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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Where should I start from if I want to learn Mathematical Modeling?

I am a student of political science and have basic knowledge of mathematics. But I need to learn Mathematical Modeling if I want to continue a research of mine. I'm willing to spend even 1 or 2 years ...
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37 views

Construct differential equation given the phase portrait (non-linear pendulum)

I am curious to know how to recover the differential equation that goes with a phase portrait. I have seen the following posts but the first one was a $y'$ (and easy enough to "do in my head") and ...
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Can a statistical model have two unknown parameters?

Is an $N(\mu,\sigma^2)$ distribution a statistical model if both the parameters are unknown? The definition I have in front of me only refers to one unknown parameter.
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Is this partial differential equation solvable?

Ok so I am asked to set up a partial differential equation and then motivate why it is solvable. I'm only 2 weeks into my course so we are not asked to solve anything yet. However, if someone would ...
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35 views

can every object be represented mathematically?

I was just wondering if all 2D/3D objects/images/shapes could be represented by equations. For example, SpongeBob 2D curve and many more. How should I approach, as in, some theories that already ...
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38 views

Help with Differential equation solution requried

Hi guys I am doing some differential equations and I got this one: I have no idea how he went from (38) to (39). When I solve it by integrating factor, the equation I have is: ...
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Is there any mathematical model to choose a good parameter?

The first plot is the relative error and storage as functions of $\lambda$, each function has five pairs of points. The second plot is the relationship between relative error and the storage. Now I ...
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26 views

A model for constant temperature of water in a container

I put some water in a container with initial temperature $T_0$ in a room, and the room's initial temperature is $T_a$. Now the container is filled to the maximum, so any more water coming in will ...
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Function representing learning review graph

I've been working on this for a while but am unable to get it right. (If anyone is curious, I'm trying to make a model that determines a user's best time to review something that he has studied, this ...
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25 views

Math Modeling Mortgage Question - $100000 mortgage paid over 30 yrs (360 months). [closed]

Your parents are considering a 30-year, \$100,000 mortgage that charges 0.5% interest each month. Formulate a model in terms of a monthly payment $p$ that allows the mortgage (loan) to be paid ...
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30 views

Non-dimensionalization of a system, what to do if we have to divide by zero?

I have some PDE system involving unknowns $u$ and $v$ and $w$ which are concentrations of some substances. I want to nondimensionalize the system, so I divide through $u$ by some number $c_u$, and ...
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fidi of Chi-square Random Field

The $\chi^2$ random field $U(t)$ with $n$ degree of freedom (dof) is defined as: \begin{align} U(t) = \sum_{i=1}^n X_i(t)^2, t\in\mathbb{R}^N \end{align} where $X_1(t),...,X_n(t)$ are i.i.d ...
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93 views

Which distribution function for diseases

I am wondering, what would be a good method for choosing a suitable probability distribution to fit a certain criteria. For example, I am wanting to choose a suitable distribution, and specify the ...
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1answer
17 views

What is the difference between a first order compartment and diffusion

Biologists use Compartment models to represent the flow and storage of fluids in an animals body. In tissue (like muscle) the diffusion of blood is more accurately represented by the diffusion ...
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30 views

Equation for human body shape

I was wondering if anyone knows about or has created an equation that models a human body in 3D space. I imagine it would be based off of a cylinder or ellipse, but I don't know for sure. Note: I ...
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43 views

Mathematical Epidemiology

Okay so this is quite a long question involving a lot of background work I have done myself but there are quite a few holes I need filling in so I'll start from the beginning. I'm writing a report ...
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11 views

Modelling a Bell-Shaped Growth Pattern

In my experiments I observed something that grows, reaches a steady-state, and then destabilizes. If the length were to be plotted as a function of time, it would look similar to a Kuznetz/Gaussian ...
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1answer
49 views

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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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 ...
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1answer
33 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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40 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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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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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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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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Why is my RK4 becoming unstable?

I'm trying to compare RK1 (Euler) and RK4 methods using a plot, so I've created some rows in Excel and am trying to plot the results. I have two particles, chained together by a spring, one of them ...
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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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21 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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17 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
33 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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28 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
34 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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32 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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41 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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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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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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28 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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1answer
41 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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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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how to implement a user-defined criteria in matlab ode solvers?

is there a way to add a user defined convergence criteria to an ode solver so that the solution is stopped? I am using the solvers in to solve fluid dynamics problems and I am not sure whether the ...
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1answer
24 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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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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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
54 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 ...
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30 views

Equilibrium Points of the SIR Model

When considering the SIR model, are there any equilibrium points other than when the whole population is recovered? $$\begin{align} \frac{dS}{dt}&=-\frac{\beta I S}{N} \\ \frac{dI}{dt}&= ...
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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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GARCH$(1,1)$ with Uniform innovations.

Consider the stochastic process {$X_t$} such that $X_t\sim$ GARCH$(1,1)$ with uniform innovations $Z_t\sim(0,1)$. When this process is strict stationary?
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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
50 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 ...
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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 ...