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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Understanding the Pareto distribution as applied to wealth

The Pareto distribution is used to say, given a particular person X, what is the pdf of his wealth. I would like to explore the reciprocal question: Given the total amount of wealth in a population, ...
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Geometrical construction for Snell's law?

Snell's law from geometrical optics states that the ratio of the angles of incidence $\theta_1$ and of the angle of refraction $\theta_2$ as shown in figure1, is the same as the opposite ratio of the ...
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why does $\frac{b\partial a}{a \partial b} = \frac{\partial \log a}{\partial \log b}$?

I am doing some background research on sensitivity and elasticity analysis, and I came across the following definitions of elasticity: $$e_{ij}=\frac{a_{ij}\partial \lambda}{\lambda \partial ...
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Deriving functions for empiracal distributions -very applied mathatics

First I am a new user of this site. Second my math background is very limited, although I do have a lot of experience in applied statistics. Component or piece part failures on high value parts($1000 ...
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Preparing for the Mathematical Contest in Modeling

The Mathematical Contest in Modeling (MCM) is coming up in a couple of weeks. With the idea that the competition is ultimately about teaching students to become better at mathematical modeling, I was ...
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What sort of mathematical methods and models are used to model the brain

What sorts of mathematical tools, models and methods and theoretical frameworks do people use to simulate the function of the brain's neural networks? What mathematical properties do different brains ...
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Is there a SoftMax distribution with confidence parameters?

This is a softmax probability distribution: $$P(i\mid w_1, w_2, \ldots, w_n) = \frac{\exp(w_i)}{\sum_{i=1}^n \exp(w_i)}.$$ It known also as Boltzmann distribution. It is used in generalized ...
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Finding a good parametric form for a model

Hello I am trying to model the relationship between two variables, say x and y. I have a number of subjects - for each subjectm I have a number of x and corresponding y, both of which are always ...
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Simple math formula to calculate average

I am making a software that deals with employee trust. I am trying to make a math formula (no need to tell that I am bad in math :) ). Here is the scenario: ...
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Taylor Series. Reusing an approximation of a function

I have this function, $e^{-x}$ bounded between 0 and 1500 and I have an approximation by Taylor Series of the same function bounded between 0 and 0.5. I would like to express my function $e^{-x}$ ...
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Immunization and Sensitivity Analysis

Frequently a company wants to match its assets and liabilities. However, perfect matching is not practical due to fluctuations in interest rates. So they hedge their risk using immunization. This can ...
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Development of a specific hardware architecture for a particular algorithm. Modelling fuctions by Taylor sSeries.

I'm trying to develop a architecture hardware to make a implementation of an algorithm that can be descompose in terms of sums, multiplications, subtractions and exponential functions. I'm trying to ...
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How to start creating Mathematical models?

I know this is a quite general question , but I've always heard about creating mathematical models in economics, social sciences, engineering,... And I would want to know what are the starting points ...
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How do I calculate the instantaneous angular speed of a spindle given a spooled radius and required feed speed?

In an attempt to model the cassette tape spooling action, I'm hoping to solve this problem. Required feed speed 5cm/second. Two Spindles with starting radius of S1: 0.8cm (empty spool) S2: 1.8cm ...
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Probability in single-lane traffic flow: What are the odds of “choke points” being encountered?

Let's say you have a single-lane road (single in this case meaning single lane in each direction, or what you could also call two-lane). Let's say you have a random number of vehicles on a given ...