge sequence and a consecutive subpat structure, the order of turning up sides must also be consecutive (as has been shown empirically). This is because each successive thumbhole is associated with a correspondingly numbered hinge, (i.e. the hinge with the number one thumbhole, etc.). Each flexing operation subtracts one from the value of each hinge, thus bringing the thumbhole with which any particular hinge is associated closer to the position for being opened up next. A subpat hinge which in in position will be opened after flexes and rotations.
If we flex along a given cycle of a flexagon, we notice that we always progress in the same direction, either clockwise or counterclockwise, along the path of the map. If we draw vectors along the edges of the map (indicating in which direction we are progressing), the vectors for a given cycle will always point consistently clockwise or counterclockwise. Whichever way they do point, their direction may be reversed by turning the flexagon over. If a second cycle is added and vectors are drawn on the map, this new cycle will have one vector in common with the first cycle, but the direction of all the vectors around the center of the map polygon representing this cycle will be just opposite from that of the vectors in the first cycle. In fact, the vectors of any map cycle which has one edge in common with any other given cycle will point in the opposite direction with respect to that cycle. This means that all of the polygons in the map of a given flexagon will be oriented; the sense of the orientation may be changed by turning the flexagon over, since in so doing all vectors are reversed.
The reason for the reversed pat structure of a subpat with respect to its large pat can now be explained. Consider the history of a proper subpat of a proper flexagon. The pat structure of this subpat will remain unchanged throughout the flexing operation (assuming the flexagon flexes left) provided it is in the left pat and provided it is below thumbhole 1, which has a hinge in the ``1'' position. This is because a flex moves all of the subpats which are below thumbhole 1 from the left pat to the right pat, unchanged in any way (i.e. uninverted). However, if this subpat is on the top of the left pat, and the flexagon is flexed, the subpat will remain in the left pat but will be inverted. A rotation and flex will reinvert it and place subpats on top of it, leaving it undisturbed for flexes thereafter. However, if we decide not to rotate, but to flex along a new cycle, this subpat alone will remain in the left hand pat. As the flexagon must always flex left (we built it that way), the first flexing operation will open up the first thumbhole to a side, , the last side up being (a) if the flexing was proceeding in an ascending order around the map (see figure 8.2a). For instance, in an order 6 tetraflexagon as shown in figure 8.2b, if we flex from 1 to 2 to 3 to 4 to 1, and then decide to change over to a new cycle, we must flex next to side 6. Although the numbering of the map is still counterclockwise, the flexing vectors have changed direction, and the flexing must proceed against the numbering. In order for the side following side (a) to be side , the thumbhole must be the lowest thumbhole in the subpat containing the new cycle, for that subpat will be inverted, making the thumbhole the top most one when the subpat is left along in the left pat. Similarly, in flexing about the second cycle (assuming there are no other cycles attached to the second one) will follow and will in turn be followed by , and so on until is reached. Since side used the first thumbhole in the subpat, sides through must use the others in order, and when the subpat constant order is inverted by the subpat's incorporation into the large pat, will be the side nearest the top. Since each thumbhole in a subpat can be associated with a single leaf, the thumbhole order becomes reversed also. Since the basic number sequence must increase consecutively when read down the pat, the pat structure for the subpat must be inverted with respect to the large pat.
Since we are on the subject of flexing operation, let us consider flexing operations other than the flex; i.e., the tubulations. For all proper flexagons, the flexes remove all but leaves respectively from the left pat and deposit them from the right pat; As has been stated before, a tubulation acts like a flex. For instance, in a tetraflexagon of order 3 (see figure 8.3a) which has a tubulation from 1 to 3, we can 1 flex from face to face and when we tubulate, we can cut the hinge and lay the flexagon out in the form of a straight strip of squares with one on the top and three on the bottom. This, then, is face (see figure 8.3b). When we want to flex from face back to , we fold the three's so that they face each other and tape the cut hinge back together. The flexagon will now open up to side 2. We should notice, however, that this process of turning the tubulation in side out has also exchanged the position of the two pats of a unit with respect to each other. This is equivalent to a rotation so in this operation, we have both flexed and rotated. | s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964358570.48/warc/CC-MAIN-20211128164634-20211128194634-00109.warc.gz | CC-MAIN-2021-49 | 6,066 | 4 |
https://www.coursehero.com/file/p2p5261/Suppose-you-are-trying-to-get-a-ticket-for-the-next-home-football-game-but/ | math | 10Figure B Suppose the following figure represents the market for gasoline. Use this figure to answer the following 3 questions. 40. (1 point) This market will have a predicted equilibrium price of _____ for a gallon of gasoline and a predicted equilibrium sales of ______. 12345678910111213140102030405060708090100110120130140150Price in U.S. dollarsMarket SupplyMarket DemandQuantity in millions of gallons
41. (2 points) Which of the following will happen if this market has an advertised price of $3 per gallon?
012345678910111213140102030405060708090100110120130140150Price in U.S. dollarsMarket SupplyMarket DemandQuantity in millions of gallons | s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780057973.90/warc/CC-MAIN-20210926205414-20210926235414-00494.warc.gz | CC-MAIN-2021-39 | 651 | 3 |
https://goleansixsigma.com/six-sigma-3-4-dpmo-visualized-infographic/ | math | The following is a transcript of the infographic above:
A Six Sigma process has a 99.99966% defect-free rate.
This is equivalent to 3.4 DPMO (defects per million opportunities), or a single defect for every 294,000 units. How small does this look? The chart illustrates 1 defect in 294,000 units with powers of magnification. | s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178376206.84/warc/CC-MAIN-20210307074942-20210307104942-00436.warc.gz | CC-MAIN-2021-10 | 325 | 3 |
https://www.tonestack.net/articles/speaker-building/frequency-response-of-speaker-cabinet-on-rear-axis.html | math | Frequency response of a speaker cabinet on the rear axis
Last edited: April 25, 2018
Approximation of the frequency response of a speaker cabinet on the rear axis with a first-order low-pass filter.
In Rear Wall Reflection Simulator and Room Boundary Simulator I've used a first-order low-pass filter to calculate the frequency response behind the speaker cabinet. The cutoff frequency of the low-pass filter is shifted according to the baffle width. Of course, there is an obvious question: what is the validity of this simple calculation?
So I compared my rear-axis frequency response calculations with some measurements. These rear response graphs are normalized to the (front) on-axis response (in other words you can see the difference between the on-axis response and the rear radiation in dB).
Before I show the results I had to make some additional remarks:
- In the far field the frequency response of a speaker behind the cabinet varies according to the angle of the measurement axis.
- In the near field the exact frequency response behind the speaker cabinet depends on both the distance of the measurement point from the cabinet and both the angle of the measurement axis.
- In the far field the minimum amount of rear radiation (where the frequency response has the steepest slope) is on the 150-degree axis and not on the 180 degree rear axis. This can be seen on the polar graphs of speaker cabinets.
The first measured curve is exported from the polar charts of a pro PA speaker (JBL AC2212-95). The speaker has a 12" woofer and the width of the cabinet is 355 mm. Unfortunately, there is no measured data below 200 Hz.
The second one is an impulse response measurement of a small, 9 cm wide and 16 cm tall "multimedia" speaker. I've set the gate time to 8 msec, and the microphone distance from the baffle is 45 cm. (In the impulse response the first 8 msec is reflection free, this gives a 125 Hz low frequency limit.)
As can be seen on the graphs the first-order low-pass filter approximation gives acceptable results. The maximum error is +- 2 dB between 0 dB and -15 dB, and only becomes larger where the response falls below -15 dB. The cutoff frequency of the low-pass filter can be shifted down or up according to the baffle width. If we need a more accurate calculation, then the geometric theory of diffraction, or modeling true wave propagation is a better choice.
Rear Wall Reflection Simulator
Measuring the sound radiation of speaker cabinet walls | s3://commoncrawl/crawl-data/CC-MAIN-2023-23/segments/1685224646937.1/warc/CC-MAIN-20230531150014-20230531180014-00595.warc.gz | CC-MAIN-2023-23 | 2,478 | 14 |
http://www.e-booksdirectory.com/details.php?ebook=4456 | math | Information Theory and Statistical Physics
by Neri Merhav
Publisher: arXiv 2010
Number of pages: 176
This document consists of lecture notes for a graduate course, which focuses on the relations between Information Theory and Statistical Physics. The course is aimed at EE graduate students in the area of Communications and Information Theory, as well as to graduate students in Physics who have basic background in Information Theory. Strong emphasis is given to the analogy and parallelism between Information Theory and Statistical Physics, as well as to the insights, the analysis tools and techniques that can be borrowed from Statistical Physics and 'imported' to certain problem areas in Information Theory.
Home page url
Download or read it online for free here:
by Claude Shannon
Shannon presents results previously found nowhere else, and today many professors refer to it as the best exposition on the subject of the mathematical limits on communication. It laid the modern foundations for what is now coined Information Theory.
by Raymond Yeung, S-Y Li, N Cai - Now Publishers Inc
A tutorial on the basics of the theory of network coding. It presents network coding for the transmission from a single source node, and deals with the problem under the more general circumstances when there are multiple source nodes.
Data compression is useful in some situations because 'compressed data' will save time (in reading and on transmission) and space if compared to the unencoded information it represent. In this book, we describe the decompressor first.
by Gregory J. Chaitin - World Scientific
In this mathematical autobiography, Gregory Chaitin presents a technical survey of his work and a non-technical discussion of its significance. The technical survey contains many new results, including a detailed discussion of LISP program size. | s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570986677230.18/warc/CC-MAIN-20191017222820-20191018010320-00140.warc.gz | CC-MAIN-2019-43 | 1,850 | 14 |
http://www.euclideanspace.com/maths/books.htm | math | The Princeton Companion to Mathematics - This is a big book that attempts to give a wide overview of the whole of mathematics, inevitably there are many things missing, but it gives a good insight into the history, concepts, branches, theorems and wider perspective of mathematics. It is well written and, if you are interested in maths, this is the type of book where you can open a page at random and find something interesting to read. To some extent it can be used as a reference book, although it doesn't have tables of formula for trig functions and so on, but where it is most useful is when you want to read about various topics to find out which topics are interesting and relevant to you.
Handbook of Mathematics - This is a really useful reference book where you can find formulas, definitions and descriptions of a wide range of mathematics. The book is very nicely bound with a flexible plastic cover.
Visual Complex Analysis - If you already know the basics of complex numbers but want to get an in depth understanding using an geometric and intuitive approach then this is a very good book. The book explains how to represent complex transformations such as the Möbius transformations. It also shows how complex functions can be differentiated and integrated.
Clifford Algebra to Geometric Calculus: A Unified Language for Mathematics and
Physics (Fundamental Theories of Physics). This book is intended for mathematicians
and physicists rather than programmers, it is very theoretical. It covers the
algebra and calculus of multivectors of any dimension and is not specific to 3D modelling.
Clifford Algebras and Spinors (London Mathematical Society Lecture Note S.) Pertti Lounesto. This is very complex subject matter, however there is a lot of explanations and it is not all proofs like some mathematical textbooks. The book has a lot of information about the relationship between Clifford Algebras and Hypercomplex Algebras.
Geometric Algebra for Physicists - This is intended for physicists so it soon gets onto relativity, spacetime, electrodynamcs, quantum theory, etc. However the introduction to Geometric Algebra and classical mechanics is useful.
Geometric Algebra for Computer Science: An Object-oriented Approach to Geometry. This book stresses the Geometry in Geometric Algebra, although it is still very mathematically orientated. Programmers using this book will need to have a lot of mathematical knowledge. Its good to have a Geometric Algebra book aimed at computer scientists rather than physicists. There is more information about this book here.
Where I can, I have put links to Amazon for books that are relevant to
the subject, click on the appropriate country flag to get more details
of the book or to buy it from them.
Mathematics for 3D game Programming - Includes introduction to Vectors, Matrices,
Transforms and Trigonometry. (But no euler angles or quaternions). Also includes
ray tracing and some linear & rotational physics also collision detection
(but not collision response). | s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296949025.18/warc/CC-MAIN-20230329182643-20230329212643-00141.warc.gz | CC-MAIN-2023-14 | 3,029 | 17 |
https://www.groundai.com/project/wetting-spreading-and-adsorption-on-randomly-rough-surfaces/ | math | Wetting, Spreading, and Adsorption on Randomly Rough Surfaces
The wetting properties of solid substrates with customary (i.e., macroscopic) random roughness are considered as a function of the microscopic contact angle of the wetting liquid and its partial pressure in the surrounding gas phase. Analytic expressions are derived which allow for any given lateral correlation function and height distribution of the roughness to calculate the wetting phase diagram, the adsorption isotherms, and to locate the percolation transition in the adsorbed liquid film. Most features turn out to depend only on a few key parameters of the roughness, which can be clearly identified. It is shown that a first order transition in the adsorbed film thickness, which we term ’Wenzel prewetting’, occurs generically on typical roughness topographies, but is absent on purely Gaussian roughness. It is thereby shown that even subtle deviations from Gaussian roughness characteristics may be essential for correctly predicting even qualitative aspects of wetting.
pacs:68.05.-n; 68.08.-p; 05.40.-a; 64.75.-g
While the physics of wetting and spreading on ideally smooth solid surfaces has meanwhile reached a status of mature textbook knowledge, a whole range of wetting phenomena on randomly rough substrates are still elusive. This is particularly annoying, as almost all surfaces of practical interest bear considerable roughness, be it due to weathering, wear, or on purpose as, e.g., in the case of sand-blasted surfaces. Clearly, this has substantial impact in many situations. For example, a drop of liquid deposited on a rough substrate will spread or not, depending on the morphology of the liquid film which develops in the troughs of the roughness. As it accommodates its free surface to the substrate topography, it may percolate across the sample. The drop will then gradually spread over the entire sample. On the contrary, if the film rather tends to form isolated domains, the drop will stay in place. Similarly, the redistribution of liquid within a granular pile, such as in humid soil or sand, may proceed along the grain surfaces only if the liquid wetting film on the grains forms a percolated structure. The morphology of a liquid water film deposited from humid air onto the surface of an electric isolator will strongly affect the performance of the latter, for analogous reasons.
There has been already a lot of research on the adsorption of liquids on rough surfaces [1-15], but this was concerned either with roughness amplitudes as small as the (nanometer) range of van der Waals forces (3); (5); (7); (9) or with rather artificial substrate topographies in the context of super-hydrophobicity (10); (11); (12); (13); (15), or with completely wetting liquids (zero contact angle) (1); (4); (6); (9). The most frequently encountered, customary case, however, is characterized by a finite contact angle, and a random roughness with typical length scales at least in the micron range. In the present paper, we consider surfaces which exhibit a random topography on scales large as compared to molecules, and are subject to adsorption of a liquid which forms a small but finite contact angle with the substrate material. Since we consider macroscopic roughness, we adopt the view that all interfaces are infinitely sharp on the length scale of consideration (sharp kink approximation (16)). As the typical length scales considered here are still small as compared to the capillary length of the liquid (2.7 mm for water), gravity will be neglected as regards its effect on the liquid surface morphologies to be described. As opposed to earlier studies which concentrated on the macroscopic contact angle and contact line (2); (8), we will try to derive the wetting phase diagram and other characteristics connected to the adsorption of a liquid film.
The first systematic study of wetting on a randomly rough substrate at finite contact angle owes to Wenzel (17). He characterized the roughness by a single parameter, , which he defined as the ratio of the total substrate area divided by the projected area. Obviously, , and corresponds to a perfectly smooth surface. The free energy which is gained per unit area when the rough substrate is covered with a liquid is then given by , where and are the solid-liquid and solid-gas interfacial tension, respectively. If this is larger than the surface tension of the liquid, , we expect a vanishing macroscopic contact angle, because covering the substrate with liquid releases more energy than is required for the formation of a free liquid surface of the same (projected) area. More specifically, force balance at the three-phase contact line yields
for the macroscopic contact angle on the rough surface. is the microscopic contact angle according to Young and Dupré. When the microscopic contact angle is reduced to , which we will henceforth call Wenzel’s angle, vanishes, and the substrate is covered with an ’infinitely’ thick liquid film. As we will see below, however, there are imprortant ramifications which are sensitive to the kind of roughness of the substrate. Furthermore, even minute deviations from liquid-vapour coexistence, as they are omnipresent in practical situations, unveil a rather complex scenario which goes well beyond eq. (1).
Ii Presentation of the problem
We describe the topography of the rough solid substrate by , where is a vector in the plane. The (randomly varying) function is normalized such that , where the angular brackets denote averaging over the entire sample area, . It is assumed that the substrate is homogeneous and isotropic, in the sense that the statistical parameters of are the same everywhere on the sample, and independent of rotation of the sample about the normal axis of the sample.
A small amount of liquid deposited on this substrate will make an interface with the surrounding gas, which can be described by a second function, . The support of is the set , which denotes the wetted area. Continuity of the liquid surface assures that on the boundary of , i.e., at the three-phase contact line, where the solid substrate, the liquid, and the gas phase meet. This line will henceforth be denoted by .
Information on can be obtained from the total free energy functional of the system, which is given by
Minimization of yields two important properties of . First of all, the mean curvature of the liquid surface, which can be written as (18)
assumes the same value everywhere on . Second, the two surfaces described by and make the same (Young-Dupré) angle everywhere on . This reflects the local force balance at the three-phase contact line.
While surface roughness gives rise to substantial contact angle hysteresis on macroscopic scales, the microscopic contact angle, , is known to be well defined on the typical (micrometer to nanometer) scale (19); (20). Nevertheless, we should be aware that even on small scales, equilibration will take time, be it by transport through the gas phase or through an adsorbed layer of molecular thickness (16); (9) (which we disregard in the present study).
The question we shall ask is the following. Given the substrate topography, , the equilibrium microscopic contact angle, , and the mean curvature of the liquid surface, , what can we predict on the function and the shape of the wetted area, ? In particular, we shall be interested whether forms a percolated set in the plane.
Based on the observation that the amplitude of most natural roughness is much smaller than its dominant lateral length scale, we assume for the present study that
which allows for substantial simplifications. Expanding then the mean curvature according to eq. (3), we obtain to first order in
Similarly, the contact angle with the substrate yields the boundary condition
on , to first order in and . We can now immediately write down a useful identity concerning these quantities. Green’s theorem tells us that
in which denotes the length of . This equation will be the starting point of the discussion to follow.
Iii Gaussian roughness
If we want to exploit eq. (8), we have to refer to a specific roughness function, . Following the overwhelming majority of the literature on randomly rough surfaces, we will start by considering Gaussian roughness. The height distribution is then
with . Below we will make use of its polynomial expansion,
iii.1 Distribution functions
For Gaussian roughness, the joint distributions of with other stochastic quantities can be obtained in a straightforward manner from multivariate analysis. As it is well known (21); (24), the joint distribution of two quantities and is then given by
where is the inverse of the matrix and is the determinant of that matrix (21). For the joint probability of and , we find
On the side, this directly yields , from which we can conclude that roughness topographies fulfilling (4) will have .
For the joint probability of and , we obtain
The fraction of the total sample area which lies within that contour is
and the total Laplace curvature of within that area is
In order to fulfill the boundary condition, eq. (6), the vertical position of the three-phase contact line, which may be symbolically written as , will vary along about an average value, . The three-phase contact line will thus approximately follow the contour line at , with excursions towards both the outside and the inside of . These will in cases represent detours, sometimes shortcuts with respect to . As a reasonable approximation, we may thus use for the length of the three-phase contact line. Similarly, we set
with . Inserting these expressions in eq. (8), we obtain
iii.2 The phase diagram
If the adsorbed material is at liquid-vapor coexistence, the mean curvature of the free liquid surface, , vanishes everywhere on . In this case, eq. (21) is fulfilled only for a certain contact angle,
Note that is independent of . This at first glance puzzling result has its origin in a peculiar property of Gaussian roughness, namely the statistical independence of and (21); (26). In other words, the probability of finding a certain slope at a given level, , is independent of . A von Neumann boundary condition such as eq. (6) can thus be fulfilled equally well at all levels of Gaussian roughness. It is therefore not surprising that no particular value of is singled out here.
It is instructive to compare with . For Wenzel’s parameter , we have
and therefore . For we obtain, from eq. (22), . Since , we see that . In other words, if the liquid does not wet the substrate well enough to fulfill the Wenzel condition, is may nevertheless well intrude the roughness topography and thus form a wetting layer. This is indicated in Fig. 1, which shows the phase diagram of wetting on a surface with Gaussian roughness. States corresponding to liquid/vapour coexistence lie on the vertical axis. Along the bold solid line, which ends at , the liquid surface can ’detach’ from the rough substrate, such that an infinitely thick liquid film may form. For , the liquid/vapour interface needs the support of the spikes of the roughness, to which it is attached by virtue of the boundary condition, eq. (6).
Let us now discuss what happens as we move off coexistence. We first define the parameter
which only depends upon the substrate topography (through ) and . Inserting this into eq. (21), we obtain
as an alternative form of (21).
This is indicated by the dashed straight line in Fig. 1, which for ends at . This line cuts through the whole range of contact angles below . At higher angles, eq. (6) cannot be fulfilled and the substrate remains dry everywhere.
iii.3 Adsorption isotherms
We can now calculate the adsorption isotherms of the system, i.e., the amount of liquid adsorbed at pressures below saturation. This is important to discuss, as almost no practical situation corresponds exactly to liquid/gas coexistence. Consider, for instance, the substrate to be located at a height above a liquid reservoir with which it can exchange material. is then given by the balance with the hydrostatic pressure and reads
For the distribution of water within a soil or granular pile at height above the water table, we find that grows to about nm as increases to m. Hence the typical curvatures to expect are of the right size for our considerations up to several meters above the water table.
A more general way to look at this situation is to consider the vapour pressure, which is reduced at finite height above the liquid reservior, as well due to gravity. The curvature is then given by the Kelvin equation,
where is the partial pressure of the adsorbed liquid in the sorrounding gas phase, is its saturated vapor pressure, its molecular volume, and is Boltzmann’s constant.
From eq. (28), with the abbreviation , we can express the adsorption isotherms in terms of as
We would, however, like to know not the position of the liquid surface, , but the total volume of adsorbed liquid. The latter can be easily expressed as
The volume at percolation, i.e. at , is . Combining eqs. (29) and (30), we can directly plot the adsorption isotherms, which are displayed in Fig. 2 for three different values of . If , remains zero for all , and jumps to infinity at .
It is important here to appreciate that the infinite adsorption one obtains at coexistence has two different meanings for contact angles above or below . While for , the liquid can detach completely from the substrate forming a bulk liquid phase, the liquid surface remains in contact with the rough substrate for . The fact that even then the adsorption isotherms tend to infinity at coexistence owes to the infinite support of the Gaussian distribution, eq. (9). We will see below that this is a peculiarity of Gaussian roughness, and not a generic feature of practically encountered roughness topographies.
Iv Non-Gaussian roughness
As we have seen so far, it is worthwhile to study non-Gaussian roughness models as well. In fact, it has been shown that many real surfaces are distinctly non-Gaussian (27); (28); (29); (30), such that the freedom in adjusting the correlation function is not sufficient to describe a relevantly large class of surfaces. It seems to be widely believed that the correlation function together with the height distribution of the topography are sufficient to characterize all physically relevant properties of a surface. Most authors even seem to believe that only the first four moments of the height distribution are relevant (including skewness and kurtosis) (27); (28); (29); (31). In what follows, we will introduce a simple roughness model which is general enough to describe roughness profiles with any lateral correlation function and height distribution, but is still accessible to the analysis given above. As a consequence, we will be able to derive, by purely analytic methods, quite general predictions about wetting, adsorption, and liquid percolation on a rough surface, which can be quantitatively applied to experimental data.
Let be a Gaussian random function, much like as discussed above, but with dimensionless codomain and unity root mean square. Hence its height distribution is
and the correlation function,
We then set
where has the dimension of a length and is a monotone, two times differentiable function. In this case the inverse of , , exists, and we have
where the prime indicates the derivative with respect to the argument.
can be directly determined from experimental topography data. If the distribution has been measured, we can derive by means of the simple formula
Note that this allows to represent any height distribution function . The correlation function of , and thereby the set of coefficients , is obtained from the data as . Fig. 3 shows a sketch of a typical . While the support of is the whole axis, the codomain is bound, because neither will there be any material outside the original (unworn) surface, nor will there be infinitely deep troughs.
Since in eq. (33) we have done nothing but distorting the assignment of vertical positions to the plane, contour lines and their enclosed areas will change in level according to , but their topolgical properties, including percolation, will remain unchanged. We can therefore directly write down the contour length with help of the new quantities,
For the joint probability of and , we obtain
where the prime now denotes the derivative with respect to the argument. The Laplace curvature is given by , which leads to intimidatingly clumsy expressions when inserted into multivariate analysis. We therefore consider here the important case when is small, such that only the second term in contributes. This is the case if
We then have
with . Now we are in shape to express the Laplace curvature inside the wetted area. In complete analogy to the derivation above, we find
At coexistence, we have again
In analogy to the above discussion, we define the parameter
iv.1 The phase diagram
The film thickness at coexistence can be derived from the zeros of , of which there are either two or none. In the latter case, the contact angle (and thereby ) is too large for forming a liquid surface between the spikes and troughs which complies with the boundary condition, eq. (6). If, however, intersects the -axis, the slope of the zeros decides upon their stability. This can be seen by appreciating that may be interpreted as a deviation from the force balance, eq. (41), as required by eq. (6). For the left zero, which is marked by an open circle in the figure, a displacement of the three-phase contact line would give rise to an imbalance of wetting forces driving it further away from the zero. The opposite is true for the right zero, marked by the closed circle. The latter is therefore stable and thus corresponds to the adsorbed film thickness which will develop. The film will be percolated if this zero lies to the right of , which corresponds to the mid-plane of (cf. Fig. 3).
If we now again consider the system off coexistence, we have
as the condition for , where
A graphical solution of eq. (43) is sketched in Fig. 5. Again, the closed circle indicates the stable solution. The liquid film will be percolated if this point lies to the right of the dashed line at , but form isolated patches otherwise. From eq. (43), we see that percolation occurs if
which represents again a straight line in the phase diagram as depicted in Fig. 6. For Gaussian reoughness, we have , , and . It is readily checked that this leads again to eq. (26) instead of (LABEL:Eq:PercolationNonGaus), and (24) instead of (42).
As in the case of Gaussian roughness, generically lies below . This can be seen from calculating
which follows from (37). On the other hand,
Since, again, , it is clear that whenever lies close to (which it typically will), we have as for the Gaussian case (cf. Fig. 6).
Inspection of Fig. 5 shows that the two points of intersection, which are marked by the closed and open circles, will merge when the dashed and solid curves touch each other in a single point. This occurs at a certain curvature of the liquid surface. For , there is no liquid adsorbed, and the substrate is dry. As is reached, the average position of the liquid surface, , jumps discontinuously to the value given by the point of contact of the two curves. As is further reduced, increases until at coexistence it reaches a value corresponding to the right zero of . Because of the phenomenological similarity of the jump in adsorbed film thickness to the prewetting transition encountered in standard wetting scenarios on flat substrates (16), we hereby propose to term this transition ’Wenzel prewetting’. When the microscopic contact angle is varied, a ’Wenzel prewetting line’ results, which is shown in Fig. 6 as the solid curve. As in the usual prewetting scenario, this line ends in a critical end point, when the solid and dashed curves in Fig. 5 intersect in only a single point. It is readily appreciated from the construction sketched in Figs. 4 and 5, however, that this can occur only for , and thus outside the physically accessible parameter range. In principle, the Wenzel prewetting line may intersect the percolation line. The latter then follows the prewetting line down to .
Let us discuss how the position of the liquid surface varies along liquid/vapour coexistence as is gradually decreased from above . This can be directly read off Fig. 4, by inverting for , and is sketched in Fig. 7. The liquid film first appears through a discontinuous jump as crosses the Wenzel prewetting line. As , the liquid surface configuration which is bound to the surface topography through eq. (6) becomes metastablee (dashed curve), and the global minimum of the total free energy corresponds to the ’detached’ liquid surface, or bulk liquid adsorption (bold line in Fig. 7).
It is tempting to try to calculate the macroscopic contact angle, , along the coexistence line for . In that range, the fraction of the sample is covered with liquid, while the remaining fraction, , still exposes the uncovered rough substrate. The liquid surface energy of the areas covered with liquid is , where is the total liquid surface area over . With the help of (46) we readily obtain
Unfortunately, there is no straightforward way to calculate . We thus content ourselves here with an upper bound for , which is obtained by setting in the above expression. Qualitatively, we can nevertheless conclude that since the jump at the prewetting line will directly enter in the lower boundary of the integral, it is clear that this jump will as well be visible in . This is in contrast to, e.g., first order wetting, where a jump in film thickness is accompanied by a continuous variation in the contact angle (16). We mention again that may be subject to significant contact angle hysteresis (2) unless long equilibration times are taken into account.
iv.2 Adsorption isotherms
It is finally instructive to discuss the qualitative shape of the adsorption isotherms in this scenario, which are sketched in Fig. 8. The curves, which are meant to correspond to different values of , follow what one would expect for the characteristic shown in Fig. 3. The jump from zero film thickness to a finite value is generic and occurs for all contact angles. As is increased, the height of the jump increases slightly, following the curvature of the maximum of . At the same time, the maximum film thickness (reached at coexistence) decreases, until it finally comes below the percolation threshold when . When , has no zero anymore, and the substrate remains dry up to coexistence.
A few more words concerning the shape of the function are in order. If were Gaussian, would be just of the form . In that case, would in Fig. 4 be represented by a horizontal line above the abscissa. The solid curve in Fig. 5 would then be a Gaussian, and the adsorption isotherms would of course be the same as in Fig. 2. However, the fact that any real roughness is bounded, as there are neither infinitely high spikes nor infinitely deep troughs, entails the boundedness of the codomain of , in contrast to the infinite codomain of . As an immediate consequence, the derivative of must finally diverge at the boundaries of its (finite!) support, which necessarily leads to bending down onto the dashed line below the abscissa in Fig. 4. This leads not only naturally to a finite at coexistence (, cf. Fig. 5), but also to the Wenzel prewetting jump in farther away from coexistence, when the dashed curve in Fig. 5 just touches the solid curve. This reveals that the shape of the adsorption isotherms we derived for Gaussian roughness above is qualitatively different from what should be expected for real roughness. In fact, it misses the whole prewetting scenario, which turned out above to be a generic feature. Once again, Gaussian roughness reveals itself as a special case, which is mathematically convenient but may be misleading when it comes to making quantitative predictions.
In conclusion, an analytic theory was presented which allows to calculate the wetting phase diagram, adsorption isotherms, and percolation threshold of the adsorbed liquid film for isotropic, randomly rough substrates with arbitrary lateral correlation function and height distribution. The results are found to depend only upon a few key parameters, which can be clearly identified and derived from experimental sample profile data. We have seen that wetting ’physical’ roughness displays a number of features which are not present for exactly Gaussian roughness, such as a prewetting transition occurring well before the Wenzel angle is reached. This could be traced down to subtle properties of Gaussian random functions, which reveal their unphysical nature only at second glance.
Since for most quantities of interest we could come up with closed analytic expressions, these results may be particularly useful for practical applications. The range of validity of the present theory extends from a few nanomeres up to roughly a millimeter, well below the capillary length of the liquid. The field of such applications is vast, including almost all situations in which a liquid comes into contact with a naturally rough surface. In particular, ramifications of wetting phase transitions, which inherently involve small contact angles, are to be expected and can now be accounted for in closed form.
Given the potential relevance of the results presented here, it will be worthwhile to work on relaxing the five major approximations we have used:
We have assumed the substrate to be chemically homogeneous.
We have assumed the curvature of the roughness characteristic to be small; eq. (38).
We have assumed isotropy of the roughness; eq. (11).
The last two are probably the simplest to tackle, while the first one appears as the most difficult to overcome. It should finally be noted that in experiments, one has to reckon with quite long relaxation times for the measured quantities, because at all levels of the roughness there are saddle points (21); (23), which act as effective pinning sites for . Equilibration will nevertheless proceed within manageable time, either via the vapour phase or via the molecularly thin adsorbed film (9).
Inspiring discussions with Daniel Tartakovsky, Siegfried Dietrich, Martin Brinkmann, Jürgen Vollmer, Sabine Klapp, and Daniela Fliegner are gratefully acknowledged. The author furthermore acknowledges generous support form BP International.
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- V. Bakolas, Wear 254 (2003) 546. | s3://commoncrawl/crawl-data/CC-MAIN-2019-13/segments/1552912202484.31/warc/CC-MAIN-20190321030925-20190321052925-00163.warc.gz | CC-MAIN-2019-13 | 28,542 | 121 |
https://my.nctm.org/blogs/nicole-hall/2019/04/10/meet-the-nctm-board-of-directors-president-elect-t?CommunityKey=0a10e770-ceb6-4514-ac1c-413a77367143&tab= | math | An expanded Q&A with NCTM President-Elect Trena Wilkerson:
What drove you to become an educator?
I loved mathematics, but I guess many say that! I also found that I really liked teaching it, making connections, and helping others to make those connections. Finding ways to help students understand (especially those who seemed to struggle with certain ideas in mathematics) is intriguing to me. I taught high school mathematics for eighteen years and found it exciting to work with students across algebra, geometry, calculus, and more. Later I became interested in teacher education and working with preservice teachers, so that led to where I am today, working with our current and future teachers of mathematics. I am always learning from them!
What are you most passionate about as a mathematics educator?
TW: Helping others see the value of mathematics and to see how it connects to them. I love mathematics and find it amazing and exciting how it all fits, connects! I want to help others to see and experience those connections—to be empowered through mathematics.
What is one of your favorite articles from earlier issues?
TW: There are so many, not the least of which is the Rules That Expire series that appeared over the years in each of the three grade-band journals! But most recently, I have used the MTMS Focus Issue on Productive Struggle (Jan./Feb. 2018) in professional development sessions with teachers across grades 5–12 over the past year. They enjoyed the problems, extending to various grade levels, making connections, exploring considerations for social justice, and examining more closely how to support learners in productive struggle for deep understanding of mathematics. I learned so much from the experienced authors who wrote those articles!
What mathematical concept or idea stands out to you?
TW: What stands out to me most is more of a process than a specific concept. I particularly like looking at mathematical connections, those within and across mathematics concepts, but also in the real world and real life. My students, friends, and colleagues often laugh at me when I have a “math encounter.” I just have to point it out and talk about it! It is so fun when they then share with me their mathematical encounters as well. | s3://commoncrawl/crawl-data/CC-MAIN-2020-10/segments/1581875145818.81/warc/CC-MAIN-20200223154628-20200223184628-00507.warc.gz | CC-MAIN-2020-10 | 2,272 | 9 |
http://thisweeksdiscoveries.blogspot.com/2016/05/colouring-numbers-takes-up-200-terabytes.html | math | Mathematical proofs can be simple or extremely difficult. But they’ve got one thing in common; they are at least a little elegant. Or just consist of 200 terabytes of data.
Two hundred terabytes look like a ridiculous amount of data, and it is. It is enough to fill the hard drives of 441 laptops and the compressed version of the data only takes already 30.000 hours to download, that’s about three and a half years. The supercomputer that ran the calculations needed 2 days, with eight hundred processors running at the same time. Nobody is, of course, going to read the proof, since that is impossible. This gigantic thing also has the world record. The proof took it from another mathematical proof that was ‘just’ thirteen gigabytes big.
|The first 7824 numbers with their valid colourings, |
the white squares can be either colour
But for what could you possibly need so much data? Well, the problem is called the Boolean Pythagorean triples problem. It asks the question if it’s possible to give each number a colour; red or blue, in such a way that there aren’t three numbers that fit into Pythagoras’ equation; a2+b2=c2. So when 3 and 5 are blue, 4 has to be red, because 32+42=52=9+16=25. As it turns out, to the number 7824, numbers can be coloured in a ‘valid’ way, but after 7824, not anymore. Up to 7824, there are 102,300 possible colour combinations, that's a 1 with 2300 zeroes. Fortunately, Oliver Kullmann and Victor Marek, the mathematician who found the proof, could slim the amount of combinations the supercomputer had to check to just under a trillion.
Where does maths end?
After this proof, a new question arose. Is this really still maths? A lot of mathematicians think otherwise. Because nobody knows why it’s possible to create double-coloured triplets under 7824, but not above. Nor does anyone know what’s special about the number 7825 that it ruins everything. Terence Tao proved the former world record problem, which needed thirteen gigabytes of data to proof, in the ‘old-fashioned’ way, so by reasoning and thinking logically, a year after the computer proved it. Many mathematicians consider that a much more satisfying way and thus the search for the proof of the Boolean Pythagorean triples problem isn’t over yet.
Click here to read more about mathmatics. | s3://commoncrawl/crawl-data/CC-MAIN-2019-18/segments/1555578532882.36/warc/CC-MAIN-20190421195929-20190421221929-00330.warc.gz | CC-MAIN-2019-18 | 2,323 | 8 |
https://www.hackmath.net/en/math-problem/6080 | math | How long have we trained on the pitch when we know that the warm-up took 10 minutes, we trained passes for one-third of the time and we played football half the time?
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