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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How many additional crews should be brought in to minimize the cost of an oil spill?

An oil spill has fouled $200$ miles of Pacific shoreline. The oil company responsible has been given $14$ days to clean up, after which a fine will be $10000$ \$/day. The local cleanup crew cleans $5$ ...
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29 views

Linear algebra of state space representation won't be linear (superposition theorem)…

After answering a question about calculating the state space representation of a circuit with 3 sources in it (the circuit is there), I had a doubt - while checking, it became clear there is something ...
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11 views

What is the correct term for the equations which comprise a mathematical model?

I have a mathematical model constructed by myself and my supervisor. In writing my report do I refer to the equations that make up this model as "constitutive equations", or is there another term ...
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19 views

Modeling predator/prey pursuit behavior?

I want to program a model of predator/prey pursuit behavior on a 2D topographical map (not predator/prey diff. eq. model!), primarily for fun, but I'd love to know if there's any literature or ...
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12 views

How can i Plot Laguerre-Gaussian mode vortex by Mathematica? [on hold]

I've been using Mathematica for a few years. I couldn't plot the Laguerre-Gaussian vortex vawefron by using the Mathematica. I know i should use the Laguerre-Gaussian function in coding, but i ...
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2answers
298 views

Phase Plane Analysis

Classify the fixed point at the origin and sketch an accurate phase portrait for the following system: $$\left\{\begin{matrix} \dfrac{dx}{dt}=36x-16y\\ \dfrac{dy}{dx}=-3x+28y \end{matrix}\right.$$ ...
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2answers
92 views

Problem in game theory related to traffic networks

I have learnt game theory for a short period of time and I am not familiar with multi-player non-zero sum games. Here is a problem from my book which I am stuck: In this road network below each of ...
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1answer
21 views

Modeling Forced Oscillations Resonance Given from Second Order Differential Equation (2.13-3)

My answer to this problem does not agree with the text's answer: $y=sin(t)-3cos(t)$ Problem to solve is to find the steady state oscillations of the vibrating system governed by the following ...
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2answers
57 views

Math theories in Game Theory

What are all the mathematical theories in Game Theory? I have taken Mathematical Modelling, including: application of linear systems, matrix operations, inverse of matrix, leontif input-output model, ...
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24 views

Maximum Likelihood Method, finding a minimum

I know that to find the minimum of a function i have to calculate its derivative. It's fine with me, i can do it but.. what is that o_O? OK, after going through my textbook, The Maximum Likelihood ...
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18 views

Saturation Modeling in ODE45

I have a machine with an arm that can move in a linear one dimensional way. There are 3 limits on the arm: The arm has boundary for its location $(x_{min},x_{max})$ The arm has limit on its velocity ...
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12 views

Linearizing the sum of product of a binary and a continuous variable

Now suppose we have this expression $z = \sum_jA[j] * x[j]$, where $A[j]$ is a continuous variable and $x[j]$ is binary variable. $A[j]$ is bounded below by zero and above by $AM[j]$ , so I know how ...
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13 views

Positivity of compartments in epidemiological model

Given the following dynamical model (system of ODEs): \begin{array} $ \frac{dA}{dt}=\Lambda-\mu A-\beta(C+D+E+F)\frac{A}{N}-\tau(B+D)\frac{A}{N} \\ ...
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2k views

Mathematical Modeling of Real-World Situations

I was considering how to model the following problem mathematically and was wondering what you thought the best way to do it is. "A takes 1 minute to cross a bridge, B takes 2 minutes, C takes 5 ...
2
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1answer
31 views

Arrange soccer fixtures with correct home - away alternation for each team

I am trying to do as the title says. I have 10 teams in the same group. Every team must play the rest once each but each of them will always alternate home and away. This means that if they play at ...
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1answer
19 views

Matrix representation from a linear function

I'm studying an opinion formation model [1] where the main rule is: $p^{(t)}_i = \frac{p^{(0)}_i + \sum_{j \in N(i)} w_{i,j} p^{(t-1)}_j}{1 + \sum_{j \in N(i)} w_{i,j}}$ Now, I'd like to represent ...
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10 views

MLGetFigure for copy Matlab figures into Excel spreadsheet [migrated]

For to copy several error histogram () figures (by a loop) into an Excel spreadsheet, I try use MLGetFigure; but I get "Undefined function ('MLGetFigure') for input arguments of type 'double' ". ...
2
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1answer
336 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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1answer
35 views

Help me find the function behind this data?

I have a function $f(x, y)$ and I have another (non-mathematical) algorithm capable of inefficiently generating the exact same results as in in a 'brute force' manner. Since I have been able to find ...
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2answers
88 views

Applications (“in everyday life”) of graph theory

EDIT another idea someone gave me was to consider flows in a network that would not only depend on the node at the beginning and at the end of a vertice but also about the vertice itself, like a ...
2
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1answer
331 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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1answer
1k 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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20 views

A prove for information restoration with 2 schedules that delete information

What kind of mathematics or technique do I need to use the following? Just pointing me in the right direction is also helpful as I love mathematics but I am not so good at it. It's a problem I have ...
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2answers
825 views

Sine and Cosine Models

This is a general question about modeling the seasons using sine and cosine functions; I am trying to use sine and cosine to model cyclic behavior in sales due to the seasons (spring, summer, fall and ...
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30 views

Understanding mathematical syntax in SO(3) - Part II

In a paper I found in internet there is a relation about mapping a matrix into a vector and viceversa. One question has been already kindly answered here, but since I'm new to this kind of syntax I ...
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1answer
32 views

Help for understanding a vectorial equation found in a paper.

Trying to implement a code for the algorithm described in this paper I found something not very clear to me that leads me to misunderstand the whole concept. To calculate the vector $\vec{b_{3d}}$ ...
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1answer
54 views

Need some help on petri nets?

Here's the question: $\qquad$ How do we go about doing this ? I have very little knowledge on petri nets. Can someone answer it for me ? (And regarding the program part , just give me an idea on ...
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1answer
45 views

Understanding mathematical syntax in SO(3)

In this paper, pp. 2, I found the following differential equation system and a statement: There are two things not clear to me: the hat map symbol seems to make mathematical symbolics shorter and ...
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1answer
36 views

Neural networks and mathematical modelling

Could you point out some reference books [accessible to an undergrad math student] that deal with the mathematical modelling aspect of neural networks?
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25 views

time varing Gaussian distribution

does there exist time varing Gaussian model? To be sepecific, a 2-D Gaussian model whose mean and covariance matrix is varing with another parameter called time. The $\mu$ (mean) and $\sigma$ ...
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1answer
99 views

How can I model the number of insects in a house?

I really don't know if this question applies here or if it makes sense, but I'm curious as to whether these ideas are commonly used. Imagine you are in a room, this room has holes, where bugs may ...
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1answer
33 views

linear programming problem - how much additional resources should I buy?

I have the following linear optimization problem: Maximize $$\sum_{i=1}^{n}x_{i}B_{i}$$ subject to the constraints $$a_{11}x_1+a_{12}x_2+\cdots+a_{1n}x_n \le l_1$$ $$...$$ ...
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1answer
46 views

How do impulsive differential equations work? Can you provide an example?

I have heard of impulsive differential equations being used in some epidemiological models of infectious disease. I haven't heard of them before in my math education, and I was wondering how they ...
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551 views

Geometrical construction for Snell's law?

Snell's law from geometrical optics states that the ratio of the angles of incidence $\theta_1$ and of the angle of refraction $\theta_2$ as shown in figure1, is the same as the opposite ratio of the ...
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1answer
20 views

How to model function with unknown exponents?

I know the Cobb-Douglass function which describes the production quantity: $$Q(K, L) = A \cdot K^\alpha \cdot L^\beta$$ Also I do know multiple assignments of K ...
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3answers
45 views

Smooth function to model a well or pit

In order to solve a Physics problem, I have to model an axisymmetric well or pit on a plane. I am looking for a function $f(x)$ that is smooth and monotonic in the domain $(0,1)$, where the origin ...
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1answer
50 views

Interperate Jacobian Determinant - Stability of Equilibriums

In my SIR model, I have the following Jacobian Matrix \begin{align*} J =\begin{bmatrix} -\alpha I & -\alpha S & \zeta & 0 \\ \alpha I & \alpha S - \beta - \rho & 0 & 0 \\ 0 ...
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1answer
51 views

Rayleigh-Bénard convection

I have a nondimensionalized linear perturbation system relevant to the appropriate pure conduction solution for Rayleigh-Bénard convection in upper planetary atmospheres under the compressible gas ...
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1answer
50 views

Assistance with Bayesian Random Effects and Mixed Effects Models

I am looking to build either a random effects or mixed effects model for a project I am working on, but have had trouble finding good sources and understanding the general structure of the model. ...
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0answers
12 views

Has anyone come across a non-constant population SIR model with infected birth?

I've come up with a seemingly new type of SIR model for one of my classes which allows for non-constant population and infected members to birth more infected members (such as is the case for many ...
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1answer
32 views

Estimating number of slaves imported before 1790

I have a statistics problem I am having a hard time figuring out how to model mathematically. The 1790 US Census counted 697,681 slaves and 59,196 free Africans in the United States. (A) assume ...
5
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1answer
548 views

How did Target figure out a teen girl was pregnant before her father did?

First of all I do not have a mathematics degree only a B.S. in finance so please take that into account when writing an answer. Generally what type of mathematics is involved here? And specifically ...
0
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1answer
28 views

Establishing a stable state withing a discrete dynamic model

Given the following discrete dynamic model: $P_0=360$ and $R_0=80$ and $t[0,200]$ $P_t=1,18*P_{t-1}-0,002*R_{t-1}*P_{t-1}$and $R_t=0,86*R_{t-1}+0,0004*P_{t-1}*R_{t-1}$ One can rewrite the ...
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0answers
16 views

Mathematical model for MILP optimisation problem- power scheduling

I am having trouble trying to formulate a mathematical model for the problem below to solve later as an MILP problem using different optimization software. I want to formulate the model so as to ...
3
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1answer
83 views

fantasy basketball model

i'm creating a fantasy basketball model (could be used in other games too) where we can project how well a player will do against another team even when the player hasn't played against a certain team ...
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1answer
37 views

What does this determinant mean?

I have the following Jacobian matrix for an equilibrium of an SIR model $$J=\left( \begin{array}{cccc} -\text{$\alpha $N} & 0 & \zeta & 0 \\ \text{$\alpha $N} & -\beta -\rho & ...
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1answer
30 views

How to find the basic reproductive number of a discrete SIS epidemic model

I have been following a textbook called Mathematical Models in Population Biology and Epidemiology. The SIS model is given by the system \begin{aligned} S_{n+1} &= \Lambda + S_n e^{-\mu} ...
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1answer
106 views

Is this probabilistic balls-and-bins problem well-defined and is my solution correct?

Problem definition: There are $n$ bins, labeled with $1, 2, \ldots, n$. Let $X_i$ be a random variable denoting the number of balls contained in the $i$-th bin. The collection of random variables ...
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2answers
37 views

Split cab fare proportional to saving made across the board

Interesting dilemma. I've figured out how to split a cab fare 3 ways (proportional to time, mileage and equally) but I've found that when the cab fare is split proportional to time and mileage, the ...
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1answer
30 views

Split a cab fare proportional to the time everyone has spent in taxi

How would you split a cab fare proportional to the time everyone has spent in the taxi? Total journey time = 19 min Fare = $17.25 ...