# Tagged Questions

The [application] tag is meant for questions about applications of mathematical concepts and theorems to a more practical use (e.g. real world usage, less-abstract mathematics, etc.)

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### Applications of Topological Complexity of configuration space

I'm starting to work on Topological Complexity of configuration spaces . Articles say that it has applications in robotic and control theory . My questions are : 1) How Topological complexity can help ...
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### A problem of Tangents on curvers

Let $X=\phi(x,y)$, $Y=\psi(x,y)$ define a transformation of the $xy$-plane to $XY$-plane. Suppose further, $\phi_x=\psi_y$ and $\phi_y=-\psi_x$. Then prove that the angle between the curves $F(x,y)=0$ ...
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### Critical Number real life applications

I've studying a lot Critical Number/Point and I have to give a presentation about it. I am searching real life applications to explain the concept, but it's difficult to find. Anyone here can give ...
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### The value of an investment in Canada Savings Bonds is modelled by $A(t) = A_0 e^{0.0255t}$… Rest of question below.

The value of an investment in Canada Savings Bonds is modeled by $$A(t) = A_0 e^{0.0255t}$$, where A is the amount the investment is worth after $t$ years, and $A_0$ is the initial amount invested. At ...
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### Invertible product of noninvertible morphisms

This question may be too broad. Under what conditions is a product of noninvertible morphisms invertible? Suppose that we model a finite number of different acts of observation (i.e., a thermometer ...
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### How to find (GEV) distribution parameters with optimization?

I'm currently trying to replicate this study with python. http://pages.stern.nyu.edu/~sfiglews/Docs/RND_draft7.pdf The section I'm currently working on is between p.17-20 in the study. The study ...
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### Where do you see cyclic quadrilaterals in real life?

I've just been studying cyclic quads in geometry at school and I'm thinking see seems pretty interesting, but where would I actually find these in the real world? They seem pretty useless to me...
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### Does anyone recognise this non-linear diffusion equation?

I'm doing some work on modelling cell migration, I've derived this particular form of a non-linear diffusion equation to describe the mean behaviour of a stochastic model I'm studying. I was wondering ...
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### How to find the system transfer function corresponding to a two dimensional matrix of optical transfer functions?

I would like to find the system transfer function corresponding to a two dimensional matrix of optical transfer function where: Each of the 3 times 5 = 15 interferometers produce 15 sets of ...
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### Advanced Linear Algebra vs Functional Analysis

I have a couple questions regarding Advanced Linear Algebra vs Functional Analysis. 1) Do these courses help in understanding or have applications in: Machine Learning Quantitative Finance, ...
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### Luminosity and Apparent flux

The stars in our Galaxy have luminosities ranging from $L_{\text{min}}$ to $L_{\text{max}}$. Suppose that the number of stars per unit volume with luminosities in the range of $L$, $L+dL$ is $n(L)dL$. ...
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### Polynomial Chaos with Beta Distribution - Standard Beta Random Variable, Transformation of Beta Random Variable

Background: I am dealing with a non-intrusive polynomial chaos expansion (e.g. here [Hosder,Walters;2010]). This means I want to represent an uncertain output $U(\xi)$, dependent on a vector of ...
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### Where is number theory used in programming? [closed]

I'm developing corporate software (for banks, insurance companies, hospitals and so on), and I am interested in number theory. I am a beginner in this area and I understand most of the theorems and ...
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### Application of Chain Rule for Paths

I'm a graduate student and I'm currently teaching multivariable calculus. I gave my students a question about a bug traveling along a circle of radius $200$cm in the $xy$-plane. We suppose also that ...
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### Applications of Integration - Work Done by a Variable Force

Question states: "A 20-foot chain weighting 5 pounds per foot is lying coiled on the ground. How much work is required to raise one end of the chain to a height of 20 feet so that it is fully ...
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### application of integration in graphics

Is Integration used in animation/computer graphics? If yes, then how it is used. A couple of example would be great . Thanks
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### Area bounded by$y^2=x^2(1-x^2)$

Find the area bounded by $y^2=x^2(1-x^2)$? I think in this way as the graph lies between -1 to 1 the area is 4 times of $\int x \sqrt{1-x^2} dx$ limits from 0 to 1. Am I correct?
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### Find the volume obtained by totating the area formed by $y=x$ and $y=\sqrt{x}$ about $y=1$

The questions asks us to find the volume of solid formed when the area between $y=x$ and $y=\sqrt{x}$ is rotated about the line $y=1$. I understand that a cone is formed. Now, to find the volume, I ...
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### Practical examples of tank mixing problems?

In calculus and differential equations, a standard example of word problems are mixing problems, with some number of tanks, and brine often being an output of the system. With one tank, I can imagine ...
### Does the “truncation function” $\langle a,b\rangle : \mathbb{R} \rightarrow \mathbb{R}$ have an accepted name or notation? [duplicate]
Given real numbers $a$ and $b$ satisfying $a \leq b$, define: $$\langle a,b\rangle (x) = \mathrm{min}(b,\mathrm{max}(a,x)) = \mathrm{max}(a,\mathrm{min}(b,x))$$ (These numbers are equal because \$a \...