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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Information Theory: Probability for the Number of Corrupted Bits [on hold]

I've met a problem in information theory that deals with probability and number of occurrences. It states that: The probability of a single bit being corrupted is $p$. Now I have an ...
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146 views

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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23 views

how do I resolve equations that are both dependant on each other

I'm working on a project concerning the ideal power equation of aerodynamic bodies seen here: $$P = \frac{1}{2}C A D v^3 + \frac{W^2}{Db^2v}$$ where $P$ = power, $C$ = coefficient of drag, $A$ = ...
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1answer
27 views

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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45 views

Develop a model for determining the optimal production schedule in a manufacturing facility

I have to formulate (linearly) the following problem mathematically: What I tried: 1. Variables Let $x_{ijk} = 1$ if, in month k, product i should be made in production line j, where ...
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25 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 ...
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26 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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15 views

How do display matrix A,b,c when using AMPL for a Linear Optimization's problem?

When solving a linear program in the form max/min c^T subject to Ax=b in AMPL is there a way to display just the matrix A, b, and c. I am using the following model file and read in matrices for the ...
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1answer
11 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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6 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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1answer
48 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 ...
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14 views

Fourier transform used for time series prediction?

For a given time series data set $(t=0,...T)$, we can use Fourier transform to data fitness $$ X(n) = \mu + \sum_{k}\left( A_k cos \frac{2\pi k n}{N} + B_k cos \frac{2\pi k n}{N} \right) +\varepsilon ...
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23 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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12 views

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. Only 1 of ...
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37 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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2answers
34 views

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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1answer
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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27 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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15 views

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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1answer
92 views

Relationship between Reproductive Ratio and Jacobian in Population Model

In class we defined the Reproductive Ratio, $R_0$ of a population modelled by SIR, SEIR,... as the average number of secondary infections caused by an average infected individual in an average ...
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1answer
417 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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27 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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1answer
83 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} ...
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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
17 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 ...
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1answer
27 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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27 views

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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18 views

Physical analogy for capacitor behavior? E.g. “water & pipes - flow & pressure” analogy for electric variables. [closed]

Have you ever heard before the analogy in which electric current is likened to amount of water per second past a point in a pipe, and voltage is likened to the pressure of the water? I'm looking for ...
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18 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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1answer
22 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

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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22 views

What would be the best method to model population growth? [migrated]

I am trying to find the best method to model the population growth in a school. In my possession I have the student count by semester in the last 16 years. Moreover the first information I consist of ...
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17 views

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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1answer
47 views

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 ...
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11 views

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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5k views

Mathematical Modeling of Real-World Situations [closed]

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 ...
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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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28 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} ...
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1answer
26 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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5answers
860 views

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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0answers
60 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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1answer
18 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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1answer
3k 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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1answer
26 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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21 views

getting points in the Equation

How can I draw a chart for $y=ax^2+bx+c$ in Microsoft Excel and get some points that are applies in the equation?
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1answer
27 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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1answer
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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2answers
145 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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1answer
41 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 ...