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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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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45 views

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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42 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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125 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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48 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 look similar but there are small differences. I am ...
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76 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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15 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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36 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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50 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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105 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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89 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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28 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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35 views

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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72 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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22 views

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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22 views

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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99 views

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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54 views

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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122 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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35 views

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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24 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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30 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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59 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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70 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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66 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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40 views

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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102 views

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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63 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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72 views

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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24 views

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 ...
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45 views

Cross-Validation

Does anyone understand the paragraph below? The paragraph comes from Cross-valiation explanation at wikipedia. "It can be shown under mild assumptions that the expected value of the MSE for the ...
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21 views

Formula for sinusoidal-like graph

Come up with a formula using cosine that satisfies the points (0,347), (1, 76), (2,295), (3, 84), (4, 243), (5, 92). The problem I have with this question is that the amplitude and the midline do not ...
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59 views

Saying something about model parameters, knowing the half-life of total protein

I have the following model: $$ \frac{dP}{dt} = -{\color{blue}k} \frac{P}{{\color{blue}C} + P} + {\color{blue}r}P_u \\ \frac{dP_u}{dt} = {\color{blue}k} \frac{P}{{\color{blue}C}+P} - ...
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55 views

Number sequences in nature.

I'm getting ready to teach the second calculus course in the 4 course sequence at my school. One of the required topics is an introduction to number sequences. I want to motivate this section with ...
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21 views

Can multimodality exist in the absence of deterministic multistability?

I am not sure if this is the right SE to ask this question; it is about mathematical models for chemical reactions. I came across an article that says that multimodality of biochemical species can ...
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52 views

Which mathematical programming method is good for solving the described problem?

I need to solve the following problem. Let's say that there are 3 clients with different time windows. For simplicity let's say that travel distance is always 10 minutes and service time is 30 ...
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1answer
57 views

Finding the basic reproduction number of a particular model

I have been reading a paper about a host-parasites models and for the model: $$\begin{array}{rll} \displaystyle{\frac{dx}{dt}}&=\lambda -dx -\beta v x & \text{Susceptible host} \\ ...
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158 views

What differential equation might model this almost-harmonic oscillator?

I need to precisely control the motion of a damped, driven (nearly) harmonic oscillator: $$ \ddot x(t) + \alpha\dot x(t) + \omega_0^2 x(t) \approx V(t) $$ I use the $\approx$ symbol because this is ...
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257 views

Differential vs difference equations in mathematical modeling

I'm reading a little about mathematical modeling and I've seen some population models based on differential equations. I've also seen some (not many) that can support both difference and differential ...
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79 views

Locally small category whose collection of isomorphism classes cannot be a set

For natural examples of locally small categories like the category $\mathbf{Grp}$ of groups, the isomorphism classes themselves are normally not sets. In a set theory like ZFC, even the collection of ...
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24 views

Method for spacing tasks over 24 hour period

I have been asked to look into devising a quicker way to balance workload over a $24$ hour workday. The scenario: $24$ hour work day $8$ hours shifts $40$ minutes break time per shift Each shift ...
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1k views

Gompertz growth model problem

The growth of tumor cells is characterized with Gompertz model. $N'=-aNln(bN),$ where N(t) is proportional to the number of cells in the tumor, while a and b denote positive parameters. ...
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39 views

Modeling a greatest integer function

I'm trying to model a function that resembles a greatest integer function. The domain is from [0, $\infty$). The inputs from 0 to 1.5 (non-inclusive) need to be mapped to an output of 0, and 1.5 to ...
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33 views

square footage to non linear time [closed]

I'm a tarp maker and I'm trying to figure out how long it takes me to move the tarp around depending on the square footage of the tarp. For instance, it takes me 2 minutes to handle a 10sqft tarp, ...
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145 views

A good book on convolutional neural networks

Good evening! Don't you know a good book on convolutional neural networks, where the next questions are highlighted: 1) How are the backpropagations for convolutional and pooling layers are ...
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280 views

Modeling with Differential Equations - Help?!?!

So here's the problem that I'm working on at the moment: Tank 1 initially contains 50 gals of water with 10 oz of salt in it, while Tank 2 initially contains 20 gals of water with 15 oz of salt in ...
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Matlab functions of variables

So I am writing a function to compute the following equations for an SIR model: So here's my code: ...
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99 views

ODE water drop modeling question

I have been working on a ODE homework which involves modeling the velocity of a drop of water falling from the sky. The ODE that models its velocity is given by: $$ mv'=kv^2-mg, \qquad ...
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74 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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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. ...