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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Basis representation for non-negative, compact support, reasonably smooth spectral function

I was wondering if anyone has ideas on representing a non-negative, compact support (from x=-1 to 1 on the real axis) spectral function as a superposition of basis elements. Ideally, the basis ...
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Prerequisite of Dynamical system and applied PDE

With a very strong intention on future research closely related to Dynamical Systems and applied PDE. What are the materials as a prerequisites which are strongly recommended to study hard during ...
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73 views

Applications of Geometry to Computer Graphics

How is differential geometry (or any type of theoretical math) related to computer graphics and/or computer programming? A friend of a friend of mine has only a bachelors degree in pure math and got ...
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1answer
25 views

Show solution to ODE's fourier series is a series of sines only

This question was given in an exam in applied mathematics, on the subject of Fourier series: Observe the following ODE: $u\left ( x \right) ^{\prime \prime}+Q \left ( x \right) u\left ( x \right) ...
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1answer
17 views

Calculate remaining space of a box/cube

Im developing an eCommerce system where items are 'logically' placed into boxes. Rather than the shipping system calculating the shipping of each item individually. The shipping will be calculated by ...
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37 views

Apps for making geometric shapes [closed]

Is there any apps for making geometric shapes? I need to make shapes like rhombus and equilateral triangles.
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1answer
64 views

Books in mathematics based on problem solving

Hi I'm looking for mathematical books that try to teach mathematical concepts by motivating and solving real life problems. For example a book in topology that is motivated by problems of planetary ...
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19 views

User of a System

Given a system with n users and each user will only use the system once (for an hour) during a year. The user will only access the system during business hours (so ...
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1answer
28 views

What are some other applied advanced probability sub-field relevant to finance?

What are some other applied advanced probability sub-field relevant to finance? I have heard Martingale, stochastic process, stochastic calculus, monte-carlo statistics I've been searching other ...
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42 views

Mathematical field theory Application in real world and other branches of Mathematics

I need to write work about applications of Mathematical field theory in real world and in other branches of Mathematics. Can someone guide me to an appropriate book, resource? Thanks, Denis.
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distance between A and B. solve with pythagorean theorem

distance between two person. person A like to watch movie by 3 unit. person B like to watch movie by 4 unit. in this case we can tell the distance between person A and B. person A is 1 unit away ...
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1answer
49 views

How many answers can be created using the elementary arithmetic operators?

If I gave you an amount of $n$ numbers, how many anwswer will you be able to create using the elementary arithmetic operators ($+, -, \times, /$)? These are the rules: All numbers ...
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1answer
18 views

Question regarding simple harmonic motion?

Hi guys, I was just wondering what the answers are for this question, as it says it's B, and I'm only getting C as an answer (attempted multiple times). Could anyone please just clarify what the ...
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PDE modeling (heat conduction and flow)

The heat conduction is expressed by a classic heat equation like $p(x) u_t + div (A(x) u) = f(x,t) $. If I look at a porous medium like this (solid+gas) the heat equation should apply too (in a ...
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1answer
36 views

I want an intutive/theoretical understanding of the $\sin(\omega t +f)$

What is the meaning of $x(t)=x_0\cos(\omega t+f)$, where $x_0$ is the amplitude, $\omega$ the angular frequency, $t$ time and $f$ phase constant? I know how to solve the mathematical problems which ...
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1answer
39 views

Are the following functions also surjective?

Let $f\colon\mathbb R\to\mathbb R$ be a surjective function. Assume that $f'$ is also surjective. Assume also that $f$ vanishe on $s=1$ of order $m$. My question is: Are the following functions also ...
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1answer
16 views

Looking to assign percentage contribution among 4 variables in a simple equation

I have a seemingly simple problem, that is giving me some trouble in solving. I have a 4 variable equation and want to determine the contribution of each variable in moving the dependent variable from ...
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1answer
136 views

Applications of Countable Infinite Sets and Power Sets

What are the possible applications of Countable Infinite Sets and Power Sets in areas that are not strictly mathematical? Also I want to know the significance they carry. What was not possible ...
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2answers
94 views

What are the other methods used to prove that a homomorphism is bijective?

The motivation can be found in: Show that $ℤ^{m}$ is a subgroup (and a free abelian group) of $ℤ^{n}$ for all $m≤n$. In a specified problem related to a dynamical system the only possibility is ...
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1answer
16 views

Bessell function of the first kind $J_v$ of the Bessel equation $x^2y''+xy'+(\lambda^2 x^2-v^2)y=0$

If we have an equation $x^2y''+xy'+(x^2-v^2)y=0$ then the solution of the first kind $J_v(x)=x^v\sum_{m=0}^{\infty}\frac{(-1)^mx^{2m}}{2^{2m+v}m!(m+v)!}$. Then how would you find the solution of ...
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Number of collisions of particles in a box. Application to epidemiology

I was surprised to see in this biology article a model assuming that the number of newly infected cells is a linear function of the number of (healthy) cells and of the number of viruses. I am not ...
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1answer
31 views

What is the practical application of local linearization

Whenever I'm studying a new topic in mathematics, the question of potential practical application is the one that matters to me the most. While it's relatively easy to come up with hypothetical cases ...
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1answer
55 views

what is difference between open and mixed queue

please consider this image: In this picture that I got it from Here write said that Network C is Open,B is Mixed and A is Closed. I want to know why C isn't mixed? ...
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56 views

Help with a game design function.

I'm working on building a 'result table' for an RPG. In said table, you compare an effect rating to a resistance rating, to find a whole number result. Essentially, for each cell I need to find Z, ...
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1answer
16 views

Meaning of multiplication by $\sin$ in $\omega$-domain

Multiplying some signal, a function of time, $m(t)$ by a cosine $\cos{\omega' t}$ causes a shift in frequency of $m(t)$, by $\pm\omega'$. But what about multiplication by a sine wave, such ...
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1answer
92 views

numerical update rule for discretized hawkes excitation process

So I think I am just misunderstanding some simple notation or something and would appreciate some help. I am trying to replicate this model in an agent based model, but I cannot seem to figure out the ...
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1answer
56 views

Analyzing the stability of equilibria

There's a model with a condition $r>\mu$: $$\begin{align} S'&=r(S+I)-\beta SI-\mu S \\ I'&=\beta SI-(\mu +\alpha)I \end{align}$$ I can easily see that the equilibria of the second ...
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42 views

Applied problem of multivariable calculus with integrals.

How to solve this problem: A medal has the shape of the portion of the plane $x + z = 1$ lying inside the cylinder $$x^2 + \frac{y^2}{2} = 1.$$ The edge of the medal is covered in cold and it costs ...
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83 views

Questions about the field scientific computing

I have heard about the field of Applied and Computational Mathematics, Scientific Computing and want to get some information. Is this a combination of computer science and mathematics? What subjects ...
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20 views

Representative value of non-square matrix

First of all, I apologise if this question is inappropriate, I wish I could be more specific - but due to the nature of it, as I am actually asking for a suggestion of some technique, that's hard to ...
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57 views

Polynomials and NSA

I'm looking for some applications of criteria of irreducibility of integer polynomials inside and outside mathematics. I was reading the CV of Filaseta, a great researcher in this area and he has ...
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2answers
84 views

Derivative application question

A girl of height $120 $cm is walking towards a light on the ground at a speed of $0.6$ m/s. Her shadow is being cast on a wall behind her that is $5 $m from the light. How is the size of her shadow ...
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38 views

Show that there exist a bijection between $ℤ$ and $A$

Let $A$ be the set of points of the form $(s,0)$ (the second component is still zero) where $s∈B⊂ℝ$ and $B$ is an infinite discrete set. My question: Show that there exist a bijection between $ℤ$ ...
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How I can construct this bijection?

Assume that there is a bijection between $ℤ/2mℤ$ and the set $\{1,2,...,2m\}$ and there is a bijection between $ℤ/2ℤ$ and the set $\{1,2\}$, so it is possible to construct a bijection from the set ...
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1answer
24 views

polynomial word problem?

My answer is wrong... I understand what I did was found the volume of the pool (cubic feet) I am supposed to get square feet.
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What is Radius of Convergence used for?

What is the applications for "Radius of convergence"? I haven't been successful in finding any information about the applications, just a lot of information about how to calculate and what it is... ...
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1answer
29 views

Finding the basic reproduction number of a particular model

I have been reading a paper about a host-parasites models and for the model: $$\begin{array}{rll} \displaystyle{\frac{dx}{dt}}&=\lambda -dx -\beta v x & \text{Susceptible host} \\ ...
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1answer
26 views

Matrices in Linear Algebra

Let: $ u: R^2 --> R^3$ be defined by: $$ u(x,y)=(x+2y, 2x-y, 2x+ 3y)$$ Give the matrix $M[u]$ in the canonical base of its definition space. This question might seem sort of stupid, but it was ...
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84 views

Practical use and applications of improper integrals

What are the most important applications of improper integrals, in particular to computer science and related fields, and to technology and engineering in general? I know that improper integrals are ...
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61 views

Differential vs difference equations in mathematical modeling

I'm reading a little about mathematical modeling and I've seen some population models based on differential equations. I've also seen some (not many) that can support both difference and differential ...
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Function application (word problem)

The problem: My work so far: $3=log(\frac{A}{A_0})$--->$10^3=\frac{A}{A_0}$ $\frac{A}{A_0}=1000$ (Am I done there?) Plugging it in: $M=log(\frac{1900000}{1000})$ $10^M = \frac{1900000}{1000}$ ...
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33 views

How to write this function?

I do not want the answer given to me, I just want assistance. Problem: Marcus invests $750 in an account that pays 9.8% interest compounded annually. Write a function that describes the account ...
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1answer
89 views

Applications of simultaneous diagonalization of quadratic forms

If $A$ and $B$ are square symmetric matrices and, additionally, one of them, say $B$, is positively defined, then there exists an invertible matrix $S$ such that $$S^{\top}\!AS=D ...
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159 views

Maximum possible variance

From this biology article, end of page 4, the author talks about a random variable which never takes value outside the range [0,1] (0 and 1 included in the range). He says that the maximum variance ...
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1answer
24 views

Amount of Liquid in Container

Given: a cuboid container, of dimensions h into w into l a rate of flow of liquid per unit time through an inlet, in a rate of flow of liquid per unit time from an outlet, out, when the container ...
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31 views

Nyquist diagram of transfer function

Transfer function of a system is given as $$G(s) = \frac{100(s+5)}{s^2(s+3)(s^2+4)}$$ Sketch the Nyquist diagram and find if the system is stable. Also find the gain margin and phase margin. Please ...
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2answers
87 views

Curve on a basketball

The sewing pattern on a basketball is composed of two great circles and a single curve that intersects each great circle twice. Does this curve have a name? Are there any parametric descriptions of ...
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17 views

When does the leading right eigenvector gives the stationary distribution?

I am trying to make sense of the meaning of the leading right eigenvector in mathematica modeling (applied mathematics). I am interesting in models of the kind $\overrightarrow v(n+1) = M ...
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1answer
131 views

Calculus - Trig Maximum Value Problem

When the rules of hockey were developed, Canada did not use the metric system. Thus, the distance between the goal posts was designated to be six feet. If Sidney Crosby is on the goal line, three feet ...
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1answer
146 views

Real world tangent functions

I am a high school math teacher and one of my students asked me for examples of real world tangent functions. Not using tangent to find a side length but a relationship that can be represented by a ...