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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54 views

What would be the explicit formula of a “dictionary” function / relation?

What would be the explicit formula of a " dictionary" function / relation that would put in the "dictionary order" all the words of a natural language ( having an alphabet)? I think that one of the ...
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1answer
73 views

Where is the usefulness of Fourier Transform I was promised? [closed]

Before I started my PDE course I heard about Fourier Transform and how useful it is (waves, heat problem, etc) but I recently finished it and all we did is solve some PDE problems where we had to ...
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2answers
284 views

Real-world applications of fields, rings and groups in linear algebra.

Real-world applications of fields, rings and groups in linear algebra. A friend of mine asked me where one could use the definitions of rings, groups, fields etc. I was very embarrassed of the fact ...
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3answers
97 views

Applications of chemical reaction networks

I have recently read a bit on chemical reaction network theory. I was wondering whether the mathematical concepts have cross-field applications like neural networks. For example, can I apply chemical ...
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0answers
33 views

Physical interpretation of Dirichlet energy for a membrane.

In the following model of a membrane with a mass particle in it, why does the integral represents the elastic energy of the system? Let $\Omega$ be an open connected region (the membrane) in $\Re^2$, ...
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1answer
44 views

Examples of applying Dirichlet's approximation.

I've seen many examples of Dirichlet's approximation being proven , or other questions regarding to the theory of the approximation on this site and others but I would like to see a concrete example ...
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0answers
36 views

Real world application of finding all simple paths on a graph

I am currently designing a general purpose graph database. Recently I have started to consider supporting the "find all simple paths between two nodes" operation on the graph. However while there are ...
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0answers
17 views

Impact of individual parts to the whole when measuring yearly performance

Suppose I have a scenario where I want to compare the performances of two different time periods, but I want to break down exactly what caused the difference in performance. I have performance of ...
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2answers
26 views

Norml, Application of derivatives

If $x+4y =14$ is normal to the curve $y^2=αx^3 - β$ at $(2,3)$, then the value of $α+β$ is? I equated the slope of the normal with the value of $-dx/dy$ and found $α=2$, how do I find $β$?
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4answers
220 views

“Class” of functions whose inverse, where defined, is the same “class”

Please excuse the amateurish use of the term "class", I don't know what the exact term is for what I'm looking for. Anyway, details. I'm asking specifically about real-valued functions on the real ...
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0answers
37 views

Integral transform with reciprocal complex exponential functions?

I tried answering a question that ended up with an expression $$\mathcal F\left\{e^{\left(\frac{2\pi j} {t}\right)}\right\}$$ Now this function we know from famous identity is $$e^{ai} = \cos(a)+i\...
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1answer
51 views

Find the interval in which $f(x)$ increases and decreases.

Let $f(x) = 2x^3 -9x^2 + 12 x + 6$ so $f'(x) = 6x^2-18x + 12 = 6 (x-1)(x-2)$ I need the intervals in which $f(x)$ strictly increases, $f'(x)>0$ when $x <1$ and $x>2$ and thus $f(x)$ ...
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0answers
61 views

Math Algorithm Needed with Aggregated Percentages (Business Scenario)

I'm trying to figure out a math algorithm, but I'm having a hard time wrapping my head around the best way. Instead of defining a complex industry-specific process, I'll construct a simplified ...
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0answers
420 views

Apps for practicing math (all levels)

I am looking for an app that I can use to PROVIDE me with math problems for practice and to stay fresh on various subjects in mathematics. This includes all levels of math (from low grade school to ...
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0answers
26 views

Exponential equation with top and bottom limits?

So I'm coding a interactive sliding bar that changes based on the value that is given. Currently the interaction between the value given and the bar is static and I would like to make it flow with the ...
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2answers
64 views

A calculus problem from high school textbook

A man 150 cm tall, walks away from a source of light situated at the top of a pole 5 m high at the rate of 0.7 m/s. Find the rate at which: his shadow is lengthening the tip of his shadow is moving ...
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1answer
65 views

Proving uniqueness of solution to 1-D Wave equation without energy conservation

We have a homogeneous string of length L fastened at its ends, performing small transverse motion in a vertical plane. The tension in the string is assumed sufficiently large for gravitational forces ...
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0answers
13 views

Bayesian Network vs MultiVariate Analysis vs Induction

I work with JS programmer on the logic for a web app. We have factors that influence a composition of a set. Envision rows in Excel that tell a set to have 5 members or 10, etc. Each row has certain ...
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0answers
28 views

Need to create a formula for points distribution in the game

There is the following data for a simple game: 3 players General points pool - 30000 Each player has a force. Initial force value - 100 During the game force indicator is changing. Min value of force ...
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2answers
365 views

Determine price elasticity of demand and marginal revenue

Determine price elasticity of demand and marginal revenue if $q = 30-4p-p^2$, where q is quantity demanded and p is price and p=3. I solved it for first part- Price elasticity of demand = $-\frac{p}{...
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0answers
19 views

Calculate weighted percentages to incorporate discounts

I apologize if I have titled this question incorrectly. I am selling products online. Customers can purchase the products plain, or they can purchase it with one of two logo design applications, ...
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0answers
15 views

Heaps' Law equation derivation

I'm actually not sure if this question is allowed on this community since it's more of a linguistics question than it is a mathematics question. I've searched extensively on the Web and have failed to ...
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1answer
36 views

how to show that (F∘T) = (T∘ F) [closed]

We have E a vector space , T and F two endomorphisms of E such as i) F got dim(E) eigenvalues of multiplicity 1 ii) each eigenvector of F is also an eigenvector of T And we have to show that (F∘...
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1answer
65 views

What is application of following exercise?

I had done following excercise. Consider the function $f:X\to Y$ where Y is compact Hausdorff space. Then $f$ is continuous if and only if the graph of $f$, $$G_f=\{(x,f(x)) \mid x\in X\},$$ is ...
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0answers
78 views

Practical applications of semidefinite programming

I am looking for practical applications of semidefinite- programming. So far, I found that the low-rank matrix completion problem (recomendendattion matrices) can be expressed as a semidefinite ...
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1answer
46 views

Given $a_0, a_1,…,a_n$ are the real numbers satisfying

Given $a_0, a_1, .., a_n$ are the real numbers satisfying $$\dfrac {a_0}{n+1} + \dfrac {a_1}{n} +......+\dfrac {a_{n-1}}{2}+a_n=0$$ then prove that there exists at least one real root of the equation ...
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1answer
152 views

Using Rolle's theorem to show $e^x=1+x$ has only one real root

Applying Rolle's Theorem, prove that the given equation has only one root: $$e^x=1+x$$ By inspection, we can say that $x=0$ is one root of the equation. But how can we use Rolle's theorem to prove ...
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0answers
89 views

What are the practical uses of Fermat's Last Theorem? [closed]

Given the wide attention it has received from the math community, what are the practical uses of Fermat's Last Theorem?
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1answer
52 views

calculus applied to fields in physics

Having trouble with the maths in this question, I realise this is a physics question so I apologise if this isn't allowed, but some mathematicians might be able to solve it well. I asked this in the ...
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0answers
10 views

Swaying string, a question regarding the derivation of formula

In my textbook, with $S=|\mathbf{S}|$, from the picture below, they derive $\int_{x}^{x+h}\rho_lu_{tt}''d\lambda=S(x+h)\sin(\alpha(x+h))- S(x)\sin(\alpha(x))+\int_{x}^{x+h}Fd\lambda$, where $F$ is [...
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1answer
26 views

Which logistic equation is better for solving this question?

So I was given a question about spread of disease: A virus is spreading through a city of 50,000 people who take no precautions. The virus was brought to the town by 100 people and it was found ...
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8answers
2k views

Practical application of matrices and determinants

I have learned recently about matrices and determinants and also about the geometrical interpretations, i.e, how the matrix is used for linear transformations and how determinants tell us about area/...
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1answer
48 views

Equations or areas where $(AA^T)^x$ or $(A^TA)^x$ are used as applications

Let $A$ be square or rectangular and $x\in \mathbb{R}$. Can you point me to equations/areas out there where $(AA^T)^x$ or $(A^TA)^x$ or their eigenvalues are used as applications? e.g. we find them in ...
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3answers
167 views

Applications of “finite mathematics” to physics

Disclaimer: I know that what follows is a biased view on applications, one of the points of the question is to eliminate some of that bias. When I think of applications of maths outside of itself, I ...
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6answers
488 views

Importance of differentiation [duplicate]

I have just started learning about differentiation. I know that differentiation is about finding the slopes of curves of functions and etc. I have many saying that differential and integral calculus ...
3
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1answer
91 views

State of art numerical algorithm for all complex roots of high degree polynomial in $\mathbb Z[x]$

I have many polynomial with high (100+) degree. The coefficients are integer. I would like to find all the roots in $\mathbb C$ of each polynomial as fast as possible. Best complexity and best ...
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1answer
37 views

Find a homeomorphism

Let $X=A\cup B \cup C$ where $A=\{(x,y) :(x+2)^2 +y^2 =1\}$ and $B=\{x^2+y^2 \leq 1\}$ and $C=\{(x,y) :(x-2)^2 +y^2 =1\}$. Find a homeomorphism between the quotient space $X/B$ and $E=\{(x,y) :(x-1)^...
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1answer
189 views

What are the practical applications of the Astroid curve?

The astroid curve is a fascinating and famous curve — but why do we care? Several famous mathematicians and physics worked on it, like Roemer, Bernoulli, and Leibnitz, but why? Is it simply for ...
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73 views

real world applications of direct sums

I understand how direct sums work and how they can be useful in proving certain conditional statements in linear algebra but it seems to me that direct sums are only useful in abstract settings. I was ...
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0answers
64 views

What problems are related with the following type of FDE?

Consider the following type of functional differential equations: $$\begin{align} \frac{du}{dt} &= F(x,t,u(x,t),u_{x,t}), & (x,t) &\in [a,b] \times [0,T] \end{align}$$ where $u(x,t)$ is ...
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1answer
37 views

Surface area of a sphere over a disc

What's the surface area of the sphere $x^2 + y^2 + z^2 = 1$ over the disc $(x-1/2)^2 + y^2 \le 1/4$ ? I've tried something, but I don't think it's right, as it's not a "nice answer" So here is what ...
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1answer
19 views

Disagreeing methods for computing pregnancy probabilities

Something that I would have thought to be dead simple nearly drove me crazy! Let's say we make a small study of women who have similar factors for becoming pregnant. Let's say the study runs for two ...
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0answers
28 views

How is it possible a ruled surface to be composed of straight lines?

And a double ruled surface is composed of two groups of straight lines. This is what gives to this shape its exceptional resistance to buckling How is it possible a curved surface to be composed of ...
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1answer
115 views

Applications of polynomial systems of equations

What are some applications of Polynomial Systems of Equations? I am doing a project with Artificial Neural Networks where I use standard ANNs with a different backpropagation algorithm to find ...
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0answers
25 views

Probability of stripes being distinguishable given probability density functions for each luminance

I have an image with seven stripes on it (or three stripes on a dark background), and the goal is to estimate the probability of whether they are distinguishable from one another. If the values of ...
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1answer
34 views

Are there applications of equivalent matrices?

Similar to the definition here, matrices $A$, $B$ $\in \mathbb{C}^{m\times n}$ are said to be equivalent if there exist some invertible $m\times m$ matrix $P$ and some invertible $n\times n$ matrix $Q$...
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1answer
16 views

Differentiated - Rates of change

A triangle $ABC$ is made out of an elastic piece of string. Vertices A and B are being pulled apart so that the length of the base $AB$ is increasing at of $3 \ cm \ s^{-1}$ and the height $h$ is ...
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0answers
40 views

“Work done” my a muscle during weight-lifting

I'm looking for a simplistic way to describe the "work" done by muscles during compound weightlifting movements. Perhaps not work in the precise physics sense, but an overall idea of how much the ...
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1answer
30 views

Purpose of rotation of a Function or Graph

You are able to rotate any function by an arbitrary angle around the origin using the formula, $$y\cos\theta-x\sin\theta=f(x\cos\theta+y\sin\theta)$$You can also do similar rotations for polar graphs, ...
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0answers
31 views

Area transformation

I have two rows of different types A and B. Every row is of the size 1$\times$N, where every element can be either 1 or -1. If we consider a single row of type A={-1,1,1,1,-1,1,-1,...} of size 1$\...