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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Mathematical modeling [on hold]

A 250 liter tank contains 100 liters of pure water. Brine containing 4kg of salt per liter flows into the tank at 5 lit/hr. If the well-stirred mixture flows out at 3 ...
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Weighted ordering of subgroups

As you may have guessed by my title, I've got no background in maths, but I think this is the right bit of StackExchange to ask in and hopefully I've picked the right tags... but forgive me if not ! ...
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Number of significant linear predictors if predictors are not independent?

I would like to determine which of a set of candidate predictors $\{x_1, x_2,\ldots, x_n\}$ are significantly relevant to the linear prediction of $y$. Typically, one can compare a full model ...
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36 views

Form of a function I can fit like a polynomial that has an asymptote on x-axis and is always positive

So I have a small list of pairs of the form $(\mathbb{R}, \mathbb{R}_{\geq 0})$ and I want to fit a function to this data. Additionally I know that as $x$ grows large in either direction $y$ tends to ...
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Rounding a real number w.r.t. a given amount of steps

Let $x$ be a real number, $x \in [0,1]$. Suppose a system can only provide a noisy signal about the value of $x$, given the granularity allowed by the system, $N \in \mathbb{N}^*$. I'm looking for an ...
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Start studying mathematical biology from basics

I am really passionate about theoretical and quantitative biology and I would like to build my future career around this topic. I've just got my bachelor's degree in biology (ecology) but scince ...
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26 views

Mathematical model of glycolysis, simplification problem

I am studying Mathematical modeling for biology processes and right now - the model of glycolysis. At some point it all comes up to a system of differential equations that looks like this: Than we ...
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26 views

how to find the optimal path for a rescue robot?

The rescue robot is searching signals in a huge rectangle area without obstacles. We assume: - only one signal source in the area in a constant location. - the robot is small enough to be regard ...
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14 views

A Mathematical Model for the measurable time of an detector

The detecting radius of the detector is 1. P is a point on the plane.When the detector move along the straight line l from bottom to top at a speed of 0.1 per second ,P can be detected when the ...
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1answer
24 views

Definition of “epidemic” when using SIR models

I haven't studied differential equations for a long time, but I have just started looking at material on the SIR model of epidemics. My problem is that the resources that I've looked at haven't given ...
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27 views

Mathematical Modeling for the Mapping Relationship

I have encountered a problem in my research and have no idea how to model the problem. To simplify the description, I tell a game with the same rule instead of the original problem. Consider two set ...
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29 views

Finding the largest eigenvalue of a sparse matrix

I would like to find the largest eigenvalue of a sparse matrix by hand- this is part of analyzing a mathematical model for infectious diseases. The nonzero entries are very complicated - hence Maple ...
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What is the minimum number of data points required to use ARIMA(p,d,q)? [migrated]

I'm using the $\mathrm{ARIMA}$$(p,d,q)$ model to predict future time series data in R (see also R's ARIMA documentation). Q: What is the minimum the number of data points we must have in the time ...
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40 views

Analytical Models for Hysteresis of Complicated Systems

I’ve been working with a system that exhibits hysteresis and I’ve found that the more common models do not work for me. I am wondering if anyone is aware of other models that might be out there for ...
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1answer
42 views

Finding a value that makes an expression negative

Background: I am working on the mathematical modeling of infectious diseases, namely HIV and TB. In the process of proving global asymptotic stability of the Disease-Free Equilibrium, I must ...
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13 views

Scorecard validation on different performance window

I am trying to build a scorecard model which predicts probability of default over the next 2 years of observation. Can someone suggest me literature which shows: A scorecard with 2 years of ...
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62 views

Units of time in simple differential equation

Very simple question: There is a well-known model in epidemiology called SIR model. It describes the changes in the number of susceptible, infectious and recovered individuals in a population. It is ...
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1answer
51 views

How can I modelize a weekly menu and minimize the total number of ingredients it contains

Hi and many thanks for reading this question. I want to create an algorithm that will minimize the total number of ingredients that are in a weekly menu. A menu is made of several recipes, for ...
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43 views

Creating a mathematical formula to price a taxi booking

I've been asked to create a mathematical formula that will be used to price taxi bookings at a local taxi company. Current system used: A table is used as a reference Variables: x is the ...
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1answer
43 views

Estimate arrival time of a ship given the average of the ships in a day in a Poisson Distribution

I'm working in a simulation of a Port where ships come to specific stations of the port. I already know that the average amount of ships is given by a Poisson distribution and the service time (On ...
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1answer
31 views

Math Finance: Arbitragefree Pricing Q vs. P

I read that the Fundamental Theorem of Asset Pricing states, that a market is arbitrage-free if there exists a riskneutral equivalent martingale measure Q~P, under which the discounted asset price ...
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PDE modeling (heat conduction and flow)

The heat conduction is expressed by a classic heat equation like $p(x) u_t + div (A(x) u) = f(x,t) $. If I look at a porous medium like this (solid+gas) the heat equation should apply too (in a ...
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18 views

Simple differential equation modelling question.

The question is: A chemical dissolves in water at a rate equal to 10% of the amount of undissolved chemical per hour. At time $t$ hours the amount of undissolved chemicalis $x$ grams. Initially the ...
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66 views

Could the birthday paradox be interpreted also about deaths?

Is the probability from the birthday paradox also true about deaths? If so, why? Or why not? I would think that it is also true about deaths, but it doesn't say so.
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How can I find a tranformation matrix/Mathematical relation between two 5th degree polynomial curves in space?

I have the equation of two 5th degree polynomials which they don't intersect with each other. Each curve is made of 100 points and these two curves look similar but there are small differences. I am ...
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35 views

How can I find a tranformation matrix/Mathematical relation between two 5th degree polynomial curves in space?

I have the equation of two 5th degree polynomials which they don`t intersect with each other .Each curve is made of 100 points and these two curves looks similar but there are small differences .I am ...
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12 views

Multiplying a binary predictor variable with another predictor variable.

Is it completely valid, to have an equation with a certain amount of variables, where two of the variables multiply each other? For example, I want to have an equation $Y = B_0 + B_1X_1 + B_2X_2 ...
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29 views

System of $2$ nonlinear DEs

Please tell me if I'm on the right track for solving the following system: $$\frac{d{U}}{dt}=a - b U -\frac{\beta U V}{U+V} \\ \frac{d{V}}{dt}=\frac{\beta U V}{U+V}-(b+c+d)V $$ Steps: $1.$ I added ...
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1answer
41 views

How did they find this equilibrium condition?

I'm studying from a book titled "Mathematical Models in Population Biology and Epidemiology" and we're dealing with SIS models. In a chapter called "Infective Periods of Fixed Length", we get to this ...
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48 views

At what point discrepancy, in the NBA, does it make sense to milk the shot clock?

I am admittedly not great with probabilities, so I am soliciting the help of the community. I am watching game 3 of the NBA Finals and I am trying to work out when it makes sense to milk the shot ...
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27 views

Linear Optimization: Minimum Cost Network Flow Model

Consider the directed graph G=(V,A) where each directed arc (i,j) $\in A$ has associated with it a distance $d_{ij}$. Formulate a minimum cost network flow model that will identify the shortest paths ...
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21 views

Model going from Normal to Log-Normal

I'm getting in a real mess at the moment over something I think is very simple, as well as the wording/terminology. I have a model - $\ln(Y(x))=a+b\ln(x)+\epsilon, ...
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Distribution of phone calls during 24h

I would like to model the amount of phone calls at each time of the day. The phone calls should follow a poisson distribution and at 12:00 there should be the peak. So, semantically what I would like ...
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38 views

Carbon dioxide molecule model

A simple model of the carbon dioxide molecule can be modeled by a system of three masses and two springs. The oxygen atoms have mass M and carbon has mass m. The springs (bonds) have spring constant ...
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Bessell function of the first kind $J_v$ of the Bessel equation $x^2y''+xy'+(\lambda^2 x^2-v^2)y=0$

If we have an equation $x^2y''+xy'+(x^2-v^2)y=0$ then the solution of the first kind $J_v(x)=x^v\sum_{m=0}^{\infty}\frac{(-1)^mx^{2m}}{2^{2m+v}m!(m+v)!}$. Then how would you find the solution of ...
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Name search for special Linear Mixed Integer Programm

I am looking for a name for the following question in literature! (and if you know it, then it would be great) I couldn't find it and due to wide audience here, presumably you know more. Thank you ...
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Is it compulsory to make transformation to the econometric model in order to have only diagonal elements on variance-covariance matrix of errors?

I need some sharped and advanced advices for the following issue ... Model and its assumptions I'm working on the methodology of a two-way error component model. Here is the model: $y_{jis} = ...
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1answer
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Does improving a model's accuracy directly improve the forecast?

Say I have a years worth of data on donut sales, and I use linear regression with variables such as daily occupancy, daily weather etc. because there is a good correlation between each variable and ...
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117 views

Function to predict processing service overload

We have a black box that for each input request a, it outputs a computed response b. The computation time for a given request varies in a stable way over time. Stable means here that it is still ...
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Playing audio files at lower % of regular speed - how long will they be? negative percentage / ratio calculation

I got a knot in my brain and can't think of this - I'm sure it's quite simple and I'll be like "duh!" once someone points it out to me... So the problem is as follows: An audio file is 30 seconds ...
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15 views

difference equation soling

Need to help sovling a differene quation :) $p_t = - \frac{p_{t-1} + \alpha + \gamma \beta}{\delta \beta}$ My Thoughts: $p_t = p_{CF} + p_p$ where $p_{CF}$ is the complementary function and $p_p$ ...
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10 views

Elliptical Cone

I have a building design in the shape of an elliptical cone. To understand the elevation of the structure. I need to draw/unfold an elliptical cone. Can somebody explain the process for the same ?
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1answer
50 views

In math, what is a chessboard + pieces?

What mathematical concept would a chessboard + pieces be? Is there any matrix where the squares are kinda related, in the same way that for example a rock relates to all the column/row, where it is.
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1answer
56 views

Analyzing the stability of equilibria

There's a model with a condition $r>\mu$: $$\begin{align} S'&=r(S+I)-\beta SI-\mu S \\ I'&=\beta SI-(\mu +\alpha)I \end{align}$$ I can easily see that the equilibria of the second ...
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1answer
50 views

Express the new parameters in terms of the old parameters (SIQR model for mathematical epidemiology)

In the model considered here the population is divided into susceptibles (S), infectives (I), isolated or quarantined individuals (Q), and recovered individuals (R), for whom permanent immunity is ...
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Does more data give you a better forecast?

Say I have a large set of data. Each data point corresponds to a particular day in the year, so for 1 year I will have 365 points. Say I have collected this sort of data for 5 years. Now, I want to ...
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Comparing populations using trigonometry.

Given the function: $$ f(t) = 62 \cos \left( \frac{2π}{2⋅46}t \right)+138. $$ The function above represents population #1. If there was a population #2 that rises considerably when population #1 is ...
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34 views

Trigonometry in Population

I was trying to find a function that would follow this model: The Y axis is population; the x axis is years. Each point is a local max or min point. Is it possible? I have no idea how to make a ...
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Trig modeling - population

A population drops from 200,000 in 1950 to 76,000 in 1996, and has risen since then. Taking into account that the population follows a sinusoidal cycle affected by environmental conditions and ...
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need equation to calculate similarity distance

Desperately need help, please. I need to write mathematically, separate equations for calculating distance so that a higher score means a and b are very similar, and a low score means not similar. I ...