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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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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104 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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76 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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2answers
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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1answer
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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1answer
110 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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2answers
36 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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259 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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43 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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1answer
85 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
114 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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245 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
117 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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27 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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62 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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1answer
80 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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97 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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65 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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4answers
239 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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92 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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79 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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270 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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46 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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145 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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2answers
411 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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1answer
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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28 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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2answers
89 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: ...
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1answer
121 views

Mathematical model building with dependent and independent variables

I have been working with data and building models on data. I have developed models in regression using cubic and power series. It works fine for variables with one dependent and one independent ...
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14 views

What's the difference between Total Sobol indices and Sobol indices?

In sensitivity analysis, Sobol indices explain the importance of an input factor $X_i$ on the variance of the output $Y$ such that: \begin{equation} S_i=\displaystyle \dfrac{V_{X_{x i \sim ...
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1answer
73 views

What is the possible equation for this problem?

I am a programmer, I am in a situation that requires a mathematical equation. I just hope to know the final equation that solves the problem (step by step solution is not necessary). Of course I will ...
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1answer
55 views

What am I doing wrong? Deriving

I'm doing the same problem as the one on pg. 5 of this link: http://www.math.lsa.umich.edu/~pwn/01~ch1_solutions.pdf I got the same answer for my equation, although my approach was slightly ...
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0answers
76 views

Nondimensionalize an equation with logs

I have an equation with logs in it. Specifically the equation takes the form: $log(Y)=\alpha+\beta_1 X_1 + \beta_2 X_2 + \beta_3 X_3$ Where $X_1$ through $X_3$ are variables. The trouble is that Y ...
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99 views

Mathematical modeling- oil spill?

An oil spill has fouled 200 miles of shoreline. The oil company responsible has been given 14 days to clean up the shoreline, after which a fine of $$10/day$ will be imposed. The local clean up crew ...
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1answer
79 views

How to Prove by definition, the given process is a Markov Process?

Define the process Xt by X0 = 1, and for t = 1, 2, . . . Xt = { uXt-1, with probability p, { vXt-1, with probability 1-p where 0 < v < 1 ...
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1answer
975 views

Linear Programming Inventory Problem

I'm still trying to get used to the nature of these problems and I'd appreciate some further explanation. ...
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1answer
729 views

Linear Programming: Three variable graphical solution

A small bank offers three type of loans: housing loans at $8.50$% interest, education loans at $13.75$% interest rates, and loans to senior citizens at $12.25$% interest. Further, it needs to ...
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2answers
776 views

Financial Linear Programming Problem

I'm very new at linear programming and I'm trying to figure out a way to approach this problem below: ...
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2answers
520 views

How to create models for solving logic puzzle

this is not about getting an answer for this problem, but to create models for solve them, below I will show a simple puzzle in order to demonstrate what I mean: Lets say two friends just left a bar ...
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1answer
36 views

Assist me to obtain an equation please?

I have a plot which contain large number of points. I want to find an equation that calculates the percentage of a certain number of these points $(x,y)$, the ones having $x>5$ and $y>80$. In ...