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
236 views

Phase Plane Analysis

Classify the fixed point at the origin and sketch an accurate phase portrait for the following system: $$\left\{\begin{matrix} \dfrac{dx}{dt}=36x-16y\\ \dfrac{dy}{dx}=-3x+28y \end{matrix}\right.$$ ...
0
votes
0answers
32 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. ...
1
vote
0answers
16 views

Difference equation representing change during the nth interval

"By examining the following sequences, write a difference equation to represent the change during the nth interval as a function of the previous term in the sequence. a. {2, 4, 6, 8, 10}" The answer ...
0
votes
0answers
21 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 ...
3
votes
0answers
143 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 ...
1
vote
1answer
56 views

Markov Chain with Memory

One of the defining characteristics of a Markov Chain is that it is memoryless: the next state depends only on the current state, and not on the set of preceding states. I'm looking for a ...
2
votes
1answer
227 views

Why does my Barabasi Albert model implementation doesn't produce a scale free network

I'm trying to implement the Barabasi Albert model to generate some scale free network matching a power law distribution of degree. I'm using a value $m = 2$ for the main parameter of the algorithm, ...
1
vote
0answers
23 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 ...
1
vote
2answers
618 views

Sine and Cosine Models

This is a general question about modeling the seasons using sine and cosine functions; I am trying to use sine and cosine to model cyclic behavior in sales due to the seasons (spring, summer, fall and ...
2
votes
1answer
822 views

Linear Programming: Three variable graphical solution

A small bank offers three type of loans: housing loans at $8.50$% interest, education loans at $13.75$% interest rates, and loans to senior citizens at $12.25$% interest. Further, it needs to ...
0
votes
0answers
24 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 ...
0
votes
1answer
29 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 ...
3
votes
2answers
62 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 ...
2
votes
0answers
43 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 ...
2
votes
2answers
20 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. ...
1
vote
1answer
264 views

How to model an aviation holding pattern mathematically?

A standard aviation holding pattern has four sections, each of which, in windless conditions, takes one minute to fly. The first is the inbound leg, which is the only one for which precise ...
0
votes
0answers
24 views

Find the expression of a function close to this drawing

I am trying to model mechanical response under constraint in materials, and I know that I need this kind of function if I want my model to be accurate. The point is, I have absolutely no idea about ...
0
votes
0answers
8 views

How to build a prediction model for exam score based on previous scores [migrated]

I am trying to construct a formula, which will take student's previous exam results (for ex: SAT) taken at particular dates and predict his future test result, given that he continues to study with ...
0
votes
1answer
65 views

Mathematical Modelling in Biology [closed]

First of all I apologise if my question is not supposed to be in this Stack-Exchange. So, I have an experiment to determine the fate of cells at certain age (see attached fig). Basically, we would ...
4
votes
1answer
58 views

A question in application of derivatives and vectors

Consider a skier who is sliding without friction on the hill ${y = h(x)}$ in a two dimensional world. The skier is subject to two forces. One is gravity. The other acts perpendicularly to the hill. ...
3
votes
1answer
31 views

Computational compass-and-straightedge constructions

I recently came across Ancient Greek Geometry, a web toy by Nico Disseldorp, and it got me wondering: is there a way to exactly model the points generated by geometric constructions, starting from two ...
0
votes
1answer
60 views

Mathematical Modelling Homework

Considering a situation in which two motorists, person A and B, share the same driving route but own different sized vehicles. Person A fills up the vehicle’s tank at a station along normal route for ...
-1
votes
1answer
216 views

Expected utility and St. Petersburg paradox

Can someone explain to me how they get the $10.94$ at the Expected utility theory section of the solutions to the St. Petersburg paradox? My problem is that they use a formula to calculate the ...
0
votes
0answers
37 views

Counting the Number of Combinations Conditionally

A bank issues 10 loans ranging from 1000 to 10000 dollars each and charges 5% interest on each loan. On average, the bank finds that 1 in 10 loan recipients defaults. If the loan that defaulted is ...
0
votes
0answers
5 views

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 ! ...
1
vote
0answers
12 views

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 ...
1
vote
0answers
37 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 ...
3
votes
1answer
55 views

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 ...
0
votes
2answers
25 views

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 ...
0
votes
0answers
31 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 ...
0
votes
0answers
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 ...
0
votes
0answers
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 ...
0
votes
1answer
27 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 ...
0
votes
0answers
29 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 ...
2
votes
1answer
124 views

Converting if else constraints into linear ones

I have the following two constraints: $$ x_1 \leq x_2 \leq x_3 \qquad \mbox{if } x_1 \leq x_3 \\ x_1 > x_2 > x_3 \qquad \mbox{otherwise} $$ Is there a way to get rid of the two conditions and ...
1
vote
2answers
305 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 ...
0
votes
0answers
34 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 ...
1
vote
1answer
44 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 ...
0
votes
0answers
55 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 ...
0
votes
3answers
297 views

How to find the length of a curved path.

We have to find a continuous model for a curved path which you then solve. A woman is running in the positive y-direction starting at x=50 (50,0) which is orthogonal to the x axis. At this point a dog ...
1
vote
2answers
65 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 ...
1
vote
1answer
53 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 ...
1
vote
2answers
49 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 ...
2
votes
2answers
557 views

How to calculate perceived value?

Is there a known formula to calculate perceived value? If I am auctioning some popular product that is worth $100 (shelf price), how much would people bid if they: Have a 1 in ...
1
vote
1answer
45 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 ...
1
vote
1answer
39 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 ...
1
vote
0answers
20 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 ...
1
vote
0answers
21 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 ...
0
votes
2answers
95 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.
3
votes
0answers
43 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 ...