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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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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70 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
302 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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458 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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86 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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79 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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63 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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409 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
278 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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46 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
114 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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542 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
164 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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111 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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38 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
41 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
88 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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89 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
69 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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29 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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195 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
199 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
273 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 ...
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2answers
186 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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79 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
84 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
75 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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33 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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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 ...
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58 views

probability with Poisson distribution

according to the experience of a bank staff,there are 2 old paper money IN EACH MONEY PACKET.if the number of old papers money,in each money packet,follow poisson distribution, a)what is the ...
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183 views

Poisson like distribution in $\left(\sum_{k=0}^{n-1} x^{2^k}\right)^{n}$?

Given $y_{n}(x)=\left(\sum_{k=0}^{n-1} x^{2^k}\right)^{n}$. An example ($n=5$) may look like $$ y_5(x)={x^{80}}+5 x^{72}+5 x^{68}+5 x^{66}+5 x^{65}+10 x^{64}+20 x^{60}+20 x^{58}+20 x^{57}+20 x^{56}+20 ...
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1answer
492 views

The intuitive understanding of $\sqrt{x}$ to model “inversely proportional / inverse square”?

Can someone lay out what the concept I am trying to convey below in a more clear manner? Square root functions are sometimes used to model non-linear relationships. The value of a square root is ...
3
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1answer
121 views

Solving $f'''+\frac{n+1}{2}ff''-nf'^2+n=0$ with $n=e^\pi$

How do I solve $$f'''+\frac{n+1}{2}ff''-nf'^2+n=0$$ with $n=e^\pi$ or arbitrary $n$? This equation occurs in my model for the time evolution of the value of Bitcoin.
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1answer
240 views

SIR Models - interpretation (epidemiology) - help!

I am doing a project on modelling the spread of diseases and am using a SIR (susceptible, infected and recovered) model to do so. I need help interpreting this plot: What does this plot say about ...
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Category modeling in quantitative Linguistics

I'm currently doing some studies on a new quantitative unit in Linguistics, the so called Motifs. A Motif is a ascending (or descending) sequence of quantitative linguistic properties. For a better ...
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2answers
137 views

Modeling dependency between two variables

I want to model the dependence between two variables. Now there are a few ways to do this, for example writing one variable as a function of the other or using correlation. I have also looked into ...
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119 views

Calculate average speed with unknown variable accelaration

I am in the middle of a vehicle tracking project where I have to calculate the distance traveled by the vehicle in a given amount of time. Data I am getting: ...
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2answers
2k views

Cleaning up the Great Lakes - Differential equation systems

Problem Details The idea of the problem is to find out how long it would take to flush the Great Lakes of pollution. They're set up as a series of five tanks and you are given inflow rates of clean ...
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220 views

Are my linear program equations correct?

Here's the problem: "An electronics company has a contract to deliver 21,475 radios within the next four weeks. The client is willing to pay 20 dollars for each radio delivered by the end of the first ...
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2answers
50 views

Simpler way to display mathematical model?

I am developing a mathematical model for the power usage (watts) of a computer device against its percentage of CPU load. So far I have: ...
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2answers
891 views

Biology: Wright-Fisher model of genetic drift

In evolutionary biology (in population genetics to be more accurate) exists the concept of genetic drift. It describes how an allele (gene variant) (that has no advantage or disadvantage in terms of ...
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1answer
145 views

Generalized Mechanism Design, Stanley Reiter diagram and Vickrey Auction

I am trying to learn this new topic, Mechanism Design and stumbled upon the "Stanley Reiter" diagram (see the top-right side on the page). I have also learned that the Second Price Sealed Bid ...
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2answers
537 views

Converting if else constraints into linear ones

I have the following two constraints: $$ x_1 \leq x_2 \leq x_3 \qquad \mbox{if } x_1 \leq x_3 \\ x_1 > x_2 > x_3 \qquad \mbox{otherwise} $$ Is there a way to get rid of the two conditions and ...
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519 views

How to model an aviation holding pattern mathematically?

A standard aviation holding pattern has four sections, each of which, in windless conditions, takes one minute to fly. The first is the inbound leg, which is the only one for which precise ...
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Modeling 4 people going to same place over 3 different places for at least 5 days

I'm trying to model a linear programming task with the condition 4 people going to the same place among 3 different places for at least 5 days. I have the variables for the time spend each person in ...
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2answers
508 views

Ideas about an Ordinary Differential Equations research work (University level)

Good afternoon to everyone, I need some ideas about a Ordinary Differential Equations research work. It is for the ODE subject that I am doing at my Mathematics degree in my University. They asked me ...
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42 views

Speed formula and least square approximation

I have some questions about a formula and least square approximation I have 14 information about the speed of a fluid inside a tube, speed, position and standard deviation. I already made a graphic ...
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167 views

Using an alternate way to write a Taylor series of $f(t+\tau)$ to derive numerical integration and differentiation formulas

In chapter 9 section 3 of An Introduction to Mathematical Modeling, the author Edward A. Bender points out that: $$f(t+\tau)=\sum_{n=0}^\infty \frac{(\tau D)^n}{n!}$$ so that $$f(t+\tau)=e^{\tau ...