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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29 views

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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21 views

Modeling Gaussian components with standard vs exact functions

I'm studying a paper on modeling DNA histograms. It presents two alternative formulas for modeling Gaussian components: Standard form: $G(x) = \frac{A}{\sqrt{2\pi}\sigma}e^{\frac{-(x-\mu)^2}{2\sigma^...
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17 views

Can sombody give me an ntuitive explanation about regression estimates as weighted averages?

I am trying to study weighted least square and found one article that sounds like it is explaining what I am trying to study. But I want to get some intuitive explanation about each calculation and ...
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47 views

Self learning complex systems modeling

I am currently a senior studying mathematics. My program is heavily focused on pure maths, however, my interests lie in the area of applied mathematics. Specifically, I am interested in the study of ...
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10 views

converting GA's fitnessfunction to mathematical expression

As part of my final report I have to explain my fitness function method using in mathematical form. However I am not very good at this. I have came up with something that I will share with you here. I ...
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27 views

Composite sinusoidal functions

Let' say you have a graph as such: !(http://blogs.scientificamerican.com/roots-of-unity/files/2014/12/sinxsin2x.jpg) ! (Black one) And you know that it's function is in the general form of cosx+...
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58 views

Formulation for solving puzzle game mathematically

I'm developing a solver for a simple constraint-based puzzle game. Here is an example of the puzzle: $$\begin{align} - \;6\; -\\ - - -\\ - \;3\; - \end{align} $$ The given 3$\times$3 grid of "clues" ...
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76 views

An algorithmic method to simplify the mathematical modeling of a reaction network using conservation laws

Consider the reaction scheme. where $S$ is the substrate, $E$ is the enzyme, $P$ is the product, $C_1$ and $C_2$ are enzyme substrate complexes. Let $[S] = s$, $[E] = e$, $[C_1] = c_1$, $[C_2] = ...
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70 views

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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18 views

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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58 views

what does it mean by this mathematical modeling

This is a mathematical model: $$ Z_{i} = \sum_{S \epsilon S'} P_{i} (S=S') $$ where set $$\ S'= \left\{ (X_0,X_1,..., X_{k-1}) | X_i \epsilon S, \forall 0≤i ≤k-1,X_i ≤X_j, \forall i ≤ j \right\...
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43 views

Natural Transformation Inductively defined?

So, I'm working on this project and I'm having some trouble with a definition. Maybe some more educated Category Theorists can help me. The context is actually not very relevant, as I just need to ...
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9 views

Distribute individuals to relevant mentors as evenly as possible

I'm working on a site that needs a matching feature, but I'm wondering if there's a mathematical model that already tackles what I'm trying to do. Users belong to Mentors, but they can choose their ...
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71 views

Mathematical Modeling

If the number of possible routes is less than 4, probability (a) will be used. All the routes will be considered and the travel time for each route will be calculated. However, if there are more or ...
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21 views

Determining relative weights of input variables

For $Q = f(a, b, c, d)$, what is a statistical test to determine the relative weight of how these variables contribute to $Q$? Better yet, how do I come up with a function for it? To put into context,...
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116 views

Mathematical Modeling of Route Optimization

Do any of you know how to come up with equations or mathematical way of representing these problems? 1) Finding probability of choosing number of routes (i) If n of routes less than 4, consider ...
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1answer
20 views

Time Series with increasing dimension

I am stuck with the following problem from research. I am not sure how to model this situation. I have a vector time series whose dimension increases with time, $t$. Specifically, let $\mathcal{X}$...
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22 views

Symmetric discrete catenary

I have to solve a problem of "Symmetric discrete catenary with odd number of particles". I've been told that knowing it has odd number of particles means that you can adjust the solution of ...
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23 views

How to calculate the cross-correlation of a halfwave?

I'm trying working on a vehicle modle and testing it with steering maneuvres standardised by the ISO. When it comes to data analysis the ISO standard says the following: 6.4 Time lag and Sine Time ...
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1answer
45 views

Discrete version of continuous SIR model

I'm working with a SIR infection model, which is $$\begin{array}{rcl} \frac{dS}{dt} & = & -\beta IS\\ \frac{dI}{dt} & = & \beta IS-\gamma I\\ \frac{dR}{dt} & = & \gamma I \end{...
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62 views

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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1answer
16 views

A function to return 1 if and only if two strings match in a certain number of characters

I want to formulate equation for comparing two strings $A$, and $B$ each of length $x$. The function should be $1$ if they are matching in at least $x-l$ characters. Otherwise the function should be $...
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34 views

Find RHS from LHS.

$A=\left[ \begin{array}{cc} 0 & 1 \\ 1 & 0 \\ \end{array} \right]<==>\left[\begin{array}{cccc} 0 & 0 & 1 & 1 \\ 0 & 0 & 1 & 1 \\ 1 & 1 & 0 & 0 \\ ...
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54 views

Damped Driven Oscillator Dimensional Analysis

So, I am studying the damped driven oscillator with the following drive force: \begin{equation} M\ddot{x}+\gamma \dot{x}+kx=F_0 \cos({\omega t}) \end{equation} where $M$ is the mass, $\gamma$ is the ...
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24 views

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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24 views

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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35 views

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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2answers
64 views

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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28 views

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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36 views

Prove multiple OLS t-test follows t-distribution

I'm trying to prove the multiple regression test has a t distribution, i.e.: $\frac{\hat B_j - Bj}{se(\hat B_j)} \sim t (df=n-k-1)$ I was able to prove $\frac{\hat B_j - B_j}{sd(\hat B_j)} \sim \...
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68 views

Stability type of logistic population equation's equilibrium points

I was working on this question: Here is what I have so far: $ (a) \ \ \text{We have the algebraic expression to find equilibrium points:} \\ \frac{dy}{dt} = ry \big[1 - \left(\frac{y}{K}\right) \...
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64 views

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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46 views

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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1answer
104 views

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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17 views

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 ...
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25 views

A property of Piece-wise continuous simple linear regression model

My fellow members I attempted to model the growth of capital of a small business person who does business with the aim of just raising his or her capital, as follows: Assumptions A fixed capital $...
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34 views

Equilibrium of an ordinary differential equation [closed]

I have been trying to show that the following ODE has either one or three non-zero equilibria, depending on the value of $r$, but with no real progress. $$\frac {dx}{dt}=rx(1-\frac{x}{K})-\frac{bx^2}{...
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39 views

Calculating remaining balance [Monthly compounding question with rate= 0.01]

Suzanne opens a line of credit at a local bank, and immediately borrows 1870 dollars. 6 months later, she repays 1060 dollars. 5 months after the repayment, she borrows 570 more dollars. 6 months ...
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80 views

interarrival time

I am trying to model the arrival rate (delay between the arrivals) of the cars in my city. I have some real data with the resolution of one minute. For example, Number of counted cars at position x at ...
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24 views

What do we call the harmonics in a discrete Fourier series representation?

In harmonic analysis using discrete Fourier series, if I'm using the 0f, 1f, 2f, 3f and 4f for representation where f = frequency, what is the correct way to say how many harmonics I'm using for ...
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51 views

How to prove that the solution of a given ODE is bounded?

Let's have an equation $$ y''(t) + \left(\frac{3}{16 t^{2}} + \frac{A}{t} -\frac{B}{t^{\frac{5}{4}}}cos(2t)\right)y = 0, \quad A > 0, \quad B > 0,\quad A < B, \quad t\in (1, \infty) $$ ...
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Implications of Choosing Incorrect Variables in Buckingham Pi

One form of the Buckingham Pi Theorem says that for $n$ variables with $k$ dimensions, the number of dimensionless quantities (or pi groups) is $n-k$. This theorem is often applied when the ...
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313 views

Response Surface Methodology using Moving Least Squares Method

I would like to obtain the response surface of a mathematical function for reliability-based design optimization (RBDO). To obtain a reliably response surface, I learned that moving least squares ...
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1answer
134 views

Physics related initial value problem (horizontal spring mass system)

Consider the horizontal spring-mass system where the spring-force is the only force acting on the mass. Suppose that a mass is initially at $x=x_0$ with an initial velocity $v_0$. Show that the ...
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How to solve the model parameters?

Find a region of the world in which arms race is occurring or has occurred. Find data about arms spending. Estimate the model parameters. I found some data on Zimbabwe's military expenditure and ...
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34 views

Apprehension in Feller's solution of a model of breakage of spores

This one is a solved example from Feller. Spores of the Fungus are produced in chains of eight.The chain may break into several parts into projectiles containing 1 to 8 pores. Find the ...
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41 views

How to quantify a relationship so that a small value increases the result and a larger value decrease the result?

The title pretty much says it all but let me break it down. I thoroughly appreciate any help. I'm trying to quantify a relationship between the difference in peaks and troughs of a wave function and ...
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24 views

Turning a word equation into a differential equation (heat transfer problem)

Question: Heat is flowing in a wall with constant cross sectional area, inside which heat is generated at a constant rate of Q $ W m^{-3}$. Write a word equation and show that the equilibrium ...
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61 views

Differential Equation Model of Motion problem.

I'm having trouble with this question. "A body is released from rest and travels the last half of the total distance fallen in precisely one second. How far did the body fall and how long did it take ...