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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what are the principal applications of symmetric matrices in physics giving examples of it's applications?

symmetric matrix is useful in many areas of sciences such as : physics . i'm very interested to know the suspect and some interesting applications of " Symmetric" matrix in physics or any branch ...
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Non-STEM applications of Calculus? [on hold]

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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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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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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2answers
58 views

Applications of $\mathbb{Z}/n\mathbb{Z}$ [on hold]

I would like someone to proof me this claim and give me its applications in mathematics if it's not a convention. Claim: for all positive integers $n$, the ring $\mathbb{Z}/n\mathbb{Z}$ is domain if ...
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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 ...
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11 views

1-D Motion , direction of air resistance in N2L

I cant seem to understand why mcx(dot) is not positive on the RHS of ma=F because it is acting in the same direction as the weight, but the answer doesnt agree, please help, I can get the DE but with ...
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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 ...
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35 views

PDE complex boundary condition

My attempt to this question was setting T''-lambda T=0 and try lambda=0, >0 and <0. However, I do not seem to have sufficient information to determent which case have non-trivial solution ( since ...
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1answer
29 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 ...
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1answer
22 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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12 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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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
68 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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35 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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12 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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10 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
58 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
35 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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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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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 ...
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1answer
54 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 ...
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2answers
63 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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78 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 ...
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60 views

Moment of inertia : How to find out perpendicular distance?

The boundary of a thin plate is an ellipse with semiaxes a and b. Let L denote a line in the plane of the plate passing through the center of the ellipse and making an angle k with the axis of length ...
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1answer
56 views

System of equations and the Brouwer's Fixed-Point Theorem.

Let's consider the following system of equations: \begin{eqnarray}{ e^{xyz} = \frac{x}{\sqrt{e^{2xyz}+1}}\\ \cos(x+y+z) = \frac{y}{\sqrt{e^{2xyz}+1}}\\ \sin(x+y+z) = \frac{z}{\sqrt{e^{2xyz}+1}} ...
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560 views

Honest application of category theory

I believe that category theory is one of the most fundamental theories of mathematics, and is becoming a fundamental theory for other sciences as well. It allows us to understand many concepts on a ...
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Application of Riesz Spaces (k/a $K$-Lineals or Vector Lattices ) to Mathematical-Economics?

From Wikipedia: "C. D. Aliprantis was a Greek-American economist who introduced Banach space and Riesz space methods in economic theory." What applications are there?
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What are some real life applications of least squares problem?

I'm looking for some applications that require solving the least square problem. I know polynomial fitting is one of them, but sure there are many others. Thanks
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Learning to Apply Mathematical Concepts ( i.e. function modelling, etc.)

Firsty, I want to state my situation clearly. I am one of those students who are incredibly good at absorbing mathematical concepts but without knowing how to apply them. I get A's but it is growing ...
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Kahler-Einstein Metrics in Physics - Topic Suggestions

I am hoping to get some topic suggestions for a presentation I have to give in a couple of weeks. The course the presentation is for is called Kahler-Einstein metrics. I would really like the ...
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36 views

partial differential equation applicational problem

As a Maths student with not much knowledge in physics, I dont understand how the "string" can be "cut" into half at x=L/2. Also, how many initial conditions(data) does this question have apart from ...
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Why are noetherian and artinian modules important?

As a TA I was recently asked to give the students an introduction to two (quite related) concepts that are new to me, noetherian and artinian modules. I intend to prove the characterisation theorem ...
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Determine the multi-dimensional relationship given the data

I have a dependent variable - A and 3 independent variables, H,V and N I have a data for all the variables and dependency relationship is based on my operational knowledge. I'd like to know what ...
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28 views

application of kinematics and the rates of change

A ladder 20 feet long leans against a vertical building. If the bottom of the ladder slides away from the building horizontally at a rate of 3ft/sec, how fast is the ladder sliding down the building ...
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Finding the rate of rising water.

Water is pouring into a conical tank at a rate of 8 cubic feet per minute. If the height of the tank is 12ft, and the radius of its circular opening is 6ft, how fast is the water level rising when ...
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2answers
62 views

Show that the cubic equation has one real roots

Show that $x^3+ax+b=0$ has a) only one real root when $a>0$ b) at most only one of it's roots are in $(-\sqrt{-a/3},\sqrt{-a/3})$ when $a<0$. For a) I supposed that it had two real roots ...
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1answer
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book to learn calculus by examples and real world applications

Don't know if it's the right question in this section I'll ask it anyway. When I study math I barely understand theorems, but after being given the examples I can understand the theory behind it. The ...
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1answer
44 views

The wave equation with forcing function

What would the solution to this problem be? $\frac{1}{x} u _t - (x u_x )_x = \frac{1}{x} \ln{x} \quad 1<x<e \quad t>0 $ $u(x,0) = \sin{(\frac{\pi}{2}\ln{x})} \quad (1<x<e) $ ...
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Name and application of a matrix encryptation method

The textbook I am using for teaching has a short section on encryptation using matrix as an application of matrix theory. The method is as follows: The persons that are allowed to encode/decode ...
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Engel Curve in Economics

I have a utility function in the form $U = B^{.67}Z^{.33}$ I am supposed to find an Engel curve assuming that the price of goods B and Z are $P_b$ and $P_z$ respectively with income level $Y$. I can ...
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Is Principal Component Analysis applicable to this type of situation?

I'm trying to model the response of ant populations to pheromones in this way: The ants are simulated as Self Propelled Particles with internal energy. They undergo acceleration due to their internal ...
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2answers
76 views

Determining how long a body has been dead using the number e

I have recently seen a quote about determining how long a body has been dead: “Dead bodies lose heat exponentially, and therefore e can be used in an appropriate equation to determine how long ...
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What problems are related with the following type of FDE with delay?

Consider the following class of functional differential equations with delay: $$\begin{align} \frac{du}{dt} &= F(x,t,u(x,t),u_{t,x}), & (x,t) &\in [a,b] \times [0,T] \\ u(x,t) &= ...
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4answers
87 views

How does Volume work with integration?

Using a cross section suppose, as described here: Area formula Paul Notes Suppose this is: $y = f(x)$. He says the volume is: $$\int_{a}^{b} A(x) dx$$ But how does area over that interval ...
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1answer
44 views

Mixed Integer Linear Programming: Construction Rods

I have an interesting problem involving linear programming. The problem is the following, I have 4 different kinds of rods (rod sized found in the local market): 9m rod 11m rod 12m rod 15m rod ...
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1answer
22 views

Volume of Revolution $f(x) = x^2$

Suppose you are given $y = f(x)$ I want to use double integrals, instead of the traditional washers. Suppose even better, $f(x) = x^2$ Find the volume of $f(x) = x^2$, $x = 0$, $x = 4$, $y = 0$ ...
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How is it possible to change the pitch and the tempo of an audio track independently of each other?

If you slow down a turntable or cassette-player, both pitch and tempo are decreased. How is it possible to change one without affecting the other?
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Question about uniform wire and its application to find centroid

A uniform wire has the shape of that portion of the curve of intersection of the two surfaces x^2+y^2=z^2 and y^2=x connecting the points (0.0.0) and (1.1.square root 2) Find the z-coordinate of its ...
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Sturm-Liouville problem with vibrations - probably easy for most.

Trying to do this one... A model for the transverse vibrations of a stretched string with variable density ρ and tension τ (both continuous and strictly positive on the closed interval [0,l]): PDE: ...