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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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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77 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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100 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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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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996 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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798 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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796 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
547 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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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 ...
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1answer
2k views

Mathematical model of Quadcopter?

I want to know how to make the mathematical model of Quadcopter? Is there any differential equation for quadcopter? I want to simulate quadcopter as a mathematical model so I want to know how can I ...
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37 views

Discovering $2D$ to $3D$ projection

I have a two dimensional plane with $U, V$ coordinates from $0,0$ to $1.0,1.0$. The $U$ coordinate is projected to $\mathbb{R}^3$ and primarily contributes to an $X$ coordinate. However, the rate of ...
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135 views

Market uptake and market share modelling

I have been trying to figure out how to model the market uptake and share. I have a model for single product launch into a market and want to make the model able to reflect competition among two or ...
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3answers
65 views

What would the equation of this graph be?

Is this a sine graph? How would I model this graph?
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80 views

Can you please help me model this curve?

I have no idea how to model this curve. Can someone please help?
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47 views

Estimate parameters in $y=y_{0}(1-\frac{t}{\tau})e^{-\alpha t/\tau}$

Given the function $y(t)$ with two independent parameters $\tau$ and $\alpha$ $$ y=y_{0}\left(1-\frac{t}{\tau}\right)e^{-\alpha t/\tau}, $$ We have two data points (experimental data) $ ...
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1answer
225 views

Simple Non-Linear ODE - would like to find solution

In the modeling of the oscillation of a meniscus in a straw, the following non-linear ODE was derived. $$y'' = 1/y - 1$$ $y$ is a dimensionless displacement that is solely a function of time. The ...
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1answer
374 views

Intuitive meaning of right and left eigenvector

I am trying to get an intuitive understanding of the meanings of right and left eigenvectors. I guess the best thing you can do is to provide examples of application. (Examples from the field of ...
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31 views

What kind of stochastic model shall I build for x(t) if $stdev(dx)$ is linear to $dx$?

I'm building a stochastic model for a process $x(t)$. I notice that daily $dx$ and spot standard deviation of $dx$ seem not related. By spot standard deviation of $dx$ means i take 30 days $dx$ ...
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1answer
62 views

What is the relative strength of each of the players in this game?

This is a real life problem. A group of people meet once a week to play a game between two teams. Each round 2 people are randomly appointed captains. Each captain takes turns picking people to be on ...
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4answers
168 views

Enlightening Mathematical Models

What is your favourite Mathematical Model? What features make it intuitive or elegant? This question is largely inspired by an example and a desire to find other's like it. Suppose we have two ...
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3answers
65 views

How to model a doubling process with errors

An original document is duplicated. With probability $p_{err}$ a mistake is made in the copy (we will dub the resulting document the "wrong" document.) Both the original and the copy (right, or wrong) ...
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38 views

Generalization problem: Efficient area of heliosat field for concentrated solar power plants

I want to simulate a concentrated solar power plant (central receiver with heliostats) in a top-down way. All the papers I read so far were based on simulation of every single heliostat. Has anyone ...
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1answer
74 views

I'm trying to understand the solution to this simple mathematical modelling question

This is an example from Gary Chartrand's "Introductory Graph Theory" (Page 8, Example 1.5). He provides an answer without actually showing the steps or working, and I am unable to figure it out. The ...
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86 views

Eigenvalue/eigenvector calculation for linearly changed matrices

I'm looking for a way to speed up my computation that involves solving a moderate size generalised eigenvalue problem (matrices 400x400) large number of times depending on the parameter $m$. The ...
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2answers
121 views

Summation notation problem

Any help is greatly appreciated! Outline: Hermione has been thinking about the imminent return of the Dark Lord, so she has been busy packing her bag with all the items required for her survival. ...
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1answer
146 views

Operations research - linear programming help appreciated.

George Weasley, the owner of Weasleys' Wizard Wheezes, recently found that his Skiving Snackboxes have become extremely popular amongst the students at Hogwarts School of Witchcraft and Wizardry, and ...
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221 views

Why does my Barabasi Albert model implementation doesn't produce a scale free network

I'm trying to implement the Barabasi Albert model to generate some scale free network matching a power law distribution of degree. I'm using a value $m = 2$ for the main parameter of the algorithm, ...
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165 views

Interpretation of Phase Portrait

I have the following system $x'=f(X)$ of ODES: \begin{align} x_1'=& -4x_1^3(x_2-2)^2 \\ x_2'=& 2x_1^4(2-x_2) \end{align} Solving for equilibria: I got $1$ at $(0, 2)$. I plotted this and I am ...
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110 views

How to define a surface $z = f(x,y)$ with flat region at centre and sigmoidally tapering towards the edges?

How do we define a continuos function $f(x,y)$ within the bounded domain $x \in [a,b]$ and $y \in [c,d]$ so that $z=f(x,y)$ has a flat surface at the centre (flat means $f(x,y)= C$, $C$ being ...
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1answer
174 views

Finding the jacobian of a differential system with a piecewise function

My system: $$\frac{\mathrm{dx} }{\mathrm{d} t}=-ax^2+y^2-\gamma z$$ $$\frac{\mathrm{dy} }{\mathrm{d} t}=- h(y)-\beta y $$ $$\frac{\mathrm{dz} }{\mathrm{d} t}=x+h(y)-\beta z $$ where $h$ is the ...
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2answers
178 views

Invert this function $y=(1-x)e^{-x}$

Consider the fucntion $f:\mathcal{R}\rightarrow \mathcal{R}$ given by the rule $ f(x)=(1-x)e^{-x} $ Now I want to invert this function(not just for fun but I have a data that seems to fit this ...
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123 views

Given average network diameter, how many nodes are three hops away.

The University of Milan found in 2011 that everyone on the Internet was, on average, 4.74 steps away from anyone else.. is that information sufficient to answer this question: What proportion of ...
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75 views

Closed-form solution

I wrote down this equation which is the mathematical model of a system. Is there any way to get $V_c(t)$ in a closed-form expression? $V_c(t+d) = V_s \cdot U\left(V_r ...
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129 views

How to solve the advection equation with spiral motion

The advection equation is : $$\frac{\partial f(x,y,t)}{\partial t} + \nabla_{(x,y)} \cdot (A f)= 0$$ With initial condition $f(x,y,0) = f_0(x,y)$. If the vector $A$ is constant, ie. $A = ...
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42 views

How to visualize a function to aid in optimization?

I am working on minimization of a function with more than two parameters. I want to see variations, local extremes, saddle points, etc. of this function to get some idea of how is this function in ...
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1answer
174 views

Euler angle in ellipsoid rotation

I am modeling an ellipsoid tumbling in a flow field. I have derived an expression for the Euler angle $\phi(t)$ of the rotation in the $x$-$y$ plane as a function of time, but its range is only $\pi$, ...
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1answer
37 views

Predicting time t given time t-n

..Hi, Everyone! I'm having a bit of trouble with a statistics/forecasting problem and I could use some help. I have temperature measurements for each hour of each day for the past 10 years. Given the ...
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18 views

simplifying equations from model

I'm using the community land model (CLM) to do some university work and I'm trying to understand some of the equations that go into the model, one example is: $$ ...
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2k views

Examples of types of mathematical models

I am a student currently doing a course on modelling and simulation. I came across the classifications of mathematical models and studied that they can classified as static or dynamic, deterministic ...
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41 views

Linear Fit Issue

Consider a quantity $Q$ that changes as a function of time. The function $Q(t)$ is not explicitly known. We know that $Q(t_{0})=Q_{0}$. Assume for $t-t_{0}\le\epsilon$, we have a method to estimate ...
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2answers
143 views

Request for reference and technical support

I am going to write my master thesis in order to become a teacher of mathematics (with second subject business management). Supported by the ERASMUS program I have the opportunity to do this in ...
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94 views

Math model - constrain GDP given different growth rates of industries

ideas needed to model national GDP given different sector growth rates subject to some contraints Given: GDP equations for $n$ industries depend on growth rates and time i.e. $g(r_1,t), g(r_2, t), ...
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1answer
86 views

Statistics on three variables/factors

I have what is probably a simple problem. I'm trying to say something about sells of candy bars. I got data of sells for a population of children. There are three parameters (factors) to this data: ...
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1answer
167 views

Edge weight function for graph instance of scheduling and allocation problem

I have difficulties developing a proper (non-scalar) edge cost function $c_e$ for my resource scheduling problem, which I mapped into a graph problem. Processes $P_i$ need resources $R_i \in ...
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0answers
54 views

is possible to deduce a formula for vaccination coverage from Whittle threshold theorem?

I am reading the article Application of Whittle’s stochastic threshold theorem to a chickenpox outbreak and I can't understand the meaning of the term "intensity" in the Whittle threshold theorem. In ...
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1answer
746 views

True Velocity and Heading

An airplane flies at $670$ MPH directly northwest. Wind blows at $70$ MPH from the west (i.e the wind is blowing towards the east). Determine the true velocity and heading of the plane. Steps: ...
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75 views

Modeling gravity field with finite elements

Well, my question is rather from applied maths area, not pure mathematics, so I am not sure that it's a place on this board for one. I want to solve a direct gravity gradiometry problem on 3D ...
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60 views

Acceleration of series convergence

everyone! I am currently struggling with following problem: compute the series $$ \sum\limits_{m=1}^{+\infty}\frac{1}{m}\sin(m\alpha)(\cos(m\beta_1) - \cos(m\beta_2)) $$ and $$ ...
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70 views

How to define an objective function that conveys the concept of selecting the best elements in a set

Consider a set of tasks $\mathcal{T} = \{t_1, \ldots, t_I\}$. Consider also a set of workers $\mathcal{W} = \{w^1, \ldots, w^J\}$, where each worker $w^j \in \mathcal{W}$ is associated with a value ...
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Question regarding the projective models of the anti-de-Sitter spaces and good online references for learning them from the scratch? (Specifics below)

As my title says above, I am trying to find answers to and also good online reference where I can find complete description of projective models of hyperbolic space, de-Sitter space and anti-de-Sitter ...