# Questions tagged [mathematical-modeling]

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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### How to find optimal policy to maximise a desired resource over time?

Each week, we can decide to do a hunt or skip it. Starting at week $1$, the available reward from that hunt is a yellow shard, then a blue shard, then a red shard, repeating in that order (so e.g. ...
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### Stick gaming questions

One person would like to go from the origin to point (2000, 2000) using stick with 1 unit length. The stick needs to be place on safe endpoints (e.g., x and y axes or other safe sticks). Please give a ...
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### Find a function $\rho:[0,1]\to \mathbb{R}$ such that a total mass of any portion $(a,b]\subset [0,1]$ of the wire is given by $M(a,b)=\int_a^b d\rho$

Consider a wire of length $1$cm with constant density $\mu$(g/cm), containing two point-like masses $m_1$ and $m_2$ grams located at $s_1=\frac{1}{3}$ and $s_2=\frac{2}{3}$, assuming the wire is ... 10 views

### Structure to model multiple hierarchies on the same entities

Say I have a set of entities and multiple hierarchies based on them, each hierarchy modeling a different type of relationship. What would be a useful structure to model this scenario? For instance, ...
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### What's a good predictive modeling approach for a very small dataset (50-100 rows) [closed]

I want to model the performance of specific athletes, but instead of taking the big data approach and letting the model generalize (something I've already done), I want to create a high bias model ...
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### Mathematical Modelling reference request

I would like to self-study MATHEMATICAL MODELLING based on the following topics: Monte Carlo simulation modelling: simulating deterministic behavior (area under a curve, volume under a surface), ...
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### How do I find the function and derivative of an unknown curve?

I have $x$ and $y$ values to plot the curve and I need to find a tangent line of slope 1 that intersects the curve (and the point at which it intersects). I was trying to do polynomial and exponential ...
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### How to solve $y''(x) + \alpha = 0$ using the Finite volume method for one-dimensional steady state diffusion?

I am sharing something that I am seeing for the first time. I must solve the following boundary value problem \begin{align} \begin{cases} &y''(x)+ \alpha = 0, \ x \in I = [0,1], \ \alpha:= \text{...
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### How to make this mathematical modeling linear?

The problem I'm dealing with has the objective to minimize the amount of people we need to hire. We have 14 contracts with 14 companies, each of which have shared with us the amount of workers that ...
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### How to find the basic reproduction number?

I have just begun studying stability of dynamic systems. I came across this model system where I have no information about the coefficients, but I assume that they are strictly positive: \begin{...
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### Why can certain variables be left out of an Objective function in Mathematical Programming?

I have an objective function that has the form: \begin{equation} \min \qquad \sum_{i} \omega_{i}x_{i}q_{i} \end{equation} Where $\omega_{i}$ is the weight of variable $i$, $x$ is the decision ...
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### State Space Representation of a discharge through a gate

I have one equation that describes the discharge through a radial gate placed in a hydro power plant, given by $$Q = \frac{dV(t)}{dt} = C_g \cdot D \cdot L \cdot \sqrt{2\cdot g \cdot H_g(t)}$$ where ...
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### Modelling - Looking for a function that is similar to a combination of a quadratic and exponential

I want to model the following dataset in this plot.plot. The dataset is posted here. The left half looks like a parabola and the right half looks like an exponential. If I use a piecewise function to ...
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### Help for generic logisitic population growth with variable harvesting problem

I am attempting to work through a common problem entailing variable harvesting of a population growing logistically. I am struggling to determine all the properties for stable harvesting. I will ...
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### Find a value $\alpha$ so that $\displaystyle\lim_{n\rightarrow}X_ne^{-\alpha n} = V$

We model a species population on an annual basis, where the number of juveniles in year $n$ is $J_n$ and the number of adults is $A_n$. Our model has the following form \begin{align*} &J_{n+1} = ...
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### Logistic ODE with negative initial condition

For the ODE with negative initial condition, say for example \begin{align*} \dot{x}= rx\left(1-\dfrac{x}{K}\right),x(0)=-K \end{align*} From the phase portrait, $x(t)$ should converge to $-\infty$ as ...
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### How to find the equilibrium point of this system?

I've been looking for the equilibrium point with the help of SymPy (Python Library). Even one of the equations cannot be found with SymPy because the solution is very long. I'm curious about the ...
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### Find the effective reproduction number for a Markovian model

I would appreciate help with what formula I should use to calculate the effective reproduction number for a general stochastic SIR model (Markovian model). I have a general stochastic SIR model (...
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### Solve the graph problem with a specific limitation.

Assume that there are a set of roads that connect the cities between A and B. We model this as a graph of $n$ nodes (cities) connected by $m$ edges (roads). Each edge weight corresponds to the time it ...
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### I want to find the most efficient way to build/structure a city in SimCity BuildIt. Where should I even start mathematically to do so?

So for those unaware, Simcity BuildIt is a city-building game where you are the mayor and aim to build and manage the perfect city. Some of the game mechanics that I wish to model are explained below.....
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### How many clients should I trust?

I hope this is the right place to put this problem. Otherwise, I beg you to teach me where to put it Supposing a laptop company organizes a month-event in which it shows and sells its new 15 laptops (...
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### What is the probability that a marble from the urn has been picked up by exactly $n$ people?

An urn starts with $m$ marbles and is then approached by $p$ people, each of which picks up $k$ marbles, discarding one and returning the rest to the urn. The urn now has $m - p$ marbles remaining. ...
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### finance mathematics [closed]

A factory contributes £1 million into a small city. It is estimated that 75% of that money is respent back into the community. Economists assume that the money is re-spent again and again at a rate of ...
1 vote
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### The coordinates of vertices in sierpinski triangle [closed]

For a given sierpinski triangle (https://en.wikipedia.org/wiki/Sierpi%C5%84ski_triangle) what are the coordinates of vertices of triangles inside the main triangle? can one have closed formula for ...
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### Biological meaning of "eigenvalue" in DDE-based population model

For example, consider a Verhulst model with delay $$\boxed{\dot N(t) = r N(t) \left( 1 - \frac{N(t-T)}{K} \right)}$$ where $r$ gives the reproduction rate and $K$ means the carrying capacity of the ...
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### Is it reasonable to multiply the output of a model by a constant in an attempt to calibrate and better match real life data?

I'm trying to model the volume change of a lake. I've developed a rough mathematical model that somewhat matches the actual volume change of the lake. However, my model doesn't quite match exactly. ...
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### How would you calculate the lifetime risk of a specific cause of death for people living today, assuming annual rates are constant?

It's been about seven years since I took differential equations, and I'm trying to wrap my head around something. This is just for my curiosity, and it's absurdly oversimplified, but I just want to ...
1 vote
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### Amplitude and frequency of undamped forced oscillations

I am solving an atypical problem. The problem is of forced undamped oscillations: $$x''(t) + 9 x(t) = 5\sin(2t) − 6 \cos(4t)$$ with initial conditions $$x(0) = 0$$ $$x'(0) = 4$$ The solution is clear ...
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### Fences question verification

For a general system of equations $x’=f(x,y)$ , $y’=g(x,y)$ a $C^1$ curve $γ$ Is called a fence if for some continuous normal $n$ to the curve we have $(f,g) \cdot n \geq 0$ everywhere along the curve....
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