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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Enumeration question. How many days does it take for a postman to deliver mail before he repeats a delivery pattern?

I've been struggling with this question for a bit, however here is the detail of the question- " a postman delivers mail to 19 terraced houses in a single row. He notices that no two adjacent houses ...
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15 views

expressing a certain relation by means of linear inequalities

I have a question and don't know whether there is a (good) solution. Given two distinct integer vectors $ p \neq q \in \mathbb{Z}_{+}^n $ with $ p_i \le q_i $ for each component. Let $ K \in \mathbb{Z}...
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42 views

Ideas Surrounding the SIRS model

We are working on the SIRS model in my physical analysis course, and I want to prove that all solutions in the triangular region $\Delta$ tend to the equilibrium point $(\tau,0)$ when the total ...
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59 views

Mathematical models in psychology

Do you know examples of application of mathematics in psychology besides statistical data processing? For example, do there exist mathematical models of addiction to Internet sites?
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50 views

Multivariational regression

I have been given following model $\ln(y)=\beta_0+\beta_1a+\beta_2a^2+\beta_3a^3+\beta_4a^4+\beta_5b$ and a set of observations that describe relation between $y$ and $\{a, b\}$. The goal is to ...
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25 views

comprehension problem on modelling the rate of change of a gas concentration into a differential equation

I need to determine the rate of change of the concentration of a few gases and I have been searching around for a suitable example. I think I have found one and I am trying to follow through and ...
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1answer
27 views

problem with solving a set of equations using ODE solvers in matlab

I have used matlab ode solvers to solve equations of the form: $$dy/dt=f(y,t)$$ in other words, where for instance say with an explicit Euler time stepping $$y^{n+1}=y^{n}+\Delta t f(y^n,t)$$ Is it ...
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12 views

Unicity of a solution for a mathematical model

In your opinion, why is so important for a mathematical model (for example an ODE or SDE system of differential equation), to admit unicity of a solution? I think that it is useful only for the ...
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18 views

Examples of state-space models that show strong homeostasis but also substantial change after critical threshold?

The question is, can can anyone provide examples of systems or math models that exhibit patterns of homeostasis but which can be exhibit substantial transitions or bifurcations after some critical ...
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22 views

Finding an optimal way to distribute government aid cases across multiple government offices

Note, this is for a friend who is an actual government employee, very real world application here, and the implications could be much more far reaching than you might think. Solving this problem could ...
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21 views

Percentage constraint for Integer programming model

Th question is as follows: There are 10 items that need to assigned to 2 categories, A and B. Each item has a weight and 30 % of the weight is allocated to A and the remaining 70% to B.The objective ...
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1answer
75 views

How to write an absolute value expression in linear programming?

My objective function for the Xpress-IVE (Mosel lang) model is minimize |a-b| where a and b the number of elements in the decision variables which are arrays. Since there is no function to ...
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35 views

Upper and lower bound of a function

here is the question : find upper and lower bound of the function $$f(x)=cos(\frac{1}{x})$$ Domain of function is all Real numbers except {1} . I tried to solve it by finding the limits of $f(x)$ as $...
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1answer
41 views

How to do an equation for whether to reboil the kettle full every hour or just boil minimum amounts?

This is not a homework question! I'm having a discussion with a cost-conscious friend about the merits of reboiling the kettle full vs only boiling minimum amounts. We're both tea-lovers. Assume: ...
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1answer
38 views

Modelling food in population dynamics

I understand that this model of food means that the amount of food available decreases as the population increases, however I do not understand the two parts underlined in green. How do these agree ...
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45 views

How to scale a ratio to a limited range?

I'm writing an app and I want to present some ratios normalized on a scale of 0 to 10. It's information like (number of issues resolved : number of issues remaining open). My idea is to write a ...
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27 views

State space representation for fractional order transfer function

What is the state space representation for the following filters? $H(s)=\frac{Y(s)}{U(s)}=\frac1{s^\frac12}$ $H(s)=\frac{Y(s)}{U(s)}=\frac1{s^\frac12+1}$ Where $u(t)$ is the input and $y(t)$ is ...
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21 views

How to find out a model function for two inputs?

I am doing a bit of machine learning for a control for an end user for a system. I am basically trying to figure out a delay number based on two inputs. Currently I collect a list of times (in ...
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1answer
32 views

Is there a formula for amalgamating speed and accuracy into a single variable?

I am performing a cognitive study in which I wish to examine the effect of an independent variable on an individual's computation accuracy and speed. Let's say the test is to have them solve a set of ...
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42 views

How to derive the error $e^{n}=M^{n}e^{0}$ from iteration $x^{n+1} = Mx^{n} + f$?

$x^{n+1} = Mx^{n} + f$ is fixed-point iteration for solving the equation $x = Mx + f$, i.e., $(I-M)x = f$. The error $e^{n} = x - x^{n}$ How does one get $e^{n}=M^{n}e^{0}$?
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24 views

Solve this area functional, area maximizing problem

Consider an airplane in motion in $R^3$ with velocity $v(t)$ in $R^3$ relative to surrounding steady air and ||$v(t)|| = v_0 > 0 $for $t$ in $[0,T]$. Assume that a wind blows with a fixed velocity $...
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41 views

a mathematic model for multi-factor rating system

I have to design a rating system for a eCommerce website. The rating with be like 1 - 5 or 1 - 100. There're multiple factors need to be considered to give the rating, like user feedback, customer ...
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34 views

Modeling Objective function using mixed integer programming formulation

I have the following objective function max 2x1 -2f(x2), where f(x2) = 3 if x2 = 0 and f(x2) = 2-5x2 if x2 > 0; can anyone help me formulate it using binary ...
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45 views

How to get mathematical model from a data set with MATLAB

I have some values imported from excel about the annual sell of a product, with 3 var, month, price, sold items I have seen how to plot a chart using curve fitting tool but I need to define a math ...
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1answer
65 views

ODE Modelling in Matlab

I need to model human hairs in Matlab by solving ODEs, but I'm struggling to understand what to do. Here is all of the provided information: I've been asked to write a function returning the $(x,y,...
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92 views

Group method of data handling (GMDH)

The task is to build mathematical model using GMDH (Wikipedia) and peform a forecast. There is initial data: x1 = 2; x2 = 2; x3 = 6; y = 18; The selection criterion to be used is the regularity ...
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13 views

bio heat equation modification

I have the bio heat equation as described .here And the solution to it is, But to this I am trying to include the effect from exercise intensity as well. So the modified bio heat equation is ...
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1answer
51 views

Tail driven inequality [closed]

In this empirical model, Lj is a measure of left-tail driven inequality and Rj a measure of right-tail driven inequality. It represents what in this article? What exactly is the meaning of ''left-tail ...
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1answer
35 views

Estimating how many spheres there are inside of a domain, only knowing one slide

Let $D$ be a domain, for example, a cylinder (like a glass of water) of height $H=500$, with circular base of radius $R=300$, which contains spheres (cells) with radius $r = 50\times 10^{-6}$ floating ...
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24 views

How to solve a system of diffusion equations (in $u,v$) in two regions with $u(x,t=0) = u_0$ and $v(x,t=0) = 0$

Let $u=u(x,t)$ be defined on $x\in[0,L/2]$ and $v=v(x,t)$ on $x\in[L/2,L]$. For $t>0$ we have the diffusion system $$\frac{\partial u}{\partial t}=D\frac{\partial^2 u}{\partial^2 x} \qquad \text{...
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A way to calculate the error of a model?

I am currently making a model for a set of raw data of sea levels from the NOAA data base. On the site, the sea level is recorded every 6 minutes. Because I wouldn't have time to copy data every 6 ...
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Predator and prey model: non-dimensionalization

I've been trying to non-dimensionalize the differential equations for the predator and prey model. I've written down the procedure below which I was using for non-dimensionalizing the differential ...
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3answers
57 views

Mixed Integer Linear Programming Conditional Constraints

I have a set of variables: $x_1,x_2,x_3,x_4$ $x_1$ is a binary integer variable while the rest are real numbers all between 0 and 1 I want a constraint such that: if $x_2+x_3+x_4$>0 then $x_1=1$ ...
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Product of two sinusoidal functions model

I'm trying to make a model of the rise and fall of sea levels. According to this explanation and image in the textbook, the product of two sinusoidal functions should look something like this: (...
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1answer
126 views

what are the practical uses of “game of life” or “langton's Ant”

A few questions: Besides looking really cool, what are the practical uses of "game of life" or "langton's Ant"? I understand how agent-based modeling itself is a potentially useful methodoly, not ...
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1answer
60 views

Bifurcation - first-order ODEs

Construct a first-order ODE with one critical point if $\left\lvert \mu \right\rvert \ge 1$ and three critical points if $\left\lvert \mu \right\rvert \lt 1$ and draw a bifurcation diagram. Having ...
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62 views

How to reduce the chemical reaction system $A+B \rightleftharpoons^{k_+}_{k_-} C$ with transfer using the quasi steady state assumption

Suppose we have the reaction $$A+B \rightleftharpoons^{k_+}_{k_-} C$$ within some reaction $\Omega\subset\mathbb{R}^3$, we assume this region to be well mixed and we denote the concentration of $A$ as ...
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18 views

Parametrize a sigmoid function given, $(0,a)$, $(b,a/2)$, $f'(b)=c$ and $\lim_{x \rightarrow \infty}f(x)=0$

I want to write a sigmoid function with the following properties $f(0)=a$, for some specified $a>0$ $f(b)=a/2$, for some specified $b>0$ $f'(b)=c$, for some specified $c<0$ $\lim_{x \...
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1answer
24 views

adding error terms to a mathematical model

I am reading a heuristic model of a herding activity of some animals. The mathematical (heuristic) model that was developed understandably includes an error term to account for a little randomness/non-...
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82 views

Advice on Mathematical Modeling with Differential Equations

I am on my fourth year studying in a bachelor program in applied mathematics and computer science and plan to write a term paper on mathematical modeling using differential equations. This will be the ...
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57 views

Finding bifurcation values of one-parameter families of first-order differential equations

Consider the following one-parameter families of first-order differential equations defined on the reals: $$ \dot x = \mu - x - e^{-x} $$ $$ \dot x = x(\mu + e^x) $$ $$ \dot x = x - \frac{\mu x}{...
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20 views

Mathematic modelisation of a gym members

i'm working on a business case, where i should run a gym (gym club/fitness club). I want to know if there's some well know mathematic modelisations ready made for that kind of cases. For instance, ...
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1answer
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How do I compute a realization of h(x) given its PDF and covariance?

Desription of problem I've added a picture of what I want to compute. In the nomenclature of the picture, I want to compute a realization of y(x) given the known distributions and constants. Let's ...
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44 views

Population Growth; Differential Equations

The population of a certain community is known to increase at a rate proportional to the number of people present at time $t$. Suppose it is known that the population of the community is $10,000$ ...
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How to find mean and covariance for a multivariate Gaussian under a linear transformation W?

While there is a related question on here and it is very informative, my case has some additional conditions. We have a likelihood function and want to find its distribution, $$ p(Y|X,W) = \prod_{i=1}...
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Estimate function given PDF and covariance

Let's say $h(x)$, random variable, represents the height of a surface, with x being the usual x-axis. The probability distribution function is: $P(h) = Ke^{-\frac{h^2}{2s^2}}$ is Gaussian, where $K$ ...
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1answer
47 views

Bilaplacian - Explanation of the (Clamped) Plate Problem

I am studying the numerical aspects of fourth-order elliptic problems now, and I came across the plate problem: Let $\Omega\subset\mathbb{R}^n$ bounded domain with Lipschitz-Boundary. Find $u$ s.t. $\...
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71 views

Theoretical justification of exponential growth differential equation

Consider a number of $x_0$ reproducing individuals and ignore death and limiting environmental factors. I've heard that the growth of such a population (of bacteria, insects, humans, etc...) can be ...
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16 views

If then condition on mixed linear integer programming

My English is not as good as yours, sorry for that. I hope you understand me. Here is the question:
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46 views

Mathematical Epidemiology Reference Request

I'm looking for a good Textbook for learning Mathematical Epidemiology. Something that I could read through and use as a future reference book. Thanks for the advice!