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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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 ...
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0answers
14 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 i'll get solid mathematical answers: I'm looking for a system that ranks event winners, but it can't require everyone to be ...
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0answers
31 views

Fourier series & Fourier transformation [on hold]

Tell me where we use Fourier series & transform in real life? Please mention an example problem which helps me to understand easily about Fourier series &Fourier transformation?
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1answer
42 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
46 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
25 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
55 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
29 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 ...
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2answers
53 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?
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2answers
414 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
62 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
681 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
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1answer
37 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
179 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
23 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
votes
1answer
58 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
40 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 ...
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2answers
74 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
votes
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 ...
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2answers
97 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
26 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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2answers
186 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
15 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
10 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
110 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 ...
3
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3answers
103 views

Puzzle: leaning a ladder at $45^\circ$ to a wall using only yourself

This question was asked to my friend in an interview. You are provided a ladder and are led to a wall. The ladder must be kept against the wall making an angle of $45^\circ$ with the floor. You are ...
1
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1answer
43 views

differential equation - rectilinear movement of a boat using propulsion

I have a problem in my differential equation book that I can't solve because it gives me data that I can't seem to fit in the equation that the book gives me. This is something that I just don't get. ...
0
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1answer
34 views

Non-STEM applications of Calculus? [closed]

I was talking with a friend, who is a liberal arts major, about the everyday applications of math. We agreed about how Algebra directly applied to the average person's life, but the only examples of ...
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1answer
39 views

Why is my phase correlation not equal to the real correlation?

If I understand the correlation theorem correctly, it states: $ f(x,y) \unicode{x2606} \bar g(x,y) = \mathfrak{F}^{-1} \left\{ F^*(u,v) G(u,v) \right\}, $ also called a phase correlation. Above ...
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0answers
23 views

A good book about theoretical ecology (Quantitative analysis of movement)

I would like to ask if anyone knows a good book to start studying animal patterns of movement. I am interested in exploring different approaches, in particular models in stochastic settings. I have ...
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0answers
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[Levenberg-Marquardt]What is the link between positive-definiteness and well-conditioning?

Working on optimization problems through neural networks, I use the Levenberg-Marquardt algorithm. I have read this assertion that I do not understand : A positive definite diagonal matrix is ...
2
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0answers
23 views

Application of Bernstein's theorem

There is a theorem due to Bernstein related to analytic functions : If $f : ]0,1[ \to \mathbb{R}$ is an absolutely monotonous function (that is a $\mathcal{C}^\infty$ function such that for ...
2
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1answer
35 views

Mixture of mixtures.

I am formulating this problem for work, so it is important that I get it right. As of right now I am only considering the case where the number of chemicals is equal to the number of pre-made ...
0
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1answer
28 views

Mixing chemicals in ratios

I am trying to figure out a mixing problem and I'm stuck because it seems to have two levels. I'm going to write a simpler form here of the problem I am working on. Say that we have 60 pounds of a ...
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0answers
17 views

How to choose assymetry for KL divergence?

I have two 2D probability distributions of eye movements of two different images. Suppose I call the first distribution of Image 1: $P$, and the second distribution of image 2: $Q$. Since ...
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0answers
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Math-a-magic: How to force all participants onto same color squares of checker board?

Setup Setup 3x3 checker board. X O X O X O X O X Rules Audience picks a random square on the board for their point of origin. [not sure if this ...
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2answers
86 views

Calculus - Finding the Linear Equation which equals area

I am really stuck on this question... I think it involves finding integration but am struggling to understand the concepts involved. I have attempted the equation $y=70$ through trial and error, ...
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0answers
38 views

Examples and applications of homogeneus models in model theory.

Does anyone know any specific examples or applications of homogeneus models, to model theory or any other branch? For example, an application would be that prime models are isomorphic in a countable ...
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0answers
14 views

Fourier coefficients for pattern analysis

There are many areas like, gait analysis, where we recognize persons by analyzing their silhouettes taken while they are at different stages of their walking where analysis also carried on in ...
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0answers
19 views

Deriving the inverse of RGB to HSV transformation

Today we had the conversion from RGB to HSV coordinates and vice versa in a multimedia systems exam. And I was puzzled between the conversion. RGB and HSV are of course the color spaces. The ...
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2answers
70 views

Need a textbook for math course

The undergrad course is called intro the applied math, and it covers: "The unit introduces some of the principal mathematical techniques such as difference equations, differential equations and ...
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1answer
41 views

Equilibrium and Stability of Nonlinear Interactions

Examine the nonlinear model: $$\triangle x_t = rx_t(1-\frac{x_t}{K})-sx_ty_t$$ $$\triangle y_t = -dy_t+\epsilon x_ty_t$$ Find the equilibrium and their stability. Here all the parameters are ...
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0answers
27 views

Hydrostatic Force on a submerged plane.

I am having trouble with question 5, it reads (ignore the Riemann sum part) : Here is what I did, and where did I go wrong?. The answer the book gives is: $6.7\cdot 10^4N$. Thank you.
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0answers
84 views

Real Mathematics in Video Games

Out of curiousity (and perhaps also to amuse my students), I am looking for examples of actual mathematics appearing in video (computer) games. Of course that sort of mathematics would probably be ...
0
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1answer
70 views

Solving Eikonal Equation

The problem is the following: I have the bidimensional eikonal equation with non-constant propagation: $u_x^2+u_y^2=u^2$ The goal is: i) To find the characteristic strips for the parametrization ...
3
votes
2answers
67 views

How can Bayesian and Frequentist approach be different?

Let's say I am trying to add numbers, like say one to ten. I can either add them in order, or I can notice that I can group them into five groups of eleven, so I suppose which method to use depends on ...
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2answers
127 views

Interesting calculus problems for beginner

Recently I started learning calculus and I think I have grasped the basics. However when calculating examples I tend to drift away and not put much effort in it. When I was learning programming in ...