# 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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### Conditional expectation and Variance

I have the interest rate model: $r(t)= x(t)+y(t)+\phi(t)$ $r(0)=0$ $dx(t)⁼-ax(t)dt+\sigma dW_1(t)$ $x(0)=0$ $dy(t)⁼-bx(t)dt+\nu dW_2(t)$ $y(0)=0$ $(W_1,W_2)$Brownian (2 dimensions) 1-...
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### Modify Nicholson-Bailey mdoel

Suppose that we modify the assumptions of the Nicholson-Bailey model in the following way: if a host has one encounter with parasitoid it gives rise to c parasitoid progeny, but if it has two or more ...
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### When fitting a polynomial to data points, how to determine the reasonable degree to use?

I have wondered the following: Suppose that there is a set of data points $(x_i,y_i)$. Then I would like to know if it is more reasonable to assume if there is a polynomial relation of degree $m$ ...
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### How to nondimenzionalize concerning the arc lenght

My question is a general one concerning mathematical modeling and the calculation of the arc lenght. There is a function $f\colon [a, b]\to\mathbb {R}$, where $f (x)$ includes a lot of parameters. ...
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### How to use the Monte Carlo method with curve fitting

I have an assignment in which I need to choose statistical data from the Australian Bureau of Statistics and fit a curve to it. I've chosen the slaughtering of bulls in NSW (first Excel file, C:143-C:...
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### Damped Driven Oscillator Dimensional Analysis

So, I am studying the damped driven oscillator with the following drive force: $$M\ddot{x}+\gamma \dot{x}+kx=F_0 \cos({\omega t})$$ where $M$ is the mass, $\gamma$ is the ...
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### Is there any tool that could turn a Petri Net into system of math equations?

I have a colored, descrete Petri Net. I have a picture. How to get a math (ODE\DE\system of equations) representation of it?
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### AHP (Analytical Hierarchical Process) for individual selection decision with equally important objectives

How can I apply AHP for individual selection decision when all the objectives are important? For example, I want to select a car. The car needs to have all the characteristics (all the components). In ...
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### Adding two sinusoidal functions together (i.e $10\sin x+\cos x$ or $5\sin x+\sin x$)

I'm doing my math exploration on modeling tide levels and wanted to know if it was possible to find a function by just looking at a graph, and knowing their points that looks like (see image on bottom)...
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### Trying to model an equation for this problem:

A drug is administered once every four hours. Let Dt be the amount the drug in blood system at t-th interval. The body eliminates a certain fraction p of the drug during each time interval. If the ...
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### How to iterate a function 8 times about a given interval of x in a Discrete Dynamical System

This is Dynamical Systems, specifically a discrete system. We are using L and R as in Left and Right such as: L=[0,0.5] R=(0.5,1] and LL=[0,0.25] LR=(0.25,0.5] and so on like that. We keep ...
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### How To Evaluate How Well a Mathematical Model Works… Modelled VS Measured Values?

Let's say I am working with a mathematical model. The output of the model is always a value between 0 and 1, and is dependent on a number of input variables. I am also measuring the same phenomenon ...
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### How can I solve this ordinary differential equation? What are the Initial/Boundary Conditions used?

I am having trouble following the solution to this problem, I can understand how to obtain the general solution but cannot figure out the conditions used to obtain the particular solution with the ...
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### Disadvantages of Non-orthogonal basis

What are some disadvantages of using a basis whose elements are not orthogonal? (The set of vectors in a basis are linearly independent by definition.) One disadvantage is that for some vector $\vec v$...
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### Writing explicit scheme - numerical methods for PDEs

I've got a problem writing a code for the explicit scheme. In the end i'd like to plot a temperature destribution for a given case. Let's say i have a material of a lenght L with given boundary and ...