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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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 ...
2
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1answer
68 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
212 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
103 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
23 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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1answer
93 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
78 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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59 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
62 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
109 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
72 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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71 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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2answers
162 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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40 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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0answers
69 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
289 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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1answer
47 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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36 views

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
35 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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30 views

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
64 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
35 views

Matrices in Linear Algebra

Let: $ u: \mathbb{R}^2 \rightarrow \mathbb{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 ...
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868 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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0answers
301 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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2answers
69 views

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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1answer
35 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
165 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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3answers
953 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
35 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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38 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
353 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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1answer
310 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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2answers
2k 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 ...
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1answer
121 views

Application of derivatives: related rates problem

Water is leaking out of an inverted conical tank at a rate of 50L/min the tank is 10m in diameter at the top. It is 6m deep at the deepest point, which is the vertex of the cone and lies on the ...
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0answers
68 views

Relationship between Reproductive Ratio and Jacobian in Population Model

In class we defined the Reproductive Ratio, $R_0$ of a population modelled by SIR, SEIR,... as the average number of secondary infections caused by an average infected individual in an average ...
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4answers
440 views

What is Cramer's rule used for?

I could have sworn I posted the question in the subject line somewhere on the internet, and I thought it was here. But I can't find it. It ought to be here in case anyone looks for it. Cramer's ...
3
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1answer
159 views

Volume vs. Surface Area Integrals

In order to find the volume of a sphere radiud $R$, one way is to slice it up into a stack of thin, concentric disks, perpendicular to the $z$-axis. a disk at any point $z$ will have radius ...
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1answer
254 views

The golden ratio in statistics of literature

Let a book, for example, or a poem... It consists in words and letters and symbols like : ;,!... Let $W_b$=the number of words of the book. Let $L_b$=the number of letters of the book. The number ...
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3answers
608 views

Britney Gallivan's paper folding formulas

According to a few YouTube videos and New Scientist, formulas exist (based on algebraic/mathematical premises, thereby making this a valid math question) to describe the limits of paper folding. The ...
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1answer
38 views

Why is chemotaxis considered an emergent behavior?

this is an applied math question. I could have posted this under a biological stackexchange, but the idea of emergent behavior or emergent properties of a system seems more appropriate to an applied ...
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0answers
449 views

Volume enclosed by two spheres (triple integral, cylindrical coordinates)

The question: Find the volume of the solid enclosed by the sphere $x^2 + y^2 + z^2 - 6z = 0$ , and the hemisphere $x^2 + y^2 + z^2 = 49 , z ≥ 0$ I set up the triple integral ...
28
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2answers
433 views

Statistics Primer for the Unwary Mathematician

I have a new position in a biology department (after being housed in a maths department) working on cognitive and population modeling. People in my lab are asking for help with applying statistical ...
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3answers
1k views

Real world situation with System of Equation with 3 variables?

Where do you run into a real world situation involving 3 variables and 3 equations? Can someone think of a specific example from business, etc? I recall taking an operations research course that ...
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1answer
131 views

Probability distribution of the product of random numbers

For applied mathematics to evolutionary biology I am often faced to have to describe a probability distribution function (PDF) which results from the product of a function in which a parameter is ...
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2answers
821 views

Surprising applications of cohomology

The concept of cohomology is one of the most subtle and powerful in modern mathematics. While its application to topology and integrability is immediate (it was probably how cohomology was born in the ...
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1answer
220 views

Real life scenario, probability model required for accidental vs supernatural causation.

A = HUMAN 1 B = HUMAN 2 A is related to B, specifically A is the father of B A goes on holiday 5 years ago, staying in a hotel in popular tourist spot near Scotland (long way from home) During ...
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6answers
8k views

Application of Composition of Functions: Real world examples?

Do you know of a real world example where you'd combine two functions into a composite function? I see this topic in Algebra 2 textbooks, but rarely see actual applications of it. It's usually plug ...
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4answers
283 views

An unexpected application of non-trivial combinatorics

PROBLEM STATEMENT Given two finite sets $A$ and $B$, each containing $s \in \mathbb N$ elements, how many pairs of functions $f \colon A \rightarrow B$ and $g \colon B \rightarrow A$ are there, ...
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1answer
1k views

Real world applications of exponential function; continous case

I am looking for interesting applications in everyday life, technology or science of exponential functions of the type: $$ f\colon \mathbb{R} \to \mathbb{R}, \quad x \mapsto ab^x $$ for the case $a ...
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2answers
42 views

Application of the spectrum of an operator

http://en.wikipedia.org/wiki/Spectrum_of_an_operator What is the application of the spectrum of an operator