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 can I adduce the mathematical model in my master thesis?

Please explain how to adduce and describe the mathematical model obtained by neural network modeling, if the model contains 50 inputs and five neurons in the hidden layer. How to show values of ...
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41 views

Curve fitting on non-linear ODE data

Background The graph below was generated by a set non-linear ODEs. For those of you who might want to know: It shows the maximum distance achieved by a cylinder when fired at a specified initial ...
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Can we abuse traffic patterns to get home earlier?

I had a heated discussion with my co-worker today, and was wondering if someone here could shed some light on this situation. The post is a bit lengthy, but I wanted to put all my intuition down in ...
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36 views

How can I correctly catalog this partition problem?

Studying the partition problems, I tried to do an special version to apply it to a kind of model of "orbits and energy levels" (explained below), but I am having problems to properly catalog this. ...
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12 views

Diffusion model - sign of boundary condition

I'm trying to compute the concentration of some pollutant in the rectangular pool. The pool is isolated from two sides (hatching in the picture), on the third side there is some cleaner which ...
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7 views

The difference between Linear Regression and SLR?

I can't find any videos or pages online explaining this in a straightforward way. Here's my understanding of it. The SLR model uses a Linear Regression Model (Y = B_0_ + B_1_X + ε). It becomes "...
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26 views

linear, homogeneous recursion, biological interpretation

Given the recursion $u_{k+1}=\frac{1}{2}(3 u_k - u_{k-1})$ find the expression of $u_k$ in dependence on the values $u_0$ and $u_1$. What is the limit as $ k\rightarrow \infty$ of $\{u_k\}_{k}$? Give ...
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1answer
53 views

Max $z = x_1(1-x_2)x_3$ s.t. $x_1 - x_2 + x_3 \le 1$

Using dynamic programming, Maximise $$z = x_1(1-x_2)x_3$$ subject to $$x_1 - x_2 + x_3 \le 1$$ $$x_1, x_2, x_3 \ge 0$$ Here's the outline of my solution 1. How is it? Let $y_2=...
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Find the price of the bond using its book value

A n year 1000 par-value bond with 8% annual coupons has an annual effective yieled of i, 1+i >0 . The book value of the bond at the end of the third year is 990.92 and the book value of the bond at ...
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26 views

Solving a differential equation for a cyclic model?

I am trying to figure out how to solve this differential equation for the initial condition, but I am completely lost and the book doesn't cover anything like this in the same section. So can anyone ...
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33 views

Models for Probability Density Functions with unknown parameters and given mean and variance

The PDF $f(x)$ of a non-negative random variable $x$ has the structure $$f(x)=\exp (a-bx-cx^{2})$$ where $a$, $b$ and $c$ are any model parameters. It is assumed that $c\ge 0$ so that $f(x)$ does not ...
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Finding equilibrium points of a system of nonlinear differential equations

I am currently working on a spatially explicit ODE model with dispersion to study the population dynamics of mosquitoes. I wish to compute the equilibrium values of the populations as functions of the ...
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43 views

Does anyone known the parametric equations for Cloud Gate?

I would like to use Mathematica to plot the famous Chicago "Bean." I couldn't find parametric equations anywhere and was wondering if anyone knew them. Thanks!
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28 views

How to analyse infinite equilibrium points?

I'm work in a predator-prey model, and for some values of parameters, the system of equations is: $x'=-(1+x)^3xy$ (prey) $y'=-P(x-1)^2y$ (predator) with $P>0$ constant. Only equilibrium ...
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1answer
21 views

Assuming a solution to a PDE

I am working on exercise involving the PDE $\frac{1}{2}{\sigma}^2 S^2 \frac{\partial^2 P}{\partial S^2}-rP+r\frac{\partial P}{\partial S}=0$ The solution I am looking at says to assume $S^{\...
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89 views

probability density function, integral 1

Let (M,W) be a continous probability space (take M=(a,b)), and let $x:M \rightarrow \mathbb{R} $ be a random variable which is bounded. Prove that $ \inf_{t\in M} x(t) \le E(x) \le \sup_{t \in M} x(t)...
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1answer
35 views

present value, continously compounded

Compute the present value of a payment of 10 000 Euro after 3 years, if the continuously compounded interest rate in the first year ist 4%, in the second year 6%, and in the third year 5%. For a ...
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Does the “truncation function” $\langle a,b\rangle : \mathbb{R} \rightarrow \mathbb{R}$ have an accepted name or notation? [duplicate]

Given real numbers $a$ and $b$ satisfying $a \leq b$, define: $$\langle a,b\rangle (x) = \mathrm{min}(b,\mathrm{max}(a,x)) = \mathrm{max}(a,\mathrm{min}(b,x))$$ (These numbers are equal because $a \...
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1answer
24 views

Different names for model with parameters specified and not?

Say I have a general model: $$y=\beta_{1}x_{1}+\beta_{0}$$ or $$y=\beta_{1}x_{1}+\beta_{2}x_{2}+\beta_{0}$$ I might be performing some operations to determine which general model to choose. Say I ...
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22 views

Disadvantages of particle swarm optimization method

I am using particle swarm optimization method. It has a lot of advantages, but I am looking for disadvantages of this method. Can you help me?
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Model linearly: What products to make, how much to make and in what plants to make them?

A company wants to make 3 new products for the upcoming week. We are given that: Each product can be made in 1 of 2 plants. At most 2 of the 3 new products should be chosen to be made. ...
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44 views

$4$ or more type $2$ implies $3$ or less type $1$

I'm having difficulties with the logic with the last part of the reformulation part of the problem below. Let $x_i$ be the the number of ships of type $i$ to purchase. For $4a:$ (the ...
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How to model the following scenario with an ODE if possible

Consider a cylinder, full of charged particles travelling through. From the perspective of looking through the tube, you would see a circle of particles and obviously this circle continues down the ...
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Are there alternatives to polygons in mathematical (computational) modelling?

So polygons are pretty standard in computer graphics, but from a mathematical perspective, one'd expect something more refined and sophisticated to be possible right? Polygons are not very ...
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Modelling a charged particle flowing travelling through a conductive pipe.

I'm on an internship and have a project to model how a charged particle might be affected by a conductive surface either side of it. Here's how I approached it: I assumed the particle had some charge ...
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behavior of the Linear system of an ODE model

I am working on a predator-prey model and the linearization about and equilibrium point $(0,e_2)$ has Jacobian matrix as follows $$\mathcal{J} = \begin{pmatrix} 0 & 0\\ b& -b \end{pmatrix},$$...
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31 views

Non-linear systems: Modelling the behavior of an oscillatory system when adding a perturbation.

I have a non-linear system of equations that describes an oscillatory system. the oscillations is generated by the interplay of two chemical species $A$ and $B$ Equation 1 \begin{align} \frac{d[B]}{...
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show if L, R, E0, and r as in (sin r t) are constant, the amplitude of the steady-state current is a maximum when the capacitance is $C = 1/ Lr^2$.

Can anybody please tell me how to start this questions. im stuck at making a differnetial eq for it because $C$ isnt constant and i dont understand where to put $C = 1/ Lr^2$. This is a second ...
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1answer
27 views

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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66 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 well....
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28 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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33 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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37 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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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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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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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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1answer
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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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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

$Pkatz(z|x,y) =$ $P'(z|x,y), if C(x,y,z) > 0$ $α(x,y)Pkatz(z|y), else if C(x,y) > 0$ $P'(z), otherwise.$ $Pkatz(z|y) =$ $P'(z|y),ifC(y,z)>0$ $α(y)P' (z), otherwise.$ $$P'(...
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38 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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54 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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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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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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1answer
53 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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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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1answer
36 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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1answer
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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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1answer
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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 $S_{3}(HTH)$?...