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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Parabola properties assumptions

I am trying to model projectile trajectory but I'm having some trouble. I didn't realise parabolas are this complicated... I have some assumptions that I would like to be clarified. If I specify a ...
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2answers
61 views

Parabola describing projectile motion.

I am trying to create a function that will generate a parabola that describes projectile motion. Here are my inputs: The starting x-y coordinate of the throw The initial x-y velocity vector. I ...
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1answer
38 views

Questions about Disease Model

A non-fatal infectious disease divides a population into two groups: normal or ill. Assume that the average number of contacts that each ill individual has with normal individuals is $a$ multiply the ...
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1answer
48 views

Discrete Dynamical Systems & Credit Card Debt: How to solve for payment

I have the following problem, taken out of Giordano, Fox, and Horton's A First Course in Mathematical Modeling: Your current credit card balance is $\$12,000$ with a current rate of $19.9\%$ per ...
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2answers
97 views

Lotka-Volterra equations modified

Okay, so I'm just learning about the Lotka-Volterra and the question I have regards the following model: $dx/dt = x(1-y/2)$ $dy/dt = -y(1 - (x/0.8) + (x^2)/4)$ I need to state what term has been ...
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42 views

Interpretation of a model

$$ \frac{dx}{dt}=ax(x-b)(1-x)-\frac{xy}{1+cx}$$ $$\frac{dy}{dt}=-ey+\frac{xy}{1+cx}$$ Make a apropriate interpretation of this model. What I thought are: $\frac{dx}{dt}\ \& \ \frac{dy}{dt}$ are ...
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16 views

Indicate whether each of the following equations is linear or nonlinear.

Indicate whether each of the following equations is linear or nonlinear. If linear, determine the solution; if nonlinear, find any steady states of the equation. $x_n=(1-\alpha )x_{n-1}+\beta x_n$ ...
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86 views

A mathematical abstraction of colours?

Does any formal system exist built upon the mechanics of Additive Colour Theory? Additive Colour Theory is the description of the behaviour of the visible spectrum of light as it combines-the ...
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1answer
41 views

Critical points of quadratic forms

Let $A$ be an $n\times n$ symmetric matrix, let $b$ be an $n$-vector, let $c \in \mathbb{R}$ and set $Q(x) = 1/2 x^T Ax-x^T b+c$. Prove that $x_0$, defined as a solution to $Ax_0=b$ is a critical ...
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1answer
26 views

find the maximum

I'm stuck in this problem (Instructions and my work is showed on the picture below) I just don't know what to do right after find the values of D, to prove that the maximum of F(D) is attained at the ...
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0answers
27 views

Modeling Question: Finding a Fit for the form W=kl(g^2)

I have a modeling question on my assignment that I am unsure about. I am given a set of points $W, l,$ and $g$. I have to find some $k$ for the data to optimally fit $W=klg^2$. At first, I tried ...
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1answer
37 views

Lotka-Volterra coordinates transformation

I would like to ask the following: Given a Lotka-Volterra predator-prey system, \begin{align} & \frac{dx}{dt}={\alpha}x-{\beta}xy \\ & \frac{dy}{dt}=-{\gamma}y+{\delta}xy \end{align} , with ...
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2answers
82 views

Lotka-Volterra First Integral and Fixed Point

I have the following problem that I am dealing with, quite a long time, I must say. Let us assume that we have a predator-prey, Lotka-Volterra system given to us by: \begin{align} & ...
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1answer
119 views

Differential Equation - Blood Alcohol

Let C(t) be the concentration of alcohol in a person's bloodstream. We propose a mathematical model which states that, once a person stops drinking alcohol, C decreases at a rate that is proportional ...
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1answer
34 views

Determining probabilities Markov Chain

If I have a Markov Chain $X_0, X_1, X_2 \dots$ that has a transition probability matrix $ \textbf{P} = \matrix{~ & 0 & 1 & 2 \cr 0 & 0.3 & 0.2 & 0.5 \cr ...
2
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1answer
110 views

Modelling Concentration

I'm currently doing a research project that involves modelling E. Coli growth in a wetland. The data I've been given is the E. Coli mass concentration ($mgC/L$) at various times throughout the two ...
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1answer
15 views

For the three measurements b=0, 3, 12 at times t=0, 1, 2 find the best parabola y=C+Dt+E$t^2$

So I know how to do least squares regression using matrices to solve for Ax=b. I simply do $A^TAx=A^Tb$. However I don't really know how to account for the second power in a typical parabola ...
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1answer
26 views

What is the least squares solution given a line passes through original and following points?

So I am looking for the line y=Dt through the origin that fits the data y=4 at t=1, y=5 at t=2 and y=8 at t=3. This is what I have done so far. I know the three equations that are supposed to be ...
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1answer
41 views

Write the system of equations describing the populations in this system…

In a closed ecosystem, we have that Frogs,represented by $F(t)$, eat fleas, represented by $f(t)$, and the fleas eat fungus, represented by $g(t)$. Assuming that fungus grows at rate A, fleas eat the ...
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1answer
60 views

Model a chemical phenomenom

I have a chemical phenomenon to model for my research. I'll try to be clear while explaining my problem. I created little molecules (let's call them "emitters"), which emit a signal. When the ...
2
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1answer
94 views

What is the process of nondimensionalizing an equation?

Question: I need to scale time by $\frac{1}{I}$ and species by $P$ for the following equation $\frac{dS}{dt}=I(1-\frac{S}{P})-\frac{ES}{P}$ where P - Size of the source pool of species on the ...
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1answer
12 views

Random Variable Modeling

I am trying to understand how to model a random variable. So using a biased coin with $P(Head) = q$. If I am to generate a random variable $Y$ that is equally likely to be either a or b depending on ...
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1answer
18 views

Finding the minimum value of $1/2 (x_{1}^2+x_{2}^2)-x_{2}b_{2}$

I am trying to find the minimum value of the following: $1/2 (x_{1}^2+x_{2}^2)-x_{2}b_{2}$ I know this is equal to: $1/2 ([x_1 x_2] Id [x_1 x_2]^T )-[x_1 x_2] [0 b_2]^T$ To find minimum we have to ...
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19 views

What is the proper name of a model that takes as input the output of another model?

Thanks in advance for the help. I am writing a paper and for the life of me can't remember the proper term for a model that works as follows. rawData -> model1 -> outputModel1 -> model2 -> ...
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1answer
54 views

Online resources for Mathematical Modeling

I'm taking mathematical modeling this semester in college and usually there are resources online to read examples and see another point of view but I'm not able to find it for this class. Can anyone ...
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1answer
38 views

Calculate migration probability matrix from distances matrix

Imagine the world-wide human populations as a series of interconnecting populations. The distances between any two populations is given by the following kind of matrix $$ \begin{matrix} ...
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1answer
89 views

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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1answer
116 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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0answers
15 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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1answer
117 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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46 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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2answers
114 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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1answer
85 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
27 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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1answer
47 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
267 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 ...
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166 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
30 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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0answers
54 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
42 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 $\vec{b_{3d}}$ ...
0
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1answer
56 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
66 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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26 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
45 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
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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
24 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
50 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
68 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
65 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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23 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 ...