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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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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58 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
224 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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47 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
243 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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63 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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1answer
212 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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100 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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57 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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1answer
160 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
144 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
54 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
139 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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2answers
467 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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2answers
296 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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55 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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1answer
39 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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21 views

relationship between two set of variable

i am trying to determine what kind of mathematical modeling could be applied following two variables,let us call them $x$ and $y$ ,namely change one variable has effect second on,i have several ...
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1answer
48 views

What is a good approximation of $(1-p)(1-q)$ as $(1-x)^2$, for $p,q \in (0,1)$?

I'm doing some scientific modeling, and I want to use $(1-x)^2$ to approximate $(1-p)(1-q)$, with $p, q \in (0,1)$. $p$ and $q$ are probabilities, and are not near zero. My intuition is that since ...
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68 views

Multivariate Dynamic Optimization Model with Costs

I'm looking for kinds of models able to describe a situation such as the one described below (what I'm actually dealing with is load balancing but this is a more concrete example): We've a got a ...
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1answer
286 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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426 views

Modelling a Water Rocket. Requires Some Validation and Help. ( WARNING : Extremely Long but Interesting Post )

Good day people of math.stackexchange.com This is a pet project that I plan to use to convince my Prof that I would rather try something similar to this than to do the prescribed project. Edit : ...
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1answer
85 views

Definition of “Density” in ecological models

in ecological populations models, the standard variable is the density of individuals, i.e. the number of individuals per space unit (area, volume). The meaning of this is intuitively clear to me, but ...
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76 views

Solving a weird Diff equation…

Good day people I am modelling a water bottle rocket. Using the conservation of mass : $$-{\rho}vA + \frac{d}{dt}∫dM = 0 \tag{1}$$ Since the mass, O2 pressure, O2 volume and velocity change over ...
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61 views

Is it possible to get function from bunch of points?

I have some points which I know the position in 3D. and that points made in sequence. for example, . (x1,y1,z1) ...
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152 views

Suggest a random phenomenon for which the Galton-Watson branching process might provide a reasonable model.

Suggest a random phenomenon for which the Galton–Watson branching process might provide a reasonable model. Be clear about the random variable beingcounted (Zn) and the interpretation of the notion of ...
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1answer
386 views

Expected utility and St. Petersburg paradox

Can someone explain to me how they get the $10.94$ at the Expected utility theory section of the solutions to the St. Petersburg paradox? My problem is that they use a formula to calculate the ...
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2answers
241 views

Linearize Non-linear Model

How can I linearize a nonlinear model using $$y=Ax^b$$ and $$y=A\ln x+B$$ I couldn't find much online using the above methods. The notes are taken from a class in Models in Applied Mathematics ...
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1answer
42 views

Models in Applied Mathematics 2nd order Systems

I have tried searching online but I don't seem to hit the right keyword to get an answer. Here is a 2nd order Probelm about Plants, the problem is that the plants Germinate in spring, bloom in ...
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2answers
104 views

How can I find a function that accurately matches a x,y scatter plot

I have a complicated piecewise function(see below), that I use in a spreadsheet to determine what a subcontractor get paid on a particular job. For example if a job is worth $$270 dollars the ...
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2answers
506 views

Modeling with First Order Equations [closed]

A ball with mass 015kg is thrown upward with initial velocity 20m/s from the roof of a building 30m high. There is air resistance of magnitude v^2/1325 directed opposite to the velocity , where the ...
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1answer
29 views

Apartment re-rental rate follow a Beta or Gamma distribution?

I'm attempting to approximate the variance within how quickly a given housing unit could be re-rented once the previous tenants vacate. Assuming notice is given, it is much more likely that it will be ...
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2answers
154 views

Why don't elliptic PDE's have a time coordinate?

Usually second-order linear PDE's are classified as elliptic, parabolic, or hyperbolic (or ultrahyperbolic) depending on the eigenvalues of the coefficient matrix. The three cases correspond to the ...
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110 views

Underdamped Oscillations of spring-mass system

At what time has the amplitude of oscillation of a spring-mass system with negligible friction decayed to 1/e of its original value? Does this time depend in a reasonable way on k, m, and c?
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34 views

Highest (lowest) index of positive time-indexed variable

I have a simple problem involving a variable $x_{it}$ representing the amount of a resource allotted to a task $i$ in time $t$. The quantity of the (renewable) resource is constrained at a value $R$ ...
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1answer
40 views

help in multiple linear regression

I am having a question in regression analysis in JMP or any other tool. I have one dependent variable $y$ and $2$ independent variables $x_1$ and $x_2$. For example: time $= y -$ per row time ( ...
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1answer
86 views

The mean infective period in a SIR Model

I'm going to quote the relevant passage in the textbook and then ask my question. The assumption that the infectives leave the infective class at rate $\alpha I$ per unit time requires a ...
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84 views

Calculating heterozygosity of a population as size increases (combine growth and genetic drift equations)

I am working on a assignment to program a genetic drift simulator and include population growth. My program works fine as far as I can tell, and I have the not unexpected result that in the time I am ...
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1answer
64 views

Probability & Forecasts

I am doing a forecast on turnover and would like to know how i can work out the probability that the next sales figure will be over a certain amount given that we have all the data from previous ...
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0answers
28 views

Center of mass in a straight rod [duplicate]

I got an assignment to prove that in a straight homogeneous rod, you can always choose a coordinate system in such a way that $\int_S x_1dx_1dx_2=0 $ $\int_S x_2dx_1dx_2=0 $ $\int_S x_1x_2 ...
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1answer
170 views

Finding Percentage Contribution of a Variable in an Equation

I have an equation, for example: $$ y=a-b+c $$ I am actually confused how exactly to find the contribution of the variables individually to the entire equation. Due to the negative sign, following ...
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1answer
182 views

How does one model independent trials in statistics.

In my probability class, we covered the proof of the following result, known as the "strong law of large numbers": Theorem. Let $(\Omega,\mathscr F,P)$ be a probability space, $\{X_n\}_{n\in\mathbb ...
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3answers
265 views

Sum of the area of all the rectangles in a rectangular

We have a rectangular shape with the size n × m meters is divided into rectangles of size 1 × 1 meters. Question: Sum of the area of all the rectangles that can be seen in that rectangular is how ...
2
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2answers
185 views

How to derive thresholds from a pooled sample of values

Question: The context of this question is actually finance, however the question itself is a statistical issue. Suppose I have the following expression: $$\rho = \frac{2\bar{x}}{(s^*_x)^2}+1 \ \ ...
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1answer
76 views

A doubt about Evans and Jovanovic (1989) economic model for entrepreneurs with credit constraints

In Evans and Jovanovic (1989) you will find a model for entrepreneurs with credit constraints. The part that is important for my question follows. Here it is the production function and the income ...
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1answer
78 views

Discrete Systems - fish population modelling question on derivation of the model

I am currently reading 'Introduction to Non-Linear Systems' by J Berry and on page 112 there is an exercise (question 5) which I don't understand, it is: The population of fish in a large lake has ...
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1answer
74 views

Scaling a cup to have a certain filling volume

I created a cup in Autodesk Inventor using lathe/rotation, ie I defined the profile and rotated it around an axis. I measured it's volume. By using Patch and Sculpt I filled the inner volume(which ...
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32 views

Prediction model from input/output observations

I want to make a prediction model for the following transformation $f:\mathbb{N}^N \rightarrow \mathbb{R}^M$ $N$ is around 20 and vectors $\mathbf{v} \in \mathbb{N}^N$ are sparse with $\sum_{i=1}^N ...
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1answer
37 views

How to find $X_i$ from this equation

Suppose $X_i=\nu_i+\frac{m-i}{m}X_{i+1}+\frac{i}{m}X_{i-1},\quad 1\le i\le m$ where $X_0=X_{m+1}=0$. I need to find an expression for $X_i$ in terms of $v_i$, $i$, and $m$. I know how to find it ...
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2answers
53 views

Turing instability in social networks

I'm doing research on this topic from Mathematical modeling. I was wondering if anyone could recomend any literature that can help me with this. All I need is application of this model on social ...