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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Differential equation modelling

I want to know where I have gone wrong. Please add a suitable title and tag.
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RINS: start - incumbent and relaxation solution have all different values

RINS: Relaxation induced neighborhood search; introduced by Danna et.al in 2010 this paper. I wanted to design an example how the RINS algorithm works to make sure that I have it completly understood ...
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NLP, Recatungular or Polar? Sine or No Sine?

Let's say we have the following complex number, $V$: $V=V_i+jV_j=V_m\angle{V_a}$ Which type of representation is better in an NLP (polar or rectangular)? The polar form leads to one nasty ...
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Newton's Law of Cooling and General advice on modeling with ODE

I have a question that goes as follows: For this question, assume that turkeys follow Newton’s law of cooling/heating. I start my oven heating at 12pm. The temperature of the oven increases linearly ...
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Book recommendation: Introduction to Traffic Flow and Traffic Models

I would like to look into the subject of traffic flow and traffic modelling. I have no prior experience with this, so it should be an introduction, preferably one with a level suited for a determined ...
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68 views

How to prove that the ellipse is a periodic orbit knowing that the orbital derivative of a function V is zero on there

The question is as follows: Show that the orbital derivative of the function $V=(1-x^2-2y^2)^2$ is zero on the ellipse $x^2+2y^2=1$, and explain why you can deduce that the ellipse is a periodic ...
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Fuzzy logic vs probability

In reading about fuzzy logic it says that fuzzy logic is different from probability. Can some one please explain how these two differ. How can this be explained to a person with no mathematical ...
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Warp shape and texture of the image into a common reference frame

I want to find object on the image using ASM and after that warp segmentation results into a common reference frame. So, I already have the algorithm of PDM and ASM and I able to find shape of object ...
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36 views

steady state or equilibrium

I need to find the equilibrium point of the following system of equation: $ds/dt = u - asi - bsw - us$ $di/dt = asi + bsw - (u + g)i$ $dw/dt = e(i - w)$ I found that $$s = \frac{u}{ai + bw + u}$$...
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How to show condition for travelling wave solution to Fisher's equation?

I don't know how to to do this one part of a problem from my (non-PDE) math course. It's about the Fisher's equation. I've never encountered it before. $$\frac{\partial P}{\partial t} = D \frac{\...
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How To Correctly Calculates Time Achievement Performance

Please kindly help. Our organization measure employee performance of time achievement with this formula: Eficiency of time is calculated by: $[(TargetTime - TimeDone) / TargetTime] * 100%$ So, ...
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47 views

Change in time interval in a Poisson distribution when squaring the probability

I have a biological process I want to study. We have a bacterial culture in which the probability of one individual getting some specific unwanted mutation is $p$. By a technical process we achieve a ...
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32 views

What is a Turing point?

What is "the Turing point associated with the bifurcation of spatially uniform solutions"? I'm primarily concerned with what a Turing point is - Google is convinced that I mean a turning point.
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What is the meaning of dimensions in the context of these equation systems

I have been looking into reducing the dimensionality of (nonlinear ordinary differential) equation systems in order to reduce online computation time. I have interpreted 'dimensions' as the number of ...
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1answer
38 views

Explicit piecewise linear approximation of a function of 4 variables

I have a table of numbers for fixed values of 4 parameters $x, y, z, t$, at this $x$ belongs to finite set of natural numbers, $y\in\{1;2\}$, $z\in\{5;10;15;20;25\}$ and $t\in\{1,2,3\}$. Is there a ...
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21 views

How can I solve the conservation of traffic PDE?

I'm trying to solve the conservation equation for traffic flow so that I can use it for an example. It is stated as follows: $$\frac{\partial \rho }{\partial t} + \frac{\partial \rho v(\rho )}{\...
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22 views

On the computation of the Hessian matrix.

I'm trying to compute the Hessian matrix of a data fit of an ODE model to some data. Below is a cut out of the instructions I'm following (which can also be found at ...
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133 views

Why is “$\pi^2= g $” where $g$ is the gravitational constant?

Some months ago a professor of mine showed us a 'proof' of why $g\approx 9.8 ~\text{m}/\text{s}^2$ (the gravitational acceleration at the surface of the Earth) is 'equal' to $\pi^2\approx9.86\dots$ ...
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53 views

What would be a good cartesian equation to represent the shape of a wine glass?

I want to find the volume of a wine glass by using either the disk or shell method (solids of revolutions). The wine glass doesn't have to be of any particular dimensions, however it should roughly ...
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66 views

Bifurcation Diagram question for Population harvesting model $P' = rP (1-\frac{P}{K}) - hP$

A deer population grows logistically and is harvested at a rate proportional to its population size. The dynamics of population growth is modeled by $P' = rP (1-\frac{P}{K}) - hP$ where $r$ (the ...
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56 views

How can I calculate missing values from a table listing of areas and prices? [closed]

I have a set of objects of different sizes (measured in square metres). I know the price of some of them. I want to use the known prices to find the missing prices. Here is the data I have: \begin{...
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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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56 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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39 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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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 exist?...
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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: $$c_{A}{(t)}=\frac{{c_{...
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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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38 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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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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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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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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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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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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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 \mathbb{Z}...
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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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57 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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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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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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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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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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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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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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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: ...