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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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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11 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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51 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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58 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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52 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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37 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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96 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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37 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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41 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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19 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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33 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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17 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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49 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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1answer
52 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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15 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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2answers
45 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
30 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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95 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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69 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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63 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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20 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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1answer
101 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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23 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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30 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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49 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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52 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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30 views

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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31 views

Function that defines a skew bell shaped curve

The following formula describes a normal bell shaped curve: $$f(x,a,b,c) = \frac{1}{1+|\frac{x-c}{a}|^{2b}}$$ I am trying to model data that exhibits has skewed bell shaped behaviour (please see the ...
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1answer
59 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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looking for asymmetric probability distribution

In physics, quantities are sometimes measured with both an upper and lower error. For example, I might say that an object's mass is $m = 10^{+0.1}_{-0.2} \text{ kg}$. In my case, these arise from ...
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62 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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39 views

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. ...
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22 views

How do impulsive differential equations work? Can you provide an example?

I have heard of impulsive differential equations being used in some epidemiological models of infectious disease. I haven't heard of them before in my math education, and I was wondering how they ...
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97 views

When graph theory cannot model the most basic problem in wireless networks. Why?

I have a set of wireless links. These links are denoted by $\mathcal{L}=\{\ell_1, \dotsc, \ell_n\}$. Every link $\ell_i$ is composed of one transmitter $s_i$ and one receiver $r_i$. Initially, all ...
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Relationship between Reproductive Ratio and Jacobian in Population Model

In class we defined the Reproductive Ratio, $R_0$ of a population modelled by SIR, SEIR,... as the average number of secondary infections caused by an average infected individual in an average ...
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39 views

How can I solve an ODE when $F(x_0)=F'(x_0)=0$ is given at an unknown point $x=x_0$ using bvp5c?

I'm attempting to solve the following ODE using MATLAB bvp5c. I've used bvp5c for other typical multipoint boundary value problems but I have no idea how to deal with ODEs with conditions given at an ...
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47 views

Predictor-Corrector for Adams-Moulton

What is the order of the corrector of Adams-Moulton type required in order to apply Milne's method for estimating the error in PECE mode? Find the coefficient of the leading term in the truncation ...
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1answer
34 views

What are the Routh Hurwtiz Criteria for 3$\times$3 Matrices?

The Criteria I know (for dynamical systems) is... The eigenvalues of a matrix are guaranteed to be negative if Tr($J$)<0 and det($J$)>0, where $J$ is the Jacobian of some 2 dimensional dynamical ...
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31 views

Conceptual Car Density

This is more a conceptual question that requires a physical answer rather than a mathematical one. The question is Explain why a density wave moves forward for light traffic. Consider both cases in ...
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49 views

Stationary distribution of a “birth-death model” that does not have Markov property

A typical birth-death process is defined such as the probability of going from any state $j$ to any state $i$ is given by: $$ p_{ij}= \begin{cases} b_i & \text {if $j = i+1$} \\ ...
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mathematical biology1

Consider the infectious disease model defined by \begin{equation} \frac{dS_3}{dt}= -\rho I_3S_3+\gamma I_3+\mu-\mu S_3\tag 1 \end{equation} \begin{equation} \frac{dI_3}{dt}=\rho I_3S_3-\gamma ...
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37 views

Determining how accurate an ellipse fit is

So I have an image of bacteria particles which are often shaped very irregularly with many grooves. Im trying to fit ellipses onto these particles so I can get a better, more smooth analysis of the ...
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42 views

Continuous superposition of bump functions

I am trying to "model" Fig 2 with a superposition of a bump function. I understand that bump functions are bounded and can be often differentiated. The bump function I have used is shown in Fig 1. My ...
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122 views

Good book for mathematical modeling

Could you recommend/suggest a good book about mathematical modeling (Not advanced) with examples about classical mechanics, dynamics, aerodynamics, chemistry, electronics and etc?
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30 views

Finding maximum displacement from a BVP

I have solved the following BVP (Border Value Problem): $$y'''' = -P, y(0) = y(L) = 0, y'(0) = y'(L) = 0$$ Where $L=4 , P=24$ The DE describing it is: $y(x) = -x^2(x-4)^2$ This apparently is ...
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Difficult transition between homogenous and heterogeneous paramaters

I'll start with an example in queueing theory. Lets assume a M/D/k queue, i.e. a queue with $k$ servers where arrival rate is determined by a Poisson process. We try to find the mean waiting time. ...
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Computing $\langle\sin(\gamma_i)\rangle= \int_{(S^2)^N} \sin(\gamma_i)p(\Theta)dS$

I'm trying to evaluate the following integral, which I know must be zero, $$\langle\sin(\gamma_i)\rangle= \int_{(S^2)^N} \sin(\gamma_i)p(\Gamma)dS$$ Where, $$\langle ...
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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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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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64 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 ...