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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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Do taxicab numbers have known “real-world” applications? If so, what are they?

The $nth$ taxicab number $Ta(n)$ is the smallest number that can be expressed as $n$ unique sums of two cubes. For example, the first non-trivial taxicab number $Ta(2)$ is $1729$, where: $1729=9^{3}+...
Eliza Wilson's user avatar
2 votes
0 answers
51 views

Computational framing of topological counterexamples [duplicate]

Bit of a soft question here, but bear with me: Topology is infamous as a source of weird counterexamples. Pretty much anyone who has been through a traditional introductory topology course can recall ...
user3716267's user avatar
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71 views

Where can I find real life problems for high school students involving solving triangles? [closed]

I have been searching for real-life problems or word problems that involve trigonometry to solve triangles, specifically employing the law of sine and cosine, suitable for high school students. The ...
Linda's user avatar
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6 votes
1 answer
97 views

Minimize travel time of a group of people with a motorbike

Problem: A group of $n$ people ($n\geq2$) want to travel from A to B but they can only either walk or use a motorbike (fit 2 people) [note that there is exactly $1$ motorbike for them to use]. Given ...
Quý Nhân Đặng Hoàng's user avatar
-1 votes
0 answers
44 views

Can you help me for prove this Elzaki transform? [closed]

a) proof $$ E[tf'(t)]=v^2 \frac{d}{dv} [\frac{T(v)}{v}-vf(0)]-v[\frac{T(v)}{v}-vf(0)]$$‎ Using Elzaki transform $$E[tf'(t)]=v^2 \frac{d}{dv} [E(f'(t))]-vE(f'(t)) $$ using$$ E[f'(t)]=\frac{T(v)}{v}-vf(...
Yaseen Tareq's user avatar
0 votes
0 answers
42 views

Probability that random variables with multinomial distribution have a common divisor greater than 1

Consider an election in which $k$ candidates compete: Let $N_{i}$ denote the number of votes for candidate $i$ in the election. How can we reasonably estimate the probability that the number of votes ...
Amir's user avatar
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-4 votes
2 answers
85 views

If $\frac{p}{p+q}$ is a negative real number, what can I deduce about complex $p$ and $q$? [closed]

Let $p, q$ be complex numbers with non-negative real parts and arbitrary imaginary parts. If $\frac{p}{p+q}$ is a negative real number, what can I deduce about $p$ and $q$? Motivation: This question ...
SRobertJames's user avatar
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0 votes
1 answer
69 views

Critical Simplices of a Discrete Gradient Vector Field

I just started learning about discrete Morse Theory and I got stuck on a corollary that in the book I'm reading is described as simply following from a lemma. Denote by $P$ an almost linear metric ...
moschops's user avatar
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54 views

How to formally justify fudge factor in this difference equation solution?

In Exercise $11$ from Section $3.3$ of Differential Equations With Boundary Value Problems by Polking, Boggess, and Arnold, we first develop the difference equation $P[n + 1] = (1 + \frac{I}{m})P[n],\ ...
user10478's user avatar
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4 votes
2 answers
110 views

pow and its relative error

Investigating the floating-point implementation of the $\operatorname{pow}(x,b)=x^b$ with $x,b\in\Bbb R$ in some library implementations, I found that some pow ...
emacs drives me nuts's user avatar
2 votes
1 answer
113 views

Standard definition of a game in game theory

Sorry for my naive question, but at the moment I can't quite figure it out. I'm consulting various documents on game theory in order to get the standard definition of what a game (and an associated ...
u31672873's user avatar
-1 votes
3 answers
53 views

How to untangle the ODE $\frac{dx}{dt} = c + \frac{px}{l_0 + pt}$? [closed]

In working on this problem, I came up with the following differential equation: $$ \frac{dx}{dt} = c + \frac{px}{l_0 + pt} $$ where $x$ is the dependent variable, $t$ the independent, and all others ...
SRobertJames's user avatar
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2 votes
0 answers
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A first course in abstract algebra Fraleigh 8th ed Section 5 Exercise 65

Cracker Barrel Restaurants place a puzzle called “Jump All But One Game” at each table. The puzzle starts with golf tees arranged in a triangle as in Figure 5.29a where the presence of a tee is noted ...
점시맙's user avatar
2 votes
1 answer
71 views

Books on the applications of group theory.

Background: Applications abound! I am aware of applications of group theory in general: cryptography. physics. chemistry. virology. computer science. anywhere there's symmetry. Outside those broad ...
Shaun's user avatar
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0 votes
1 answer
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Maximum and Minimum of a cubic function

Maximum value of function $y = x^3-5x^2+2$ a) 5 b) $\infty$ c) 2 d) -5 We know to find maximum value of a function we take first derivative of the function and make it zero and get some point. And ...
user342326's user avatar
0 votes
1 answer
34 views

Appropriate model to represent negative numbers

Negative numbers can be introduced by means of temperature, but it does not make sense to multiply two negative temperatures. Moreover, it is even objectionable to say 20°C is twice as hot as 10°C. A ...
apprenant's user avatar
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0 votes
0 answers
16 views

Software for Exportable NURBS surfaces from Parametric Equations $x=f(u, v), y=f(u, v), z=f(u, v)$ (Must be Suitable for Engineering)

The title pretty much says it all. Is there any software out there that lets you input 3D parametric equations without having to go to the trouble of writing a bunch of code and then lets you export ...
Johnny's user avatar
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2 votes
0 answers
48 views

How to generalize curvature to n dimensions parameterized by time instead of arc length?

I am a novice in mathematics in general and even more so in differential geometry. Currently, I am looking to generalize the Frenet-Serret formulas to $n$ dimensions. At the moment, I am interested in ...
pedro colombino's user avatar
0 votes
1 answer
41 views

How to solve an ODE where the rate is directly proportional to two amounts?

Two chemicals in solution react together to form a compound: one unit of compound is formed from $a$ units of chemical $A$ and $b$ units of chemical $B$, with $a + b = 1$. Assume the concentration ...
SRobertJames's user avatar
  • 4,450
10 votes
2 answers
347 views

Applications of Linear Programming to pure mathematics

This semester I'm taking a course in Linear Programming. While the topic is very interesting, all the applications I can find about this topic seem to be outside of mathematics. What are some ...
Carla_'s user avatar
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1 vote
0 answers
106 views

What is the Equation for the Batista-Costa Minimal Surface?

The Batista-Costa surface is a triply periodic minimal surface. Three photos of part of the same surface are below: where the first two were taken form the research paper: The New Boundaries of 3D-...
Teg Louis's user avatar
-1 votes
1 answer
63 views

About vector spaces over finite fields [closed]

I've been dabbling with matrix computations in finite fields, and I've stumbled upon a pattern that I can't understand. Perhaps someone here could shed some light on it? So, here's what's happening: ...
joeren1020's user avatar
0 votes
0 answers
81 views

Is torsion of a multivariate curve defined in n-dimensional space?

I understand that torsion is a concept specific to three-dimensional spaces. Despite searching on Google, I've struggled to find how to extend the concept of torsion to an n-dimensional space. Is it ...
pedro colombino's user avatar
0 votes
2 answers
44 views

Query regarding approach to solve a given differential equation.

There's a equation $$N(t) = N(t)\frac{P(t,z)}{B}-C\frac{d(P(t,z))}{dz}$$ $$N(t) = A\frac{dP(t,z)}{dt}$$ Constants: B, C=3.9878*10⁻⁷, $A=0.11941$, Variables: N(t) is a function of t and is defined at a ...
Qwerty's user avatar
  • 101
1 vote
0 answers
34 views

In what situations would using means other than arithmetic/geometric/harmonic make sense?

I understand some use cases for arithmetic (standard), geometric (average growth of two successive discrete growth rates), harmonic (average velocity when consecutively traveling the same distance ...
joelproko's user avatar
0 votes
1 answer
44 views

What does it mean to divide an area by a distance?

Let's say for example we divide 2m^2 by 1m, the result is 2m. What is the physical interpretation of this? I mean, dividing an area by a distance makes no sense to me.
0149234's user avatar
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0 answers
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Applications of highly oscillatory integrals

I was reading a series of articles on numerical integration of highly oscillatory functions, e.g., S. Olver, Numerical approximation of highly oscillatory integrals S. Xiang, H. Wang, Fast ...
Vl F's user avatar
  • 11
0 votes
1 answer
129 views

What are the possible applications in maths and physics of vector fields along smooth maps?

I am currently working on a problem related to singularities of mappings between manifolds with metrics and the interplay of metric singularities with mapping singularities. Given a smooth map $F:M\...
Siddharth Panigrahi's user avatar
3 votes
1 answer
79 views

A real-world example for a centralizer property

Context: I'm re-studying basic group theory and looking for "real-world" examples/puzzles that can be translated into abstract group theoretic statements. By real-world I mean not something ...
David Kubecka's user avatar
1 vote
0 answers
79 views

Using the trapezoidal rule for the Maxwell-Boltzman function

Background I approached my physics professor with question 1 from this LibreTexts resource. (at the bottom of the page), to better understand the material via self-study. Question Using the Maxwell-...
Jessie's user avatar
  • 1,426
0 votes
0 answers
31 views

Application of threshold functions from random graph theory

I would like to know if anyone knows about some applications/models where those threshold functions from random graph theory, defined by $$ \lim_{n \to \infty} P(\mathbb{G}_{n,p} \in \mathcal{F}) = ...
GG314's user avatar
  • 114
28 votes
4 answers
6k views

Consider a man who travelled exactly 2 km in two hours. Is there a one-hour interval when he traveled exactly 1 km?

Question : Consider a man who travelled exactly 2 km in two hours. Is there a one-hour interval when he traveled exactly 1 km? Can we make a mathematical argument? I have written my attempt in an ...
whoisit's user avatar
  • 3,227
0 votes
1 answer
44 views

Rate of change of ordinates and abscissae

The question that I am stuck at goes like this: On the curve $y^3=27x$, the absolute value of rate of change of ordinate is greater than the absolute value of rate of change of abscissa in the ...
Harikrishnan M's user avatar
22 votes
5 answers
2k views

What do physicists mean when they say something is "not a vector"?

It's common for physicists to say that not every 3-tuple of real numbers is a vector: “Well, isn’t torque just a vector?” It does turn out to be a vector, but we do not know that right away without ...
SRobertJames's user avatar
  • 4,450
5 votes
4 answers
387 views

Numerically computing eigenvalues -- what is it useful for?

Cross-posted on Scientific Computing Stack Exchange Are there real-world applications that call specifically for eigenvalues rather than singular values? Top eigenvalue is useful to establish ...
Yaroslav Bulatov's user avatar
1 vote
0 answers
38 views

How is rate of change dx/dt in ladder problem doesn't match the actual rate of change.

The pictures above describes the question. We have to find the rate of change in x-axis direction. The answer is derived from implicit differentiation and is $4/3$. The process is: [y(t) gives y-axis ...
user avatar
0 votes
1 answer
102 views

What is the Divergence of a Spherically Symmetric Vector Fields?

A vector field is spherically symmetric about the origin if, on every sphere centered at the origin, it has constant magnitude and points either away from or toward the origin. A vector field that is ...
SRobertJames's user avatar
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0 votes
0 answers
44 views

Formula like Elo rating but for games where the outcome is numeric?

I'm working on a problem that involves ranking based on pairwise comparisons (it's for a scientific problem, not actually for games). My comparisons return a numerical score (in practice roughly ...
Alex I's user avatar
  • 173
4 votes
6 answers
684 views

Is $x^3$ really an increasing function for all intervals?

I had an argument with my maths teacher today... He says, along with another classmate of mine that $x^3$ is increasing for all intervals. I argue that it isn't. If we look at conditions for ...
Maddy's user avatar
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4 votes
1 answer
101 views

Interpretation and evaluation of tensor operations in Fourier space calculation

I am attempting to implement a model outlined in this paper: General magnetostatic shape–shape interactions Background This model allows the calculation of magnetostatic interaction energies between ...
JasonC's user avatar
  • 81
0 votes
1 answer
171 views

Is there a self-correcting iterative method for approximating pi without using transcendental functions?

The Newton-Raphson method is an iterative method for finding a root of a function, and it is self-correcting in the sense that any error in the initial input is reduced with each iteration so that it ...
noumenon28's user avatar
0 votes
0 answers
68 views

What are some practical, non set-theoretic applications of the transfinite recursion theorem

I found some applications of the transfinite recursion theorem within set theory. For example, to prove the following theorem: A set $A$ is infinite if and only if there exists a one-to-one function $...
Tran Khanh's user avatar
2 votes
0 answers
76 views

Applications of group theory/abstract algebra [duplicate]

Before voting down, I would this text to be read. This is not exactly a question regarding a hint to solve an exercise of a list or an exam, but a question involving the possible utility of which is ...
Emmy N.'s user avatar
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0 votes
0 answers
32 views

Probability analysis in passengers taking trains in a FCFS way under capacity constraint

Suppose there are two trains: Train 1 and Train 2 have different departure times ($t_1$ and $t_2$) and capacities ($c_1$ and $c_2$). There are two types of passengers, Type 1 with $d_1$ passengers ...
Yuzhen Feng's user avatar
2 votes
1 answer
59 views

Book reccomendations on applications of math

I was always fascinated with pure math, but lately I've been increasingly more interested on applications of math (preferably algebra/topology but other fields would be interesting too) in the real ...
Artus's user avatar
  • 973
0 votes
0 answers
46 views

What are applications of changing limit and differentiation/integration?

I know the following theorems but don’t know their usefulness. If a series $\{f_n\}$ of Riemann integrable functions on $[a, b]$ uniformly converges to $f$, $f$ is Riemann integrable and $\lim\limits_{...
MathMan's user avatar
  • 103
3 votes
1 answer
134 views

A "perfect" (chess) rating system

Assume we want to have a player rating system with the following conditions: For simplicity, no draws. If A wins against B with ratings $a,b$, their new ratings are $a'=f(a,b),b'=g(a,b)$. Most ...
Hauke Reddmann's user avatar
0 votes
1 answer
98 views

Best approximation of ellipse for collision detection.

I'm working on a personal JavaFX project, and I need to check if two sprites overlap. Originally, I modelled them as ellipses. I was then able to then simplify the problem into checking the ...
Ryan de Barros's user avatar
0 votes
0 answers
14 views

Help needed Applications Fourier transform on sound wave propagatiom

[This image show an example in a textbook that am having difficulty in understand how they get 2.12.81 and 2.12.82][1] Kindly help with the value of B [1]: https://i.sstatic.net/k4HaF.jpg
Fatai Noah's user avatar
1 vote
1 answer
90 views

The absurdity of $\Gamma(x)$'s minimum, and can it be applied to the factorial?

I know that the Gamma function can be used as a representation of the factorial, but, at the same time, it is an extrapolation of $x!$. The Gamma function is cool and all, but what are its ...
sreysus's user avatar
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