Questions tagged [applications]

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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17 views

Examples of applications where submodular functions are used to promote diversity?

I have often seen the terms submodular functions / submodular function optimization and promoting diversity thrown together. What are examples of standard submodular functions that are used to promote ...
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Prove the application $\Phi$ is bijective.

I am working on a problem set and I need some assistance with an exercise. The exercise goes as follows: Let $A$ be a ring and $I \unlhd A$ an ideal. Given the natural projection $\pi : A \rightarrow ...
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Computer project on GPS using linear algebra

I am searching for a computer project that I once found it online but unfortunately didn't save it. The project lies within the domain of numerical linear algebra and its topic is about Global ...
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51 views

Application of Graph Theory in Electrical Circuits

I've been learning about electrical circuits, and I can see how Graph Theory naturally lends itself well to problems with circuits. I was wondering what some examples of applications of Graph Theory ...
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32 views

What is the use of the theorem on expection on a function of a random variable?

If $X$ is a random variable, then the expectation of $X$ is defined as $$E[X] = \sum_{x} x p_{X}(x)$$ Where $p_X$ is a pmf on $X$. If $g$ is a real valued function then I learn the following theorem $$...
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Understanding Hill Plot of the Genetic Toggle Switch Model

I am currently conducting research on the genetic toggle switch (Gardner et al., 2000.), as simple genetic circuit featuring two mutually repressing promoters. I am trying to fully understand a plot (...
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2answers
46 views

Line $y = mx$ through the origin that divides the area between the parabola $y = x-x^2$ and the x axis into two equal regions.

There is a line $y = mx$ through the origin that divides the area between the parabola $y = x-x^2$ and the x axis into two equal regions. Find m. My solution: When I compute my answer, I get $1-\frac{...
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69 views

Modeling a Heat PDE

I am trying to answer the following question... Consider a wall made of brick $10$ centimeters thick, which separates a room in a house from the outside. The room is kept at $20$ degrees. Initially ...
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72 views

Analysis, Matrix Exponential, Infimum and Limit

I was working in this problem for a long time and I didn't have success. Someone could help me, please? The problem: Let $f: \mathbb{R}^{n^2} \times \mathbb{Z}^{n} \longrightarrow \mathbb{R}$ defined ...
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2answers
73 views

Can we clarify this “accumulated money flow” application of integration?

I read about this model/application in Calculus with Applications, 11th Edition by Lial, Greenwell, and Ritchey (example), where if you have a function $f(t)$ that models some revenue stream, the rate ...
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38 views

Ray tracing in nonuniform media; did I write this second order differential equation as two first order differential equations correctly?

Both answers to the Physics SE question Ray tracing in a inhomogeneous media* arrive at some form of the equation below and one links to Florian Bociort's dissertation Imaging properties of gradient-...
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Cryptography problem:Calculate the values of A and B corresponding to an LCG that generated the sequence mod 19 starting with the numbers (3,10,11).

I don't know if this is the right place to ask this question (although the question is purely mathematical), but let's go anyway. I'm a little confused, from what I understand in the image formula $$ \...
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171 views

Uses for eigenvalues of unitary matrices

The eigenvalues of a unitary matrix lie on the unit circle. What are some applications in which the eigenvalue distribution of the matrix is important? For instance, that the eigenvalues are clustered,...
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Least area of rectangle into which two squares, sum of whose area is $1$, are placed so that their interior points don't overlap

For any $2$ squares, the sum of whose area is $1$, a rectangle of area $A$ exists into which the squares can be placed without overlapping of interior points (Assume that the square are to be placed ...
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Changes of percents in the result of a poll will be very small after one thousand of polls submitted?

I saw an admin of an Instagram Channel created a poll with two option. and he said the following after a while: Statistics is interesting, َafter one thousands of people voted, the results in percent ...
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92 views

What uses does the product log function have?

I've been looking into complex functions and how to plot them in programing languages like Python and JavaScript. I still am wondering how to do stuff with complex functions like in my previous ...
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What are some applications of projective Fraïssé limits?

I am looking for some applications of projective Fraïssé limits. For example are they related to a theorem in set theory or topology? Also is there any modified version for them? (like the version of ...
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Applications of Hamiltonian Decompositions

A Hamiltonian decomposition of a given graph is a partition of the edges of the graph into Hamiltonian cycles. What are some applications of Hamiltonian decompositions? In what ways are they important ...
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56 views

Could there be exact solutions to the Lane-Emden equation for real n≥0 other than 0, 1, or 5?

This Astronomy SE answer says With a constant $k$ and the polytrop index $n$. This is a result of the solutions of the Lane-Emden equation $$\frac{1}{\xi^2} \frac{\mathrm{d}}{\mathrm{d}\xi} \left(\xi^...
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Understanding representation of Cauchy stress tensor for the simplest plane steady flow

Consider the simple problem of a flow between two plates, one at $x_2=0$ and one at $x_2=h$ with the bottom one held stationary and the top plate moving in the $x_1$ direction with velocity $V$. Also, ...
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How to find the second focus of an ellipse in a cartesian coordinate system

For a university project, I'm creating a to scale (using real values of distance, mass etc) simulation of the solar system using Python with the aim of demonstrating Kepler's Laws. Currently, I have a ...
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34 views

Modelling interest with differential equations (IVP)

Problem : you set a bank account, with initial value k, the bank will pay you continuous interest of 12% per year. a) write an initial value problem for your account balance y(t) after t years Sol: $$...
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1answer
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Show that $\prod_{i=1}^{n}\text{Aut}(G_i)\to \text{Aut}\Big(\prod_{i=1}^{n}G_i\Big)$ is injective

Let $G_1,...,G_n$ be groups. Show that there exist an injective morphism $\xi:$$\prod_{i=1}^{n}\text{Aut}(G_i)\to \text{Aut}\Big(\prod_{i=1}^{n}G_i\Big)$. I would like to know if my proof holds, ...
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1st order linear differential equation application in electric circuits

I have the following 1st order linear differential equation: $$L\frac{dI}{dt}+RI=E_0\sin(wt).$$ where $L$, $R$ and $E_0$ are constants. The goal here is to discuss the case when $t$ increases ...
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589 views

St. Basil's cathedral, Moscow steeple shape

Onion-shaped dome cathedral architecture seen here appears to include in its lower part a geometry of positive, and in upper (steeple) part negative Gauss curvature. The corresponding elliptic and ...
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Problem from Plane Trigonometry (S.L. Loney) [duplicate]

Q. A square tower stands upon a horizontal plane. From a point in this plane, from which three of its upper corners are visible, their angular elevations are respectively are 45 ∘ ,60 ∘ , and 45 ∘. ...
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What is the fixed “p” percentage I should increase my investments every month to reach a target

I have been learning about SIP. The gist of it is that you invest on regular basis like monthly or quarterly. The basic example is that you invest 100 every month so it looks like. ...
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1answer
31 views

Mathematical expression for physical forces in pendulum ODE

A 16 lb weight is suspended from a spring having a spring constant of 5 lb/ft. Assume that an external force given by 24 sin (10t) and a damping force with damping constant 4, are acting on the spring....
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40 views

How to read the surface plots?

I was reading this paper and I could not understand this figure. How do you read these kind of graphs? How to interpret the twists and folds; it's not like heat maps that are intuitive. Any help ...
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Application of billiards

Studying billiards is a difficult problem in general, even in pretty simple cases it has plenty of interesting properties. I would like to understand what can be applications (mathematically or in ...
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Why the groups of an isosceles triangle and molecule $H_2O$ are different? [closed]

Why the groups of an isosceles triangle and molecule $H_2O$ are different?.Why it both are not the $C_2.$ It seems like it both have all the same symmetry,but suddenly different groups.
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Line Tangent to Two Non-Equal Circles on a 2D Plane

If I have two circles, say Circle A is on the origin of a cartesian plane and Circle B is placed at a point with a known horizontal and vertical distance from the origin. The diameters of both circles ...
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1answer
38 views

Ranking objects using least squares

I need to develop an application to automatically rank objects. This is the use case: I have a set of objects, all of which have the same set of properties. For example, a set of cars, all of which ...
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1answer
38 views

Stokes flow for a falling sphere

I am following this document on Stokes flow. It is stated that "if we have a falling sphere, doubling the velocity will double $\sigma_{ij} (= -p\delta_{ij} + 2\mu e_{ij})$", but I am ...
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1answer
73 views

Compound interest - relationship between $\frac{r}{n}$ and $r$?

The compound interest formula $A=P\left(1+\frac{r}{n}\right)^{nt}$ is usually used in examples where you are given a nominal annual rate and then calculate the accrued amount, where $\frac{r}{n}$ is ...
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1answer
82 views

What is the real life application of group theory other than coding and cryptography [duplicate]

What is the real life application of group theory other than coding and cryptography if any and how can one apply group theory to them.
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Applications for vector spaces without inner product.

Vector spaces may not be equipped with an inner product (for instance this question). Mathematically, one can study such spaces in its own right, but I was just wondering: is there a scientific ...
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4answers
206 views

Favorite application of the fact that disjoint compact sets are distant (i.e. $A$ compact, $B$ closed, $A \cap B = \varnothing\implies d(A,B)>0$)?

This problem is quite popular (A and B disjoint, A compact, and B closed implies there is positive distance between both sets has currently 70 upvotes, not to mention the endless horde of repeats that ...
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1answer
40 views

Elementary group theory applications [duplicate]

I'm taking an algebraic structures class and we are doing a lot of work involving group theory. Specifically, dihedral groups, abelian groups, isomorphisms, cyclic groups, and others. I'm finding it ...
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1answer
34 views

Hyperbolastic rate equation of type II already has its initial condition in it?

I'm modelling some real-world gene expression data with various growth models including linear, exponential, and Verhulst growth but not all of the genes are showing these forms of time-dependence. ...
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32 views

Real world applications of Schanuel's Conjecture

I'm doing my senior capstone on Schanuel's conjecture and in my final presentation I wanted to discuss why this conjecture is important. I have found tons of applications in field theory and proving ...
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24 views

The relationship between scattering width and radar cross section

I have a question regarding Knott's book on radar cross section (RCS). Specifically, I am interested in the relationship between the 3D RCS, $\sigma_{3D}$, and the scattering width (2D RCS), $\sigma_{...
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43 views

Understanding Klein bottle filters

I'm very new to topology, however, I am working on a Convolutional Neural Network, and I stumbled upon topological neural networks. There are very few papers on this topic, but from what I've read, ...
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2answers
97 views

What are the oldest mathematics that have no applications to other fields?

In popular culture, mathematics are often split between applied mathematics, which provide tools for science and engineering, and pure mathematics, that are somewhat useless. Although this distinction ...
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Show that $K=\{T\in\mathcal{L}(V,W): T\ \text{not injective}\}$ is not a subspace of $\mathcal{L}(V,W)$

Suppose $V$ and $W$ are finite-dimensional with $2\le\dim(V)\le\dim(W)$. Show that $K=\{T\in\mathcal{L}(V,W): T\ \text{not injective}\}$ is not a subspace of $\mathcal{L}(V,W)$. My attempt is to pass ...
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24 views

Drawing Venn diagram to describe a real life process (problem with nonexistent intersection)

I'm going to ask my question by making a visual analogy. Say, I need to create (and describe) a Venn diagram to match a real life process. Analogy (pic.): with time there are more and more Black Cars ...
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1answer
28 views

Do Dyck Words or Dyck Paths Have Manifestations in Nature?

Working with the Dyck language of well-balanced strings of parentheses, I am led to wonder what, if any, phenomena the concept relates to in the natural world - in the same sense that Fibonacci ...
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29 views

Interpretation of an ODE

I'm currently writing a thesis on fraction calculus. I've defined fractional derivatives and fractional diferential equation. When solving one I've arrived at this ODE: $$y'(x)(a-x)+3y(x)=\frac{y(x)}{...
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2answers
42 views

Volume by disk perpendicular to $x$ axis [closed]

Find the volume of the solid formed when region enclosed by $y=x^{1/2},\quad y=6-x$ and $y=0$ revolves around $x$ axis. Can I use the equation for finding solids by splitting the solid into 2 parts? ...
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1answer
25 views

Finding the formula for T from Newton's Law of Cooling

I think I got a wrong answer because I skipped a particular step which seemed optional. I'm still not too sure what happened though and would appreciate your help... Background: Newton’s law of ...

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