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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Differentiation of unit force vector

I was reading a paper and don't know how the following was derived. Given that $f = \begin{bmatrix} \ddot{x} \\ \ddot{y} \\ \ddot{z} + g \\ \end{bmatrix}$ and ...
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61 views

Reference request to study mathematical modelling

I'm interested in learning mathematical modelling. The course structure is appealing to me and just because of my interest I have already learned complete calculus and differential equations very ...
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22 views

Acceleration problem involving a toy rocket launching upward

So, I have attempted this problem several times, yet I fail to get the correct answer. My question implies that a toy rocket is basically being launched ground up, so y (height) would be 0.00 m and ...
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31 views

Modeling change

can you help me to solve this question? A Killer Virus: You have volunteered for the Peace Corps and have been sent to Rwanda to help in humanitarian aid. You meet with the World Health Organization ...
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28 views

show that an ordinary differential equation has T periodic solution

I have $dx/dt=-x^3(t)+h(t)$ where h(t) is a smooth, T-periodic function. Show that $x'(t)$ has a periodic solution. So I tried solving the function as letting $h(t) =sin(t)$ and $cos(t)$ which are ...
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29 views

Does mathematical modeling assist in learning how to derive equations?

I am hoping someone can provide a starting point to the question: Would mathematical modeling be a good place to start learning how to derive equations and functions from a set of data? For example, ...
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39 views

Exchange Rate Dynamics

Due to my project in mathematics I am trying to understand the dynamics of exchange rate. Consider the following: $$\dot{p}= \pi \ln (D/Y)= \pi[u+\delta(e-p)+(\gamma -1) y-\sigma r] \ \ \ \ \ \ \ \ ...
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25 views

Modeling a graph with edge dependencies

Let $G = (V, E, D)$ be a simple graph, where $$D = \{(\{v_1, v_2\}, V^\prime) \mid \{v_1, v_2\} \in E \mbox{ and } V^\prime \subseteq V \setminus \{v_1, v_2\}\} \enspace ,$$ that is, the set of ...
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26 views

least-squares estimation

I want to write a computer program that findes the least-squares estimates of the coefficients in the following models: 1) $y = ax^2+bx+c$ 2) $y= ax^n$ can you help me what should I do?I don't have ...
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Why does adding a term $5f'(t)$ to $5f''(t)+10f(t)=0$ cause damping?

So we have a differential equation to model an oscillator: $$5f''(t)+10f(t)=0$$ Where the initial conditions are $f(0)=0$ and $f'(0)=4$. It is given that $f(t) = \frac{2\sqrt 2}{5}\sin\sqrt2 t$. ...
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9 views

How to find the effects of the parameters with the Latin Hypercube Simulation?

We are working with an epidemic model where we have 21 parameters which affect the $R_{0}$-value. We want to study the effect of those parameters on the $R_{0}$-value with the Latin Hypercube ...
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27 views

help understanding math notation for algorithm

$Pkatz(z|x,y) =$ $P'(z|x,y), if C(x,y,z) > 0$ $α(x,y)Pkatz(z|y), else if C(x,y) > 0$ $P'(z), otherwise.$ $Pkatz(z|y) =$ $P'(z|y),ifC(y,z)>0$ $α(y)P' (z), otherwise.$ ...
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35 views

Optimisation/Control in lieu of knowing the future …

I’m interested to hear about the methods that would be best applied to an optimization/control problem. Context: I’m looking at the concept of ‘peak shaving’ in power networks, which are achieved by ...
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18 views

3rd order polynomial with a covariate?

I'm a physiologist by profession. I've conducted a research study that examines the effect of altitude on sustainable power output (let's call this variable CP) in cycling. A 3rd order polynomial ...
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1answer
46 views

Root mean square function (RMS) in the ODEs of a dynamical system

I am trying to obtain the differential equations of a dynamic system in which one of the blocks calculates the RMS of a signal. When arranging the ODEs I see that the differential version of the RMS ...
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39 views

Prove that taking the inverse Fourier transform of frequency returns time.

If we evaluate the inverse Fourier transform of X(w) how do we know we get x(t) back? Link to X(w) and x(t) equations I know that integrating in the frequency domain results in getting information ...
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1answer
24 views

Important subjects for biological systems modelling

which subjects and tools are important for a person who wants to start modelling biological systems? For example, everyone knows that calculus is really important to step in any mathematical ...
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51 views

Determine the optimal number and location of the plants and pipelines in the 7 cities.

There are 7 cities, up to 4 plants to be made in them and up to 18 pipelines to be made connecting them. Determine the optimal amount of plants and pipelines to be made, the optimal locations of the ...
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8 views

Help finding TF from a mechanical system

I have been working on this past for a bit and I keep running into the same roadblock where I am having problems approximating the third order polynomial I get in the denominator of the transfer ...
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25 views

4th order Runge kutta with system of coupled 2nd order ode MATLAB

I tried using Runge-Kutta methods to approximate motion equations in matlab but it turn out wrong. $$ M\left(\frac{d^2x}{dt^2}\right)=F_n(\cosΦ - u\sinΦ) \\ M\left(\frac{d^2z}{dt^2}\right)=F_n(\sinΦ + ...
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How to compute Simple Linear Regression equation not using Least Squares Estimators?

I know how to compute the Simple Linear Regression (SLR) equation using Least Squares Estimators, $b_0$ and $b_1$. But I was given the following table: $$ \begin{array}{c|lcr} & \text{mean} ...
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19 views

Replication in the multi-period binomial model.

For the solution: Just wanted to ask for $V_{3}(HTH)$ I get $S_{1}(H)$ and $S_{3}(HTH)$ to give me the same maximum value of $16$ so would it also be right if I used $S_{1}(H)$ nstead of ...
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1answer
44 views

Choose which plants to build to maximise profit

What I tried: Let $y_i = 1$ if plant $i$ is to be constructed and $0$ otherwise Let $c_{ij}$ be transportation cost per-unit for whatever the plants produce delivered from plant $i$ to ...
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88 views

Maximise population coverage subject to budget constraint

Let $t_i =$ $1$ if transmitter i is to be constructed and $0$ otherwise, $c_j =$ $1$ if community j is covered and $0$ otherwise. Obj func: Max $$z = [10, 15, ..., 10] \cdot c$$ s.t. ...
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82 views

What if the 'or' is exclusive instead of inclusive?

The context is an integer programming problem on choosing projects to maximise profit. I think (b) i. changes if 'either project 1 or project 3' means 'project 1 xor project 3' rather than 'project 1 ...
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20 views

Residual plot in the logarithmic model.

We've got some data containing two variables, where $x$ is the predictor and $y$ is the response variable. We make a model of the form of: $$y=\alpha+\beta \cdot x + \epsilon$$ Then we see that in the ...
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42 views

Population Growth problem using Malthusian Law and the Logistic Model

In 1980 the population of alligators on the Kennedy Space Center grounds was estimated to be $1500$. In 2006 the population had grown to an estimated $6000$. (A) Using the Malthusian Law for ...
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discrete population model, nondimensional

Re-formulate the following discrete population dynamic model in non-dimensional form: $x_{k+1}= r (1- \frac{x_k}{x_c}) x_k$ Notation in the lecture: $x_k$..size of population after k iterations, ...
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69 views

Linear Programming Mixed Assortment of Nuts

Below is a problem on Linear Programming. I think I have a start to it, but I'm in a rut right now so I was wondering if I could receive a little help. Here's the problem A candy store sells three ...
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43 views

Is this DE separable or homogeneous?

Differential Eq is $$\frac{(3y^2-t^2)}{y^5} \frac{dy}{dt} + \frac{t}{2y^4}=0$$ Is it linear in $y$ or $t$? Is it Bernoulli in $y$ or $t$?
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Symbol of equivalence between two functions except by constant

There is a symbol $\propto$ to show that two functions are proportionate to each other. Is there a symbol to show two functions differ by a constant? Say $f(x;y) = 2x + y$, I want something that is ...
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37 views

What is a good criteria for naming theorems/conjectures/lemmas?

Wikipedia, proofwiki, planetmath, and many others have various ways of naming theorems (and proofs and conjectures). I'm making a similar project, and am trying to create a searchable database of ...
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18 views

What is a Markovian time evolution model?

Supose I have to constuct a dynamical model for a random variable $X$ . Then I have read that for atmospheric and environmental purposes, a popular and flexible collection of models are (one-step) ...
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20 views

Transfer function of mathematical model

Im trying to derive a transfer function from by books end of the chapter exercise, but i can in no way match it with the given solution(given by our instructor). I was hoping if you can explain me ...
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1answer
17 views

Is $Φ^T$ a linear operator which transforms simultaneous equations such that we obtain LMS solution?

The below explanation is long winded, if you already know about using pseudo inverse to find the best fit solution to a set of simultaneous equations please go down to the tl;dr The Problem Given a ...
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309 views

Why is it important to find both solutions to a second order linear differential equation?

Given the equation $$y'' + y=0$$ A solution is $y=\sin(t)$ Why can't we stop there since we know a way to solve the system? Why should we consider all of the ways to solve the system? I would ...
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23 views

Differential equation modelling

I want to know where I have gone wrong. Please add a suitable title and tag.
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23 views

RINS: start - incumbent and relaxation solution have all different values

RINS: Relaxation induced neighborhood search; introduced by Danna et.al in 2010 this paper. I wanted to design an example how the RINS algorithm works to make sure that I have it completly understood ...
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16 views

NLP, Recatungular or Polar? Sine or No Sine?

Let's say we have the following complex number, $V$: $V=V_i+jV_j=V_m\angle{V_a}$ Which type of representation is better in an NLP (polar or rectangular)? The polar form leads to one nasty ...
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48 views

Newton's Law of Cooling and General advice on modeling with ODE

I have a question that goes as follows: For this question, assume that turkeys follow Newton’s law of cooling/heating. I start my oven heating at 12pm. The temperature of the oven increases linearly ...
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30 views

Book recommendation: Introduction to Traffic Flow and Traffic Models

I would like to look into the subject of traffic flow and traffic modelling. I have no prior experience with this, so it should be an introduction, preferably one with a level suited for a determined ...
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1answer
66 views

How to prove that the ellipse is a periodic orbit knowing that the orbital derivative of a function V is zero on there

The question is as follows: Show that the orbital derivative of the function $V=(1-x^2-2y^2)^2$ is zero on the ellipse $x^2+2y^2=1$, and explain why you can deduce that the ellipse is a periodic ...
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46 views

Fuzzy logic vs probability

In reading about fuzzy logic it says that fuzzy logic is different from probability. Can some one please explain how these two differ. How can this be explained to a person with no mathematical ...
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12 views

Warp shape and texture of the image into a common reference frame

I want to find object on the image using ASM and after that warp segmentation results into a common reference frame. So, I already have the algorithm of PDM and ASM and I able to find shape of object ...
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35 views

steady state or equilibrium

I need to find the equilibrium point of the following system of equation: $ds/dt = u - asi - bsw - us$ $di/dt = asi + bsw - (u + g)i$ $dw/dt = e(i - w)$ I found that $$s = \frac{u}{ai + bw + ...
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How to show condition for travelling wave solution to Fisher's equation?

I don't know how to to do this one part of a problem from my (non-PDE) math course. It's about the Fisher's equation. I've never encountered it before. $$\frac{\partial P}{\partial t} = D ...
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15 views

How To Correctly Calculates Time Achievement Performance

Please kindly help. Our organization measure employee performance of time achievement with this formula: Eficiency of time is calculated by: $[(TargetTime - TimeDone) / TargetTime] * 100%$ So, ...
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47 views

Change in time interval in a Poisson distribution when squaring the probability

I have a biological process I want to study. We have a bacterial culture in which the probability of one individual getting some specific unwanted mutation is $p$. By a technical process we achieve a ...
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29 views

What is a Turing point?

What is "the Turing point associated with the bifurcation of spatially uniform solutions"? I'm primarily concerned with what a Turing point is - Google is convinced that I mean a turning point.
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31 views

What is the meaning of dimensions in the context of these equation systems

I have been looking into reducing the dimensionality of (nonlinear ordinary differential) equation systems in order to reduce online computation time. I have interpreted 'dimensions' as the number of ...