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.

learn more… | top users | synonyms

1
vote
1answer
113 views

mathematical biology

Consider the single species population model defined by $$\frac{dR}{dt} = \frac{gR}{R+R_m} - dR,$$ for $t > 0$, where $g,R_m$, and $d$ are all positive parameters and $R(0) =R_0$. (a) Describe ...
1
vote
2answers
292 views

There are 5 servers. Each server has 1% downtime. What's the probability that at at least three servers are down?

There are 5 servers. Each server has $1$% downtime. What's the probability that at at least three servers are down? My reasoning is the following: A) There is $(1-0.01)^5$ probability that $5$ from ...
1
vote
0answers
20 views

Analyzing a recurrence model: equilibriums, stability and periodic behavior.

In orer to increase my knowledge in math I decided to analyze the following recurrence relation (logistic growth in ecology) $$N(t+1) = N(t) (1 + r(1-\frac{N(t)}{K}))$$ I found the equilibriums by ...
1
vote
2answers
101 views

A model for the spruce budworm population

A model for the spruce budworm population $u(t)$ is governed by $$\frac{du}{dt}=ru\left(1-\frac{u}{q}\right)-\frac{u^2}{1+u^2}$$ where $r,q$ are positive dimensionless parameters. The nonzero stedy ...
3
votes
0answers
34 views

Mathematical interpretation of pressure (gradient)

I'm having some problem with the following. Usually, the pressure of some mass on an area A is defined by $$P=\frac{F}{A}$$ where $F$ is the force of the mass exerted due to gravity. However, here ...
0
votes
0answers
13 views

Derivation of the Richards equation

I know the derivation of the Richards equation from two-phase flow equations and assuming that one pressure is constant (e.g. the books of Bear). However in the paper of Alt, Luckhaus and Visintin ...
0
votes
1answer
28 views

How to show the monotonicity of exponential growth?

I have a basic exponential growth model given by $N'(t)=N(t)\times r$ where $N(t)$ is the current population and $r>0$. My problem is to show if the initial population $N(0)=N_0>0$, then the ...
0
votes
0answers
52 views

Difference between polyhedral, CSG and B-rep

I am working on the 3D object modeling project. I found objects can be represented in the form of Polyhedrol model, CSG (Constructive Solid Geometry) model, and as well as B-Rep (Boundary ...
0
votes
0answers
16 views

relationship between two set of variable

i am trying to determine what kind of mathematical modeling could be applied following two variables,let us call them $x$ and $y$ ,namely change one variable has effect second on,i have several ...
0
votes
1answer
45 views

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 ...
0
votes
0answers
35 views

Finding general solution to a non-linear discrete time recurrence relation

I am faced to a non-linear discrete time reccurence relation and I can't find the general solution. The first question is: Is there a general recipe for finding the general solution to non-linear ...
1
vote
0answers
31 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 ...
2
votes
1answer
150 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 ...
4
votes
0answers
227 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 : ...
0
votes
1answer
40 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 ...
0
votes
0answers
68 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 ...
0
votes
0answers
50 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) ...
0
votes
0answers
35 views

Mathematical model of iris patterns

There seems to be some googlable information on recognition of iris patterns, but is there a generative model of such patterns? Specifically, if you simulate the mathematical model and render the ...
0
votes
0answers
165 views

Solution of the equation.

I have the following equation and I am interested in to find out the value of $r$, $(1-r)^3+3(1-r)h^2-3h(1-r)^2-\dfrac{wh^3}{KM}=0$ I simplified this equation to the following equation, ...
1
vote
0answers
43 views

Suggest a random phenomenon for which the Galton-Watson branching process might provide a reasonable model.

Suggest a random phenomenon for which the Galton–Watson branching process might provide a reasonable model. Be clear about the random variable beingcounted (Zn) and the interpretation of the notion of ...
-1
votes
1answer
180 views

St. Petersburg paradox!!!!

Can someone explain me how they get the $10.94$ at the Expected utility theory section (Solution to the paradox) {see the link below}. My problem is that they use a formula to calculate the Expected ...
0
votes
0answers
28 views

Variable Growth Rate and Logistic Model

I am reading my notes and I am unable to understand what the following means or how it can be interpreted. A logistic Model is given by the equation \begin{equation} ...
-1
votes
2answers
102 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 ...
0
votes
1answer
33 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 ...
0
votes
0answers
24 views

Basic excavation of a well

I'm working on a project and was hoping someone may be able to lend a hand confirm a few things or point me in the right direction if I'm wrong. The scenario is currently basic and as follows: There ...
2
votes
2answers
61 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 ...
-1
votes
2answers
53 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 ...
0
votes
1answer
23 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 ...
2
votes
2answers
101 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 ...
1
vote
0answers
47 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?
1
vote
1answer
68 views

Which math software?

As a math student interested in mathematical modelling, which math software should I start with (mathematica, matlabe, octave, or what else?)?
1
vote
0answers
22 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 $R$ ...
0
votes
1answer
33 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 ( ...
0
votes
1answer
57 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 ...
2
votes
0answers
41 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 ...
0
votes
1answer
44 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 ...
0
votes
0answers
25 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 ...
0
votes
1answer
62 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 ...
1
vote
1answer
52 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 ...
1
vote
3answers
228 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 ...
1
vote
2answers
141 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 \ \ ...
0
votes
1answer
61 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 ...
0
votes
0answers
22 views

propability of largest samples of repeated random divisions

I have a bunch of numbers $A_1=\{a_{1,1},\dots,a_{n,1}\in\mathbb R^+\}=\{1,\dots,1\}$, that get multiplied by independent uniformly $[0,1]$ distributed samples, e.g. $a_{i,2}=X_ia_{i,2}$. This process ...
0
votes
1answer
43 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 ...
0
votes
1answer
60 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 ...
1
vote
0answers
25 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 ...
0
votes
1answer
34 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 ...
0
votes
0answers
44 views

Solving interpolation between line and quadratic functions

I have two functions with known coefficients as follows: $$ f_1(x) = x^2 -2x + 2 $$ $$f_2(x) = 108 x - 206 $$ and I know that $$ (1-z) f1(x) + z f2(x) = 0 $$ $$ (1-z) f1'(x) + z f2'(x) = 0$$ ...
1
vote
2answers
42 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 ...
0
votes
1answer
45 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 ...