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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Sine and Cosine Models

This is a general question about modeling the seasons using sine and cosine functions; I am trying to use sine and cosine to model cyclic behavior in sales due to the seasons (spring, summer, fall and ...
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2answers
48 views

How I can express this mathematically?

I'm working on a OR project. I have a code which fixes my problem which uses the constraint ((a =< b) or (c =< d) or (e =< f)) = True I need to rewrite this condition as mathematical ...
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21 views

Probabilistic model of parallel web servers

Note: The following probabilistic model of parallel web servers is abstracted from an engineering project. I am not good at probability theory and I am seeking some evaluations and suggestions. ...
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1answer
35 views

How can I solve an ODE when $F(x_0)=F'(x_0)=0$ is given at an unknown point $x=x_0$ using bvp5c?

I'm attempting to solve the following ODE using MATLAB bvp5c. I've used bvp5c for other typical multipoint boundary value problems but I have no idea how to deal with ODEs with conditions given at an ...
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11 views

How do impulsive differential equations work? Can you provide an example?

I have heard of impulsive differential equations being used in some epidemiological models of infectious disease. I haven't heard of them before in my math education, and I was wondering how they ...
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1answer
79 views

When graph theory cannot model the most basic problem in wireless networks. Why?

I have a set of wireless links. These links are denoted by $\mathcal{L}=\{\ell_1, \dotsc, \ell_n\}$. Every link $\ell_i$ is composed of one transmitter $s_i$ and one receiver $r_i$. Initially, all ...
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18 views

Formula for a Skewed Distribution

I'm trying to create a model of some data, using a skewed normal distribution. I have the following data: Mean Median Standard Deviation from the mean Standard Deviation from the median I've been ...
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29 views

Stationary distribution of a “birth-death model” that does not have Markov property

A typical birth-death process is defined such as the probability of going from any state $j$ to any state $i$ is given by: $$ p_{ij}= \begin{cases} b_i & \text {if $j = i+1$} \\ ...
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25 views

Euler Bernoulli beam

A simple model of the beam subjected to bending stresses is given by Euler-Bernoulli differential equation. Finite element discretization leads to a system of liniar equations.As discretization size ...
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24 views

Predictor-Corrector for Adams-Moulton

What is the order of the corrector of Adams-Moulton type required in order to apply Milne's method for estimating the error in PECE mode? Find the coefficient of the leading term in the truncation ...
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18 views

Forced harmonic oscillator [on hold]

I am completely stuck, any help or advice would be appreciated, big thank you. The motion of a forced harmonic oscillator can be described by the differential equation $$y''(t) + γ\,y'(t) + y = ...
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0answers
23 views

Relationship between Reproductive Ratio and Jacobian in Population Model

In class we defined the Reproductive Ratio, $R_0$ of a population modelled by SIR, SEIR,... as the average number of secondary infections caused by an average infected individual in an average ...
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26 views

What statistical tests for headache journal? [migrated]

I track my pain levels in an online spreadsheet along with daily habits and trigger events. I want to test whether changes in my pain over time follow a trend (not concerned whether it is linear or ...
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1answer
28 views

What are the Routh Hurwtiz Criteria for 3$\times$3 Matrices?

The Criteria I know (for dynamical systems) is... The eigenvalues of a matrix are guaranteed to be negative if Tr($J$)<0 and det($J$)>0, where $J$ is the Jacobian of some 2 dimensional dynamical ...
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2answers
132 views

Computing $\langle\sin(\gamma_i)\rangle= \int_{(S^2)^N} \sin(\gamma_i)p(\Theta)dS$

I'm trying to evaluate the following integral, which I know must be zero, $$\langle\sin(\gamma_i)\rangle= \int_{(S^2)^N} \sin(\gamma_i)p(\Gamma)dS$$ Where, $$\langle ...
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24 views

What is the relation between cellular automata, biology and its computational aspects? [closed]

Please explain me what is a cellular automata. I don't know nothing about them so start to the very beginning. Please put a lot of emphasis on their relation with biological and physical phenomena, ...
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22 views

is following model stationary?

I am interested if following model is stationary,model is represented by following formula $$ x(n) = \sum_{p=1}^{P} a_p \cos(2\pi f_pn + \phi_p) + \epsilon(n) $$ $n$ is changing from $1$ to $N$, I ...
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1answer
17 views

Conceptual Car Density

This is more a conceptual question that requires a physical answer rather than a mathematical one. The question is Explain why a density wave moves forward for light traffic. Consider both cases in ...
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21 views

Model If-Then-condition [closed]

Is there a possibility to model the condition: "If x > 0 , then y = 1" with linear (in-) equalities, if $x \geq 0$ and $ 0\leq y \leq 1 $ and integrality is not allowed in the model? If I could ...
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1answer
49 views

mathematical biology1

Consider the infectious disease model defined by \begin{equation} \frac{dS_3}{dt}= -\rho I_3S_3+\gamma I_3+\mu-\mu S_3\tag 1 \end{equation} \begin{equation} \frac{dI_3}{dt}=\rho I_3S_3-\gamma ...
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0answers
29 views

Determining how accurate an ellipse fit is

So I have an image of bacteria particles which are often shaped very irregularly with many grooves. Im trying to fit ellipses onto these particles so I can get a better, more smooth analysis of the ...
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1answer
24 views

Continuous superposition of bump functions

I am trying to "model" Fig 2 with a superposition of a bump function. I understand that bump functions are bounded and can be often differentiated. The bump function I have used is shown in Fig 1. My ...
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3answers
35 views

Good book for mathematical modeling

Could you recommend/suggest a good book about mathematical modeling (Not advanced) with examples about classical mechanics, dynamics, aerodynamics, chemistry, electronics and etc?
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1answer
13 views

Finding maximum displacement from a BVP

I have solved the following BVP (Border Value Problem): $$y'''' = -P, y(0) = y(L) = 0, y'(0) = y'(L) = 0$$ Where $L=4 , P=24$ The DE describing it is: $y(x) = -x^2(x-4)^2$ This apparently is ...
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1answer
207 views

Phase Plane Analysis

Classify the fixed point at the origin and sketch an accurate phase portrait for the following system: $$\left\{\begin{matrix} \dfrac{dx}{dt}=36x-16y\\ \dfrac{dy}{dx}=-3x+28y \end{matrix}\right.$$ ...
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10 views

Difficult transition between homogenous and heterogeneous paramaters

I'll start with an example in queueing theory. Lets assume a M/D/k queue, i.e. a queue with $k$ servers where arrival rate is determined by a Poisson process. We try to find the mean waiting time. ...
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28 views

Why does the price term in Vega disappear for a European call option?

In my course, I have been asked to prove a number of statements about "the Greeks" from the Black-Scholes model for pricing a European call option with no dividends and a strike price of $K$. One of ...
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1answer
51 views

nullclines with variables

I know how to solve nullclines, the following link is very helpful http://mcb.berkeley.edu/courses/mcb137/exercises/Nullclines.pdf However I don't understand how to solve equations that have only ...
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1answer
571 views

Linear Programming: Three variable graphical solution

A small bank offers three type of loans: housing loans at $8.50$% interest, education loans at $13.75$% interest rates, and loans to senior citizens at $12.25$% interest. Further, it needs to ...
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15 views

Derivation of the advection equation

Is there a good derivation of the advection equation available online? By that I mean the equation $\partial_t u = -\nabla( \vec{v} u)$ I know a good explanation for the one-dimensional case ...
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1answer
68 views

Real life scenario, probability model required for accidental vs supernatural causation.

A = HUMAN 1 B = HUMAN 2 A is related to B, specifically A is the father of B A goes on holiday 5 years ago, staying in a hotel in popular tourist spot near Scotland (long way from home) During ...
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1answer
41 views

Maths concept for salient point in graph data

I have collected data concerning the total post counts of users in an online forum (see graphic). What I am hoping to do is compare the language of 'first posts' with the language of 'later posts'. ...
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238 views

How to find the length of a curved path.

We have to find a continuous model for a curved path which you then solve. A woman is running in the positive y-direction starting at x=50 (50,0) which is orthogonal to the x axis. At this point a dog ...
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36 views

Sensitivity of coefficients in ODE

I am trying to formulate a mathematical model as part of an op-research problem, and I'm running into a roadblock concerning differential equations of a certain kind; I was hoping to understand if ...
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2answers
64 views

mathematical biology (steady-states)

non-dimensionalisation equation: \begin{equation} \frac {du}{d\tau}=\frac{\overline{\lambda}_{1} u}{u+1} -\overline{r}_{ab}uv -\overline{d}u \end{equation} where $\overline{\lambda}_{1}= \frac ...
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1answer
66 views

Modeling gravity field with finite elements

Well, my question is rather from applied maths area, not pure mathematics, so I am not sure that it's a place on this board for one. I want to solve a direct gravity gradiometry problem on 3D ...
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1answer
216 views

There are 5 servers. Each server has 1% downtime. What's the probability that at at least three servers are down?

There are 5 servers. Each server has $1$% downtime. What's the probability that at at least three servers are down? My reasoning is the following: A) There is $(1-0.01)^5$ probability that $5$ from ...
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32 views

Eloquent method to analyse a four dimensional system ODEs qualitatively

Given a nonlinear four dimensional system of ODEs, I have found the fixed point and linearized to acquire the Jacobian. I am beginning to calculate the eigenvalues of the Jacobian from the quartic ...
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52 views

Mathematical Biology and modelling

Consider the two species competition model given by $$ \frac{da}{dt }= \frac {λ_1 a} {a+K_1} - r_{ab}\cdot ab - da, \ \ \ \ \ \ \ \ \ \ (1)$$ $$\frac{db}{dt }= λ_2 b (1-\frac{b}{K_2}) - ...
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1answer
89 views

Mathematicals biology

Consider the two species competition model given by $$ \frac{da}{dt }= [λ_1 a /(a+K1)] - r_{ab}\cdot ab - da, \ \ \ \ \ \ \ \ \ \ (1)$$ $$\frac{db}{dt }= [λ_2 b *(1-b/K2)] - r_{ba}\cdot ab , \ ...
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1answer
18 views

Trouble finding equilibrium points

I'm working on a nonlinear predator prey model and am struggling finding my equilibrium points. I've done this three times and gotten three different answers. I'd appreciate if someone could check ...
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1answer
103 views

mathematical biology

Consider the single species population model defined by $$\frac{dR}{dt} = \frac{gR}{R+R_m} - dR,$$ for $t > 0$, where $g,R_m$, and $d$ are all positive parameters and $R(0) =R_0$. (a) Describe ...
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3answers
781 views

How to formulate constrained optimization problems

For a constrained optimization problem, there can be different formulations. For example, consider the problem with the following formulation: $$\min_{x \in X \subseteq \mathbb{R}^n} \, f(x), $$ ...
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1answer
136 views

Combining probabilities from different sample spaces

I'm working on a project whereby I'm supposed to determine whether two objects (parts of moving machinery) will be in physical contact with one another given the uncertainty in their positions. I know ...
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Analyzing a recurrence model: equilibriums, stability and periodic behavior.

In orer to increase my knowledge in math I decided to analyze the following recurrence relation (logistic growth in ecology) $$N(t+1) = N(t) (1 + r(1-\frac{N(t)}{K}))$$ I found the equilibriums by ...
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2answers
62 views

A model for the spruce budworm population

A model for the spruce budworm population $u(t)$ is governed by $$\frac{du}{dt}=ru\left(1-\frac{u}{q}\right)-\frac{u^2}{1+u^2}$$ where $r,q$ are positive dimensionless parameters. The nonzero stedy ...
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32 views

Mathematical interpretation of pressure (gradient)

I'm having some problem with the following. Usually, the pressure of some mass on an area A is defined by $$P=\frac{F}{A}$$ where $F$ is the force of the mass exerted due to gravity. However, here ...
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8 views

Derivation of the Richards equation

I know the derivation of the Richards equation from two-phase flow equations and assuming that one pressure is constant (e.g. the books of Bear). However in the paper of Alt, Luckhaus and Visintin ...
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1answer
24 views

How to show the monotonicity of exponential growth?

I have a basic exponential growth model given by $N'(t)=N(t)\times r$ where $N(t)$ is the current population and $r>0$. My problem is to show if the initial population $N(0)=N_0>0$, then the ...
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19 views

Difference between polyhedral, CSG and B-rep

I am working on the 3D object modeling project. I found objects can be represented in the form of Polyhedrol model, CSG (Constructive Solid Geometry) model, and as well as B-Rep (Boundary ...