A mathematical model is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modelling.

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Finding Percentage Contribution of a Variable in an Equation

I have an equation, for example: $$ y=a-b+c $$ I am actually confused how exactly to find the contribution of the variables individually to the entire equation. Due to the negative sign, following ...
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58 views

How does one model independent trials in statistics.

In my probability class, we covered the proof of the following result, known as the "strong law of large numbers": Theorem. Let $(\Omega,\mathscr F,P)$ be a probability space, $\{X_n\}_{n\in\mathbb ...
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229 views

Sum of the area of all the rectangles in a rectangular

We have a rectangular shape with the size n × m meters is divided into rectangles of size 1 × 1 meters. Question: Sum of the area of all the rectangles that can be seen in that rectangular is how ...
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145 views

How to derive thresholds from a pooled sample of values

Question: The context of this question is actually finance, however the question itself is a statistical issue. Suppose I have the following expression: $$\rho = \frac{2\bar{x}}{(s^*_x)^2}+1 \ \ ...
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61 views

A doubt about Evans and Jovanovic (1989) economic model for entrepreneurs with credit constraints

In Evans and Jovanovic (1989) you will find a model for entrepreneurs with credit constraints. The part that is important for my question follows. Here it is the production function and the income ...
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23 views

propability of largest samples of repeated random divisions

I have a bunch of numbers $A_1=\{a_{1,1},\dots,a_{n,1}\in\mathbb R^+\}=\{1,\dots,1\}$, that get multiplied by independent uniformly $[0,1]$ distributed samples, e.g. $a_{i,2}=X_ia_{i,2}$. This process ...
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45 views

Discrete Systems - fish population modelling question on derivation of the model

I am currently reading 'Introduction to Non-Linear Systems' by J Berry and on page 112 there is an exercise (question 5) which I don't understand, it is: The population of fish in a large lake has ...
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61 views

Scaling a cup to have a certain filling volume

I created a cup in Autodesk Inventor using lathe/rotation, ie I defined the profile and rotated it around an axis. I measured it's volume. By using Patch and Sculpt I filled the inner volume(which ...
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26 views

Prediction model from input/output observations

I want to make a prediction model for the following transformation $f:\mathbb{N}^N \rightarrow \mathbb{R}^M$ $N$ is around 20 and vectors $\mathbf{v} \in \mathbb{N}^N$ are sparse with $\sum_{i=1}^N ...
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34 views

How to find $X_i$ from this equation

Suppose $X_i=\nu_i+\frac{m-i}{m}X_{i+1}+\frac{i}{m}X_{i-1},\quad 1\le i\le m$ where $X_0=X_{m+1}=0$. I need to find an expression for $X_i$ in terms of $v_i$, $i$, and $m$. I know how to find it ...
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46 views

Solving interpolation between line and quadratic functions

I have two functions with known coefficients as follows: $$ f_1(x) = x^2 -2x + 2 $$ $$f_2(x) = 108 x - 206 $$ and I know that $$ (1-z) f1(x) + z f2(x) = 0 $$ $$ (1-z) f1'(x) + z f2'(x) = 0$$ ...
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42 views

Turing instability in social networks

I'm doing research on this topic from Mathematical modeling. I was wondering if anyone could recomend any literature that can help me with this. All I need is application of this model on social ...
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1answer
45 views

probability with Poisson distribution

according to the experience of a bank staff,there are 2 old paper money IN EACH MONEY PACKET.if the number of old papers money,in each money packet,follow poisson distribution, a)what is the ...
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47 views

Poisson like distribution in $\left(\sum_{k=0}^{n-1} x^{2^k}\right)^{n}$?

Given $y_{n}(x)=\left(\sum_{k=0}^{n-1} x^{2^k}\right)^{n}$. An example ($n=5$) may look like $$ y_5(x)={x^{80}}+5 x^{72}+5 x^{68}+5 x^{66}+5 x^{65}+10 x^{64}+20 x^{60}+20 x^{58}+20 x^{57}+20 x^{56}+20 ...
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119 views

The intuitive understanding of $\sqrt{x}$ to model “inversely proportional / inverse square”?

Can someone lay out what the concept I am trying to convey below in a more clear manner? Square root functions are sometimes used to model non-linear relationships. The value of a square root is ...
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29 views

change the differential equation $\frac{\partial h}{\partial t} =- \frac{\partial uh}{\partial x} - \frac{\partial vh}{\partial y}$ into matrix form

I am modelling the shallow water equations. One of the equations is \begin{equation} \frac{\partial h}{\partial t} =- \frac{\partial uh}{\partial x} - \frac{\partial vh}{\partial y} \end{equation} ...
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99 views

Solving $f'''+\frac{n+1}{2}ff''-nf'^2+n=0$ with $n=e^\pi$

How do I solve $$f'''+\frac{n+1}{2}ff''-nf'^2+n=0$$ with $n=e^\pi$ or arbitrary $n$? This equation occurs in my model for the time evolution of the value of Bitcoin.
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77 views

SIR Models - interpretation (epidemiology) - help!

I am doing a project on modelling the spread of diseases and am using a SIR (susceptible, infected and recovered) model to do so. I need help interpreting this plot: What does this plot say about ...
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30 views

Category modeling in quantitative Linguistics

I'm currently doing some studies on a new quantitative unit in Linguistics, the so called Motifs. A Motif is a ascending (or descending) sequence of quantitative linguistic properties. For a better ...
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66 views

Modeling dependency between two variables

I want to model the dependence between two variables. Now there are a few ways to do this, for example writing one variable as a function of the other or using correlation. I have also looked into ...
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49 views

Calculate average speed with unknown variable accelaration

I am in the middle of a vehicle tracking project where I have to calculate the distance traveled by the vehicle in a given amount of time. Data I am getting: ...
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112 views

Are my linear program equations correct?

Here's the problem: "An electronics company has a contract to deliver 21,475 radios within the next four weeks. The client is willing to pay 20 dollars for each radio delivered by the end of the first ...
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38 views

Simpler way to display mathematical model?

I am developing a mathematical model for the power usage (watts) of a computer device against its percentage of CPU load. So far I have: ...
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268 views

Biology: Wright-Fisher model of genetic drift

In evolutionary biology (in population genetics to be more accurate) exists the concept of genetic drift. It describes how an allele (gene variant) (that has no advantage or disadvantage in terms of ...
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45 views

How to linearize a Maxmin constraint

Currently I have this linear programming model: Max_a(X) s.t. Max_c(Min_b(F(a,b,c))) <= some constant *Max_c meaning to maximize the following equation by just changing c, and the same applies ...
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90 views

Generalized Mechanism Design, Stanley Reiter diagram and Vickrey Auction

I am trying to learn this new topic, Mechanism Design and stumbled upon the "Stanley Reiter" diagram (see the top-right side on the page). I have also learned that the Second Price Sealed Bid ...
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1answer
123 views

Converting if else constraints into linear ones

I have the following two constraints: $$ x_1 \leq x_2 \leq x_3 \qquad \mbox{if } x_1 \leq x_3 \\ x_1 > x_2 > x_3 \qquad \mbox{otherwise} $$ Is there a way to get rid of the two conditions and ...
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263 views

How to model an aviation holding pattern mathematically?

A standard aviation holding pattern has four sections, each of which, in windless conditions, takes one minute to fly. The first is the inbound leg, which is the only one for which precise ...
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32 views

Modeling 4 people going to same place over 3 different places for at least 5 days

I'm trying to model a linear programming task with the condition 4 people going to the same place among 3 different places for at least 5 days. I have the variables for the time spend each person in ...
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2answers
125 views

Ideas about an Ordinary Differential Equations research work (University level)

Good afternoon to everyone, I need some ideas about a Ordinary Differential Equations research work. It is for the ODE subject that I am doing at my Mathematics degree in my University. They asked me ...
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28 views

Speed formula and least square approximation

I have some questions about a formula and least square approximation I have 14 information about the speed of a fluid inside a tube, speed, position and standard deviation. I already made a graphic ...
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63 views

Using an alternate way to write a Taylor series of $f(t+\tau)$ to derive numerical integration and differentiation formulas

In chapter 9 section 3 of An Introduction to Mathematical Modeling, the author Edward A. Bender points out that: $$f(t+\tau)=\sum_{n=0}^\infty \frac{(\tau D)^n}{n!}$$ so that $$f(t+\tau)=e^{\tau ...
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82 views

Mathematical model for magic square

As I spent some time on magic squares, it seems like the magic squares can be formed only with a odd number of rows/columns? Is it that.? If so why? is there a mathematical model that explains magic ...
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2answers
44 views

What are the limitations of modelling a piano sound with the 'play' option of the software Wolfram Mathematica?

'Play' is an input availabe on Wolfram mathematica, which shows how a wave would sound and I am asking myself what the limitations of this input are, in what aspects it does not represent 'real' sound ...
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63 views

Financial mathematic with Feynman-Kac

I have a really big task in financial mathematics and a small part of it (to set up the problem), I need to write a PIDE (the Feynman-kac) where we estimate options with jumps. It is derived from the ...
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1answer
107 views

General solution to Wright-Fisher model - Diploid selection

Wright-Fisher models are classical theoretical results in evolutionary biology. There are two discrete time models, one for haploid selection and one for diploid selection (the meaning of these models ...
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73 views

General solution to Wright-Fisher model - Haploid selection

Wright-Fisher models are classical theoretical results in evolutionary biology. There are two models, one for haploid selection and one for diploid selection (the meaning of these models does not ...
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244 views

Mathematics for Computer Science

What are the various forms of mathematics that may be required in a computer scientist career? Say someone one day wants to prove things like P vs. NP, and meanwhile be writing advacned algorithms for ...
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50 views

Preparation for modeling in grad school

I'm currently a first year grad student in an applied math program. I really love modeling, but everything in my modeling course is flying way over my head. Where can I look for a decent ...
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93 views

Understanding degrees of freedom in a standard linear model

So I'm taking a class in applied regression analysis right now, and it is being taught with no theory whatsoever. I am TOTALLY lost on the concept of degrees of freedom. All I've been told / can find ...
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2answers
83 views

Using derivative to estimate change overestimates change between two states

I have a profit function in which revenue is given by the state of a variable y at each point in time t: R=y[t]-y[t]^2 and costs depend on the change in y from the previous state so that large changes ...
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293 views

Why the $Vega$ of the Black Scholes Model is at its maximum for at-the-money options?

In my course script, it is said that the Vega of the Black Scholes Model is at its maximum for at-the-money options. In order to verify this, I did the following calculations: In the Black Scholes ...
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47 views

Linear Programming- are my equations correct?

A dairy produces cheese, milk, sour cream, and yogurt. Suppose: Every 100 lbs of cheese requires 2 units of plant capacity, 3 workers, and 7 gallons of culturing additive, and gives $1,500 in ...
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149 views

Simple 2D Voronoi Diagram Question with 3 Points

This is a HW question for the course MAT480 (Mathematical Modelling I) at Athabasca University. I'm taking this distance course for credit in order to graduate sooner. Having a hard time putting all ...
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How can I prove that assuming a power law forcing to drive incompressible turbulent flows leads to a scale invariant turbulent energy spectrum?

To maintain incompressible turbulence, the incormpressible Navier Stokes equations $$ \frac{\partial u_i}{\partial x_i} = 0 $$ $$ \frac{\partial u_i}{\partial t} + u_j\frac{\partial u_i}{\partial ...
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172 views

Formalizing quantities that have units

This is a bit of a weird idea, so any advice on how to make it clearer would be welcome. Please leave a comment. Suppose we're using mathematics to study electronic circuits. We're probably ...
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425 views

Time Series: Expected value autoregressive model

I have some trouble solving the following question: Given is model $X$: $X_t = (W_t -1)*W_{t-1}$ Where $W_t$ is the stationary process: $W_t = p*W_{t-1} + Z_t$ Where $Z_t$ is distributed ...
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62 views

How do you determine mathematical “weight” for abstract concepts? [closed]

I hope this is a good question for this community because it has been circling my head for a lot of time. How can I determine how much an abstract concept weighs in a mathematical formula? Let's ...
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29 views

Can i form equation(formula) out of input and output?

I have set of 12 (x,y) where f(x) = y. Is it possible to find out f(x) in terms of x like f(x) is (x*x)-2x+3 from just those 12(x,y) pairs? I do not mind if whatever will be the output for 'x' other ...
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95 views

Simplex and mathematical models: Truncating expresion to 0 if negative

Is there a simplex compatible way to model an expression that "truncates" (sorry for not finding a better word for it) the value to 0 if it turns negative? I have the following restrictions: ...