# Tagged Questions

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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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 ''left-tail ...
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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 ...
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### Mathematic modelisation of a gym members

i'm working on a business case, where i should run a gym (gym club/fitness club). I want to know if there's some well know mathematic modelisations ready made for that kind of cases. For instance, ...
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### How do I compute a realization of h(x) given its PDF and covariance?

Desription of problem I've added a picture of what I want to compute. In the nomenclature of the picture, I want to compute a realization of y(x) given the known distributions and constants. Let's ...
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### Population Growth; Differential Equations

The population of a certain community is known to increase at a rate proportional to the number of people present at time $t$. Suppose it is known that the population of the community is $10,000$ ...
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### How to find mean and covariance for a multivariate Gaussian under a linear transformation W?

While there is a related question on here and it is very informative, my case has some additional conditions. We have a likelihood function and want to find its distribution,  p(Y|X,W) = \prod_{i=1}...
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### Estimate function given PDF and covariance

Let's say $h(x)$, random variable, represents the height of a surface, with x being the usual x-axis. The probability distribution function is: $P(h) = Ke^{-\frac{h^2}{2s^2}}$ is Gaussian, where $K$ ...
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