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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30 views

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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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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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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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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526 views

Why does my Barabasi Albert model implementation doesn't produce a scale free network

I'm trying to implement the Barabasi Albert model to generate some scale free network matching a power law distribution of degree. I'm using a value $m = 2$ for the main parameter of the algorithm, ...
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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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11 views

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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46 views

Damped Driven Oscillator Dimensional Analysis

So, I am studying the damped driven oscillator with the following drive force: \begin{equation} M\ddot{x}+\gamma \dot{x}+kx=F_0 \cos({\omega t}) \end{equation} where $M$ is the mass, $\gamma$ is the ...
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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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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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430 views

Phase Plane Analysis

Classify the fixed point at the origin and sketch an accurate phase portrait for the following system: $$\left\{\begin{matrix} \dfrac{dx}{dt}=36x-16y\\ \dfrac{dy}{dx}=-3x+28y \end{matrix}\right.$$ ...
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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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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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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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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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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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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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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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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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3k views

Linear Programming Inventory Problem

I'm still trying to get used to the nature of these problems and I'd appreciate some further explanation. ...
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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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491 views

How to model an aviation holding pattern mathematically?

A standard aviation holding pattern has four sections, each of which, in windless conditions, takes one minute to fly. The first is the inbound leg, which is the only one for which precise ...
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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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383 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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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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368 views

Heat Equation Derivation and Mean Value Theorem

Farlow book PDEs for Scientists and Engineers pg. 27 shows derivation for Heat Equation. It starts by stating Net change of heat inside $[x,x+\Delta x]$ = Net flux of heat across boundaries + Total ...
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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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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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1answer
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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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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Examples of types of mathematical models

I am a student currently doing a course on modelling and simulation. I came across the classifications of mathematical models and studied that they can classified as static or dynamic, deterministic ...
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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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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 ...