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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How do you scale a set of number such that they sum to 0.5 after scaling

Suppose I have a set of numbers of various different values (>0.0). I want to scale these numbers so that they all sum to 0.5. The scaling is required so that the relative strength of the numbers with ...
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Good similarity metric of models

I have a bunch of models that are being produced by some code I have. Many of them are different types but let's say for the simple case that all models can be represented by $\beta_0...\beta_n$. I ...
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52 views

Modelling a transfer function for plant/system empirically

In an attempt to learn about PID controllers, I'm designing a small desktop thermal control system. I have a power resistor mounted to a heatsink, with a thermister placed nearby to measure ...
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42 views

Stochastic Calculus For Finance: Conditional Expectation of Binomial Tree Model

I'm reading through Stochastic Calculus For Finance Volume 1, page 32. The conditional expectation of $S_2$ knowing $1=H$ is $p*S_2(HH) + q*S_2(HT) = 0.5*16 + 0.5*4 = 10$ But how do I calculate ...
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57 views

Applied mathematics commonly needed in the following industries

I was just wondering if anyone could shed more light on specific topics in applied mathematics or other skills (programming, etc) commonly used in the following industries: oil and gas, ...
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35 views

Establishing a inequality

I need to establish an inequality containing $19$ terms in $7$ variables. My problem arises in the context of proving that the HIV-only Quasi Disease-Free Equilibrium of a HIV-TB co-epidemic model ...
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67 views

Swimming Problem - How can I do this?

I have a problem with the following diagram. The triangle is just a possible path and may not be the shortest. If the boy has to get to the destination in the fastest way possible: What ...
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1answer
26 views

How to get the chemical form of the the lotka-volterra ODEs

I know how to work from a chemical equation to an ODE, as described here: http://brunel.ac.uk/~cspgoop/uploads/ode_chemical_network.pdf How do I go the other way? I want to convert the ...
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30 views

Unusual Probability Question

Wheel of fortune: Assume that the probability for an angle φ is P(φ) = λ$φ^2$. The game pays $1000 times the angle. a) What is λ? b) Find the expectation and the variance of the game. Comments: ...
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30 views

Generalize discrete Lyapunov equation for n-th order linear dynamics system

My specific application is analysis of dynamic textures using linear dynamics systems of the form $$ I(t) = Cz(t) + w(t) \\ z(t + 1) = Az(t) + Bv(t), $$ where $I(t)$ is the original signal, $z(t)$ ...
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36 views

Looking for advice on a math project

I had an idea of modeling the evolution of population in the dining hall (just the section where people get their food, not where people eat their food) and discussing the properties of this Dynamical ...
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24 views

How to form an equation from given graph

Hello, How can I form the mathematical equation from the given characteristics? I have attached here the excel file data of X andY axis along with the formed graph. I want to form the mathematical ...
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30 views

Check if intervals overlap

I have a set of activities $A$, where each activity $i \in A$ has a starting date $s_i$ and an end date $e_i$ (or equivalently a starting date and a duration $d_i$). Therefore, each activity can be ...
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38 views

Predicting profit with price variation

I am currently working on a high school project that aims to predict profit from X amount of items to Y amount of profit based off a deviated sale price. For instance: I sale 10 cookies for 10 ...
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31 views

trends in mathematics

I study mathematical modelling and was asked to prepare a translation of an article for the English classes. So I want to find something up to date, that would help me to choose the direction of my ...
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69 views

Mathematica Question regarding NSolve

I'm trying to solve for 2-cycles for the equation $$x=xe^{r[1-x]}$$ using Mathematica. I've tried using NSolve, FindRoot, and Solve. When I use NSolve I input it as $$\textrm{NSolve}[xe^{r[1 - xe^{r[1 ...
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60 views

A way to check the accuracy of a Markov chain?

I am not sure whether I should post this question on MSE or SSE. I will post it here 1st to see if I can get some feedback. Say I have a finite discrete Markov chain constructed maybe using some data ...
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55 views

How to find a transfer function the transfer function from angular velocity to the current used by the motor? [closed]

I need to find the transfer function of a control system with the input being an angular velocity (from a sensor measuring the rotation of a wheel of a vehicle) and the output being a current used to ...
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19 views

Regularity of the surface of a crystal

If I want to model the surface of any random crystal, is it safe to assume that it is the graph of a Lipschitz function. Is there a precise result from physicists? How wrong would it be if I assume ...
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19 views

Error of standard deviation of a Bradley Terry model

I have a set of pairwise comparisons which I can fit the Bradley-Terry Model to. I am fitting it using a simple iterative algorithm according to Algorithm 1 of A Generalized Bradley-Terry Model: From ...
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1answer
53 views

Mathematical Description for Steam Rising from a Cup

I was staring at a cup of coffee I have on the desk just now. The light shines through the water vapor as they rise from the cup. The shape of the steam is not completely random, as it drift from ...
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141 views

Efficient free alternative to *Mathematica*

I am searching for a free alternative to Mathematica. By efficient, I mean that it should have every (or at least almost every) function that you can find in Mathematica, including for example Number ...
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44 views

What resources (books, videos, etc) to help develop math thinking skills?

I am a applied mathematics major and have taken basic undergraduate coursework up to multi-variable calculus, ordinary differential equations, and elementary linear algebra. I am currently taking ...
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19 views

Help on understanding tax bracket computation

Warning: some codes Tax Bracket: 1 up to 5,070 ---- 10% ...
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48 views

Differential Equation Model ODE45 Matlab

The following system of differential equations is intended to be solved with the usage of matlabs ode45 function: $\frac{d\theta}{dt} = w(t)$ $\frac{dw}{dt} = \frac{1}{0.85s}(160 rad/s*u(t) - ...
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69 views

Including non-markovian processes in a birth-death process

Current model I want to model a stochastic system with a birth-death (Markovian) model. I therefore have this kind of $n$ times $n$ (where $n$ is the number of possible states) transition matrix: ...
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16 views

Given $y=h(x,a)$ , is it always possible to invertibly transform into $f(y)=g(a)G(x)$?

This a question from stats but I bet there is a mathematical answer to it. Stats: "Criterion for non-linearizability of a reduced model ($y=f(x,a_{i})$).So given any reduced form non-linear model ...
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47 views

How can you find orbits of period 2 of the tent map

$f(x) = \begin{cases} \mu x &\text{ for } 0\leq x\leq 0.5 \\ \mu(1 - x) &\text{ for } 0.5 < x \leq 1 \end{cases}$ I am to find the orbits of period 2. By using google I found an example ...
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158 views

Parabola investigation

Edit 4: I added the below picture for clarity I'm trying to figure out how to find the angle between the red line and the blue line, but I have no idea how to start. (I have a feeling that this ...
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52 views

Population dynamics calculation

I am trying to solve the question: A population of protozoa develops with a constant relative growth rate of 0.7944 per member per day. On day zero, the population consists of two members. ...
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62 views

Linear nonhomogenous ODE

Solve: $$y''(t)=-y(t)-\cos(t),\ \ \ \ \ \ y(0)=y'(0)=0$$ I'm sorry that I have no approach to solve it. In my solution I have the hint to solve it with resonance but I don't know anything ...
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174 views

Finding a general equation for number of paths through grid

I started with a 4x4 grid (although I want to eventually generalize for an n x n grid). You must move through a grid on the squares, not on the grid lines. The number of paths for path length = 1 is ...
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34 views

Prove $\sigma_V=x\sigma_S$. (Financial Mathematics)

Prove that the standard deviation of the value $V(T)$ at time of any portfolio $(x,y)$ at time $T$ in a one-step binomial is given by $\sigma_V=x\sigma_S$, where $\sigma_S$ is the standard deviation ...
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32 views

Describe as a system of differential equations

How is it possible to describe the $\dfrac{du_c}{dt}$ and $\dfrac{di}{dt}$ as a system of differential-equations? $$ u_s = u_r + u_l + u_c\\ i = C\frac{du_c}{dt}\\ u_l = L\frac{di}{dt}\\ u_r = Ri\\ ...
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18 views

Mathematical models for self healing robotics

Does anyone know about any attempts to mathematically model self-healing (autonomous repair) robotics ? or any existing mathematical models about this ? When a robot or machine suffers from damage or ...
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42 views

Poisson Modeling/ Queue Theory - Reference Material

Can anyone reccomend some practical reference material related to building and implementing queueing theory models. using stochastic (prefferably Poisson) processes? We are looking to build out a few ...
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22 views

Could the word “continuum” be applied to theposition of the hands of an analog clock?

The word "continuum", in term of measurement, is defined as: models explain variation as involving gradual quantitative transitions without abrupt changes or discontinuities. In contrast, ...
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25 views

What is distinction between Functional Linear Regression and Functional Linear Models?

Thanks in advance for the help. I want to make sure that I understand two concepts correctly. A functional linear model is a particular type of linear model while functional linear regression is the ...
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How do you go about formalizing a concept?

I am reading Godel Escher Bach. I love it. In the first few chapters, the author shows what a formal system is and gives examples that eventually lead to a typographical formal system of strings that ...
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71 views

Find the difference equation for {2, 4, 16, 256, …}

Write a difference equation to represent the change during the nth interval as a function of the previous term in the sequence. b. {2,4,16, 256,...} I know that an= 22n but I can't figure out how to ...
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30 views

Quantifiers and Mathematical Modelling

When we are in the context of pure mathematics, quantifiers are everywhere. When we are in the context of mathematical modelling, quantifiers usually disappear. For instance, in statistics we often ...
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96 views

Game theory: Bidding strategy during an auction in a card game

I'm trying to create a mathematical model for the auction process in a card game called Pitch. The specific question I'm interested in solving is: Let $p_i$ represent the probability of a specific ...
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40 views

Creating a mathematical formula to calculate the stock price based on 4 factors

I'd like to create a mathematical formula that calculates the stock prices of taxi bookings by plot (a plot is a postcode region) based on the following variables so that they mimic share prices e.g. ...
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236 views

Can we rotate a 3D lattice of deformed spheres?

EDIT by EricStucky: The full text of original post below for reference, but I have talked with the OP in chat and believe that this is the mathematical core of the question. Suppose that we have ...
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25 views

I need to model a population where every component have a fixed life span.

I have a certain population, which growth is function of a certain factor. I have already modeled the growth. Now I need to impose that every individual in the population have a fixed life length. Can ...
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31 views

Optimizing choice of data points with known model

my question is fairly simple to explain but I'm not quite sure how to solve it. Basically lets say I am measuring some value at 8 time points. I get to choose these 8 time points. I also know the ...
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58 views

How to represent R function dexp mathematically?

I need help representing this line of code mathematically. exp(sum(dexp(x,prop_theta,log=TRUE)) - sum(dexp(x,cur_theta,log=TRUE))) Thanks for your help in ...
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83 views

How do you formulate a vague notion into a mathematical expression?

I am a software engineer wanting to learn math. I also do a little bit of drawing. What I am wondering is, how do you formulate a vague notion of something you're trying to model into a mathematical ...
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63 views

How to model a real-world graphical structure into a mathematical formulation?

I am trying to learn how to model programming problems in a mathematical way. I am a software engineer, but have recently been running into road blocks where I can't solve some problems very ...
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43 views

How to determine new dimensionless variables when non-dimensionsionalizing a system of ODEs?

I am following this a research paper called "Evolution of Within-Host Antibiotic Resistance in Gonorrhea", which can be found here. I have one question regarding the method of non-dimensionalization. ...