# Questions tagged [mathematical-modeling]

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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### Why life expectancy calculate as 1/μ in SIR model?

In the SIR model, when the death rate is μ, life expectancy is calculated as 1/μ. Can anyone explain it intuitively?
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### Initial margin covariance matrix [closed]

I am trying to replicate the following example in order to calculate IM : https://www.clarusft.com/isda-simm-in-excel-equity-derivatives/?amp=1 I am stuck at the last step (impossible to find the ...
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### What is the physical and mathematical meaning of nonsymmetric mass, damping and stiffness matrix of a linear fluid-solid interaction modeling problem?

Suppose the problem of the subsonic flow over a simply-supported rectangular plate as bellow. According to the assumptions of incompressible, inviscid and irrotational flow, and using perturbation ...
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### Need help in quantitatively modeling solubility of carbon dioxide in beer.

I'm trying to model a 3D surface which reflects the solubility of $CO_2$ in beer. An empirically derived chart is available at this link. Solubility is empirically related to the pressure of $CO_2$ in ...
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### Find Variants in list<list<int>>

Have a mathematic solution for this: I have some list<list> For example List{ List1 = {1,2,3} List2 = {4,5} List3={6} List(n) {k} } How can I find all ...
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### Discover where car is parked when car is using adjacent parking strategy to hide in N garages [duplicate]

The car can be parked in n garages lined up in a row. Each night the car is parked in some garage, and each day it is reparked to garages adjacent to the garage where the car was parked the previous ...
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### Reference request: converting discrete models to continuous models

I have been reading a bunch of papers which take discrete models or agent-based models and convert them to continuous PDE models, using Continuum Mechanics, or such methods. Can anyone recommend a ...
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### How to develop a continuous function for known pattern? [closed]

I am given a range of x and y and would like to develop a continuous function f(x). Meaning ...
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### Positivity of solutions of an ODE system with non-negative initial condition [closed]

I have an ODE system that takes a mathematical model describing the dynamics between HCV and the immune system. My question is about the proof that the solution of the system is non-negative if the ...
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### Laguerre tessellations in real world

Aside from microstructures, where are Laguerre tessellations used in mathematical modelling?
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### Geometric mean is to arthithmetic mean as arithmetic mean is to what?

I am interested in a type of "mean" $r$ associated to a set $\{a_1,a_2,\dots,a_n\}$ where $$e^r=\frac{1}{n}\sum\limits_{i=1}^n e^{a_i}.$$ I will call this the "? mean" for now ...
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### Capacity planning and modelling

I have a business case in which I am going to model how many devices are required given the predicted workload in a series of monthly cohorts in the next ten years. The work could come from multiple ...
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### Picking numbers from a list with Gaussian distribution (programming implementation)

If we have values: $x \in [0, 100]$ I would like to implement a method, where the bigger the value, the less likely it is that it will be picked. (something like a Gaussian curve, but with maximum at ...
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### Can someone help me solve this? Finding revenue function given two different prices and quantities

Have a Math for Econ intro course exam coming up and this question showed up in one of my past papers, I am afraid I do not know exactly what to do. Can anyone help me solve it? The following is the ...
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### Can you modeling complicated dynamics without using differential/difference equations?

Let's imagine there is a phenomenon I want to understand. I have a few multivariate time series about the phenomenon but not a lot. I don't know how the variables are related to each other but from ...
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### Rewriting system of second order differential equation as system of first order

Given a charged particle moving in an electromagnetic field. We have $N$ amount of point charges placed in $\mathbb{R}^2$ on the coordinates $p_i$. We also have a free particle moving in $\mathbb{R}^2$...
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### Conditional modelling of a binary variable based on the values of two continous variables

I want to model a binary variable $(b)$ from two continous variables $(x_{in},\:x_{out})$. These variables are $0\leq x_{in} \leq x_{max},\: 0\leq x_{out} \leq x_{max})$. I want the following three ...
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### Numerical solution of a Projectile motion problem

Lets consider the situation of a rocket launched from the ground onto some impact function $f(x)$. Assume that the impact function is just the $x$ axis, hence the projectile hit the ground at the same ...
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### Is this SEIRD disease model a linear or non-linear least-squares fitting problem?

This is a system of ODEs I have set up to model a disease. I'm trying to fit the parameters for this model for a given data set using a least squares fitting algorithm. The parameters are the Greek ...
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### How to determine equilibrium points numerically for linear stability analysis of the following Predator-Prey system?

Consider the following system, \begin{gather*} N_{t+2}=N_t\exp[r(1-\frac{N_t}{K})]\frac{1-e^{-aP_t}}{aP_t} \\ P_{t+1}=N_t[1-\frac{1-e^{-aP_t}}{aP_t}] \end{gather*} how should I go about ...
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