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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4
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55 views

What mathematics topics pertain more towards applied mathematics?

I'm entering my second year of undergrad (majoring in mathematics), and I've found that I am really bad at Linear Algebra, but very good at Calculus and Differential Equations. I'm hoping to venture ...
1
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1answer
37 views

Solve this question involving temperatures?

So I am given 2 formulas: $$ \frac{dT}{dt}=-k(T_t-T_s)$$ Where $\frac{dT}{dt}$ rate at which the object's temperature is changing $T(t)$ is the temperature of the object at time $t$ $T(s)$ is the ...
3
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1answer
34 views

Applications of algebraic graph theory

What are some subtle, or non-obvious applications of algebraic graph theory? Obviously it can be used to study anything directly involving graphs (for instance, the wikipedia page mentions ...
-1
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2answers
26 views

Differential Equations applications in Computer Science

I'm writing a project on differential equations and their applications on several scientific fields (such as electrical circuits, polulation dynamics, oscillations etc) but i'm mainly interested in DE ...
1
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1answer
15 views

General equation for distance over grid with diagonals

I understand the difference between Euclidian, Manhattan and Chebyshev distances. My question is: How to calculate a distance metric from point1 to point2 on a grid including diagonals given that ...
1
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1answer
35 views

How to distribute money between people

I was thinking of the following problem: Suppose I have an agency that offers workshops to companies. There are four different "type/rank" of professionals in my agency that could give these ...
1
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1answer
25 views

Verify a scanned barcode with math

I have an id number that needs to be read off a sheet of paper with a barcode by a scanner. Most of the time this will work flawlessly but sometimes there are mistakes (like if paper is partly torn). ...
1
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0answers
29 views

How to show that a seperatrix exists for the Fisher-KPP equation

We have the Fisher-KPP equation: $\frac{\partial u}{\partial t} = \frac{\partial^2 u}{\partial x^2} + ru(1-u)$ We can reduce this to a second order ODE: $cu_{\xi} = u_{\xi\xi}+u(1-u)$ where $\xi = ...
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0answers
28 views

Who knows Krotov's Method in Optimal Control Theory

I'm finishing my PhD thesis about applications of optimal control theory in the field of energy harvesting. In the course of my PhD I dealt with different ways to compute optimal controls, and I found ...
1
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1answer
45 views

Equilibrium solutions of a differential equation and their nature

I need some help with the following the differential equation $$ \dot{x}=x^{4}-3x^{3}+2 $$ I found that the equilibrium solutions are $x \approx 1, 2.9196, -0.45982+-0.68817i$. If you someone could ...
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0answers
8 views

Indexing interactions between and withing entities

I'm trying to create/find an index to compare/order systems with multiple entities based on the diversity of the interaction between the entities. Assume you have few systems of entities that can ...
0
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1answer
25 views

Considering small perturbation determine whetherit is a stable or unstable node

This is the part of the question I do not understand. I'm given an nonlinear equation for a population, let's say $$ \dot{x}= x^{4}-3x^{3}+2 $$ So we are asked to find the equilibrium points, one is ...
2
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1answer
36 views

Application of convex functions in economy [closed]

I have read in some texts that convex functions has application in economy. I want to see some clear examples of such applications.
0
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1answer
38 views

Displacement x of a system

Displacement x of a system satisfies $$ 3\ddot{x}+8\dot{x}+5x=43+2y-7\dot{y} $$ where $y=4\cos(t)$. If $x=0=$ $\dot{x}$ at $t=0$, find $x $and describe the motion that occurs at large times. Thanks ...
1
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1answer
17 views

How does measurement error affect the standard error of regression coefficients?

How does inclusion of the measurement error in the model, as $$Y_i + \varDelta_i = bX_i + \varepsilon_i$$ affect the standard error of least square estimators $\hat{b}$ of coefficients $b$? If I ...
0
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1answer
19 views

If the tangents at

If the tangents at $P(1,1)$ on the curve $y^2 =x(2-x)^2$ meets the curve again at $Q$ then points of $Q$ is of the form $(3a/b,\, a/2b)$ so I have to find $a$ and $b$.
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0answers
20 views

Why Klein Maskit Combination Theorem is important?

I am learning basics about Kleinian Groups. Recently, I read the proof of Klein Maskit Combination Theorem. I want to know about some good applications of this tool. Please share some references.
2
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3answers
56 views

Derive the equations of motion and determine whether angular momentum is conserved

Suppose that the gravitational force is not given by the inverse-square law, and instead is $$ F_{grav}=(\frac{A}{r^{2}}+\frac{B}{r^{4}})\hat{r}, $$ where A and B are real constants. Derive the ...
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2answers
30 views

Continuous Compound

You own an antique that is currently worth 1500, and whose value increases linearly at a rate of 175 per year. If the prevailing interest rate remains constant at 5%, per year compounded continuously, ...
0
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1answer
35 views

LN word problem

measurement of a child's ability to learn is given by the function $$L(t)=\frac{ln(t+1)}{t+1}$$ where t is the child's age in years, for $0 ≤ t ≤ 5$ At what age does a child have the greatest ...
6
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0answers
62 views

Is there a polynomial $p$ such that it is bijective and $ p: \mathbb{Q}^n \rightarrow \mathbb{Q}$ for $ n>1$ ??

Let us define a polynomial $p$ defined as follow $$p: \mathbb{Q}^n \rightarrow \mathbb{Q}.$$ I acrossed this question in mind. Is there a polynomial $p$ such that it is bijective and $p: ...
1
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1answer
43 views

Finding the Zeros

A word problem gives this cost equation and asks to find the x where the average cost is minimized, to do so, I need to solve for average cost and derive it and then set it to zero and solve; $c(x) = ...
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1answer
30 views

Can anyone answer this with the steps of Assumption > Given > Formula > Solution?

The height in feet of a bottle rocket is given by the function $h(t)=160-16t^2$, where $t$ is the time in seconds. How long will it take for the rocket to return to the ground? What is the height of ...
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3answers
44 views

Modelling interest with differential equations (Interpretation)

I am having trouble interpreting the meaning of this differential equation model for interest on an account. The problem is as follows: Assume you have a bank account that grows at an annual ...
1
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1answer
24 views

Ranking event winners with a portion of total participants.

This may not be the place for this question, but its the one place I know where I'll get solid mathematical answers: I'm looking for a system that ranks event winners, but it can't require everyone ...
0
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1answer
50 views

Current applications of the central limit theorem for binomial distributions

The central limit theorem in the binomal distribution case, also known as the De Moivre–Laplace theorem was historically used to approximate the binomal distribution with the normal distribution. I ...
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2answers
51 views

Physical applications of Chebyshev's equation.

As reported by Wikipedia, Chebyshev's equation is the second order linear differential equation $$(1-x^2) {d^2 y \over d x^2} - x {d y \over d x} + p^2 y = 0 $$ where $p$ is a real constant. Has ...
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1answer
30 views

How do I calculate the gravitational force exerted by a thin ring of uniform mass M?

I'm working on a problem and can't seem to get it. Find the gravitational force exerted by a thin uniform ring of mass M and radius a on a particle of mass m lying on a line perpendicular to the ...
2
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4answers
61 views

The Significance of Linear Approximation

I want to know what makes linear approximation so important (or useful). What I am aware of in my current state of limited understanding is that linear approximation is one of the applications of a ...
1
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1answer
35 views

Probability distribution of the number of heterozygous sites

We'll consider a stretch of DNA on a chromosome and we'll be looking at specific sites that are at certain distances on from the others. The distance between any two sites is express in centiMorgan ...
0
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2answers
54 views

Why do left and right switch when direction is reversed? [closed]

If I make a left turn during a trip, it becomes a right turn on my way back. Why is this?
1
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2answers
424 views

Can any function represent something in the real world?

We know that the volume of a cube can be represented by the function: $V(x)=x^3$, where $x$ is side length. $x^2$ can represent the volume of some material that has a constant side ($1$). The function ...
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2answers
64 views

Can car traffic be managed by mathematical formula? [closed]

How car traffic is managed? Is it managed by mathematical algorithm? Or by human(operator)? If it's by operator, can it be managed mathematically? Or is it by physics? By what theories/formula? ...
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10answers
704 views

What are the most prominent uses of transfinite induction outside of set theory?

What are the most prominent uses of transfinite induction in fields of mathematics other than set theory? (Was it used in Cantor's investigations of trigonometric series?)
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2answers
78 views

The roots of $x^4+4x^3+5x^2+2x+2=0$ one root being $-1+i$ are [closed]

The roots of $x^4+4x^3+5x^2+2x+2=0$, one root being $-1+i$ are what? please solve this problem, i need the process of solution
1
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1answer
39 views

What are some Applications of Hermitian Positive Definite matrices?

I am learning about Hermitian positive definite matrices and the way that they can be decomposed with Cholesky decomposition. I have learned that these matrices deserve special attention for how often ...
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4answers
191 views

Applications of algebraic topology?

Terribly sorry if this has been asked, but I'm not about to search 382 pages of technical questions in the field. I am trying to develop a very basic understanding of what algebraic topology is ...
2
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0answers
24 views

Can I adjust linear growth of a a subpopulation to a linear decay of the general population?

I need to estimate the amount of CF patients in Poland in the next four years. I have: estimations of the Polish population for the future years a CF patients' register for the last couple of years ...
3
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1answer
60 views

Does measurability really matter?

I am studying applied math and I currently got stuck on proving that a function, which emerges in a model is measurable (Borel functon), so we can integrate it. I know, that there are examples of ...
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0answers
48 views

Optimisation Problem for Pipe Nesting

I work in a company where we are supposed to produce and send pipes using trucks to buyers. Pipes of smaller diameter can be nested inside pipes of larger diameter while sending to minimize number of ...
7
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2answers
75 views

Imaginary $\cos^{-1}$ value significance?

When I was bored in AP Psych last year, I jokingly asked myself if there was a cosine inverse of $2$. Curious about it, I tried calculating it as follows: $$ \begin{align*} \cos (x) &= 2 \\ \sin ...
3
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1answer
41 views

What languages does Zipf's law not hold for?

Despite reading on a book of mine that all languages of all times obeyed Zipf's law, the english Wikipedia article only says most. Is it correct? If so, is a counterexample known?
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0answers
28 views

Why we should study “sub-energy” function and what are its applications in mathematics?

I read some papers in optimization and I found this term "Sub-energy function" that is a new mathematical term to me. Aside from "its a large area in mathematics," why we should study it? What's its ...
5
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2answers
107 views

What's interesting in latus rectum?

I'm a maths teacher in Italian secondary school and I've been spending some time trying to construct "meaningful" problems about conic sections. I particularly like problems which focus on practical ...
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0answers
24 views

How to find an optimal solution for a missing player in a double-elimination tournament

Say that you have a double elimination tournament consisting of four teams with 2 players. Each of those teams of partners could be: (A,B), (C,D), (E,F), and (G,H), where A is B's partner, C is D's ...
2
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1answer
31 views

Finding $f-$invariant subspaces

How could you know, given a linear application $f:\mathbb R^n\to\mathbb R^n$, the $f-$invariant subspaces of arbitrary dimension? For example, let $f:\mathbb R^4\to\mathbb R^4$ with associated matrix: ...
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192 views

Physical meaning of linear ODE $xy''+2y' + \lambda^2 x y = 0$

As reported by Wikipedia - Sinc function, $y(x)=\lambda \operatorname{sinc}(\lambda x)$ is a solution of the linear ordinary differential equation $$x \frac{d^2 y}{d x^2} + 2 \frac{d y}{d x} + ...
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0answers
16 views

Research into the application of Jacobi matrices

The general real infinte hermitian Jacobi matrix is written in the form $$ \textbf{$J$}:= \ \left( \begin{array}{cccccc} b_1 & a_1 & 0 & \cdots & 0 & \cdots \\ a_1 & b_2 & ...
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0answers
12 views

Which argument in KL Divergence minimization?

The KL divergence $D_{KL}(p||q) = p^T\ln(\frac{p}{q})$ is not a distance measure because first of all it is not symmetric. In applications, one usually has a prior distribution, say $y$, and wants ...
4
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1answer
117 views

Why more than 3 dimensions in linear algebra?

This might seem a silly question, but I was wondering why mathematicians came out with more than 3 dimensions when studying vector spaces, matrices, etc. I cannot visualise more than 3 dimensions, so ...