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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Mathematical (or physical) formulation of life

I recently started to have interest in the characteristics of life. Especially, I wonder if there are some kind of mathematical description of the true meaning of life and how it is emerged. Why does ...
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1answer
180 views

Mathematical idea behind tax bracket

This may be a lame question. The tax bracket is a way to calculate the tax based on the taxable income. For example Imagine that there are three tax brackets: 10%, 20%, and 30%. The 10% rate ...
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119 views

Good model to reward contributions

I hope you guys find this an interesting question. Imagine you want to implement a system that rewards people for their contributions (regardless of quality or any external assessment). What is a good ...
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1answer
291 views

Problem with ratios, dimensionless quantities

I've been trying to understand how a ratio of two of the same units gives a dimensionless quantity. It makes no sense to me. For example, density in terms of mass and volume: $$d = \frac{m}{V}$$ ...
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1answer
354 views

Classify the fixed points at the origin

Consider the linear system $$\frac{dx}{dt}= -3x+2y, \frac{dy}{dt}= ax+6y, a \neq -9$$ classify the fixed point at the origin? Is the correct approach to investigate the steady states and how these ...
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1answer
714 views

Stationary points of an ODE-system (again)

There is another exercise where I am given a non-linear system of ODEs and a question that confuses me: Consider $$x'=x(y+1)\\ \text{ and }\\ y'=xy+2.$$ "Determine stationary points of the ...
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1answer
355 views

System of ODEs and Lyapunov function

I've tried to solve a little problem that goes as follows: Consider a system of ODEs: $$x'=y-x^3\text{ and } y'=-x^3-y^3$$ And the function $$L(x,y)=\frac{1}{2}y^2+\frac{1}{4}x^4.$$ Now I shall show ...
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181 views

Describe the nature of the fixed points

I have the following system describing a free-market economy: $$\frac{dp}{dt}=\alpha r,\qquad \frac{dr}{dt}=-\beta r$$ Where $\alpha$ and $\beta$ are positive constants, $p$ is the price and $r$ the ...
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415 views

Why does this example of Hardy-Weinberg equilibrium not work?

Background Info Hardy-Weinberg equilibrium is a mathematical model of the frequencies of alleles (i.e., versions of a gene) in a population. The model states that the frequency of the 2 alleles in a ...
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1answer
68 views

Need some help on petri nets?

Here's the question: $\qquad$ How do we go about doing this ? I have very little knowledge on petri nets. Can someone answer it for me ? (And regarding the program part , just give me an idea on ...
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1answer
203 views

Sunk cost auction modeling.

Consider the following auction concept. I call it a "SUNK COST AUCTION" Each person bids, but you pay all of the money that you bid for every bid you make. So, if you bid \$1 that \$1 is gone, even if ...
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1answer
232 views

Problem with continuity of a piecewise function

I am stuck with a homework problem which is about the modelling of tumor growth by ODEs. The function $A(t)$ is the amount of drugs in the patients blood. During some intervals (namely, $(n,n+\tau)$, ...
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972 views

How to design a weighted formula with multiple inputs?

Apologies if this is the completely wrong verbiage for this sort of thing... kinda new to this. We're designing a social website, where users on the site have several statistics associated with them. ...
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1answer
53 views

Reduce the range of weighted sum

i am using this weighted sum How to build a function that gives recent years higher weight? but I am getting values in the range 1- 0.0000002 How can I reduce this range ? Make it something like ...
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0answers
68 views

How are these operations the same? How to convert a multiplication in a different form?

I am reading on a specific operation, how it should be done in order to avoid overflow during multiplication. The operation is: $$( A * \text{state} ) \% M;$$ This is susceptible to overflow. The ...
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1answer
244 views

Cubic population model question

Have the following population model, $$ \frac {dN}{dt}= cN(N-k)(1-N)$$ The first stage of the question is to investigate the steady states, however im a little stuck on finding the solution to the ...
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1answer
76 views

Detecting lines and circles in x/y datasets

I'm trying to do some simple gesture recognition. Circles, I'm assuming, will simply be a set of points which are all within some specified distance range from center. Lines on the other hand, I'm not ...
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2answers
146 views

How to build a function that gives recent years higher weight?

I want to have a value for users between 0-1 , that shows how much they like movies of specific type depending on how many movies they have watched and movie type ( comedy , etc ). I have a data of ...
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2answers
737 views

Looking for function of bell-like curve that peaks quickly.

I'm writing a little Sage/Python script that would graph the cumulative effects of taking a particular medication at different time intervals / doses. Right now, I'm using the following equation: ...
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1answer
704 views

Rate of Loan Principal being repaid function evaluation

I am trying to obtain the function which gives the rate at which the principal of a compound interest loan is being repaid at. So over the life of the loan the total amount to be paid back is ...
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1answer
411 views

Mathematics From Futurama

Dear Professor Farnsworth, We at D.O.O.P are trying to mathematically model a rocket ship fueled by your employee Leela's pet Nibbler's pooped Black matter. Obviously this rocket ship is fueled by ...
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3answers
2k views

Calculating time of flight of object (Mechanics - horizontal elevated launch)

I need help with the following question: A smooth spherical object is projected horizontally from a point of vertical height H = 25.78 metres above horizontal ground with a launch speed of u = ...
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2answers
2k views

Calculating initial velocity (horizontal launch)

I need help for the following question: In a long jump event, an athlete jumps a horizontal distance of 7.56m. The athlete was airborne for 3.04 seconds. The acceleration due to gravity is taken as ...
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2answers
373 views

Practical physics problem about distance between lines.

I am a software engineer and I’m developing a soccer game. I have a solution for this problem based on Newton law and I’m using Newton method to solve the equation I got. I’m here because I think ...
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1answer
121 views

Solving $4t+{2\over t-3}+{2\over3}=0$ [duplicate]

Possible Duplicate: How would I rearrange this equation to make the subject $t$? The scenario is as follows: A sub-atomic particle is travelling in a straight line through a tubular ...
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1answer
158 views

How would I rearrange this equation to make the subject $t$?

$$s(t) = 4t + \frac2{t-3} + \frac23$$ where $s$ represents the position of either particle in the tubular cloud-chamber measured in centimetres, while $t$ represents the time in nano-seconds. It's ...
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1answer
627 views

How did Target figure out a teen girl was pregnant before her father did?

First of all I do not have a mathematics degree only a B.S. in finance so please take that into account when writing an answer. Generally what type of mathematics is involved here? And specifically ...
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1answer
159 views

Modelling a difference equation question?

Stuggling with this one: In a simple economic model, time t is set up as a discrete parameter (possibly referring to days or months), while demand $D_{t}$ and supply $S_t$ are described in terms of ...
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0answers
118 views

Mathematical model for my experiment?

I'm running a benchmark to find the efficiency of a my computer. There are $p$ control variables say, $x_1,x_2,...,x_p$ and one output variable $Y$. For example, every time I run an experiment I ...
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1answer
109 views

Equation model for project effort.

It is my first time here, so I hope I'm keeping on topic. I wanted to find an equation where I could use the variables which affect the amount of work, in a way that feeling it the variables, I'd ...
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2answers
263 views

Stochastic predator-prey

My system is a simple $P$ vs $I$ foxes- vs rabbits model given by: $$ \begin{cases} \frac{\mathrm{d}I}{\mathrm{d}t}=& \alpha_I+\lambda_IP- \gamma_II -\delta_IPI;\\ ...
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2answers
2k views

11th grade level exponential growth problem?

A certain strain of bacteria that is growing on your kitchen counter doubles every 5 minutes. Assuming you start with only one bacterium, how many bacteria could be present at the end of 96 ...
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Mathematical Modeling of Real-World Situations

I was considering how to model the following problem mathematically and was wondering what you thought the best way to do it is. "A takes 1 minute to cross a bridge, B takes 2 minutes, C takes 5 ...
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1answer
179 views

Von Mises width at half height

I'm fitting the following Von Mises type function to some data: $(A/2\pi)e^{k\cos(\theta)}+C$ where A and k are positive. I want to calculate the width at half height from the lowest point of the ...
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176 views

economic modelling asked for

I am putting together a proposal for a system of economic exchange which links a transaction of money through a period of time, and subjective relationship evaluation between two people. How can it be ...
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1answer
346 views

Heat Equation Derivation and Mean Value Theorem

Farlow book PDEs for Scientists and Engineers pg. 27 shows derivation for Heat Equation. It starts by stating Net change of heat inside $[x,x+\Delta x]$ = Net flux of heat across boundaries + Total ...
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1answer
118 views

Non-analytical equation

Suppose I have integrated a differential equation numerically using some time-interval $\delta t$. How might I determine the accuracy of the result? Does solving simultaneous equations reduce the ...
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1answer
453 views

Question Based On Mathematical Modeling [Applied Functions]

An example of a calulus book reads: A rectangular storage container with an open top has a volume of $10$ m . The length of its base is twice its width. Material for the base costs $10$ per ...
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1answer
87 views

How to change Hermite function to have a same shape with moving extremum point and zeros

If somebody has a experience with polynomials. How to set this Hermite function to have a general minimum where I want on $x$ axis, for example in $0.5$. Is it possible to be in analytic form ...
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2answers
341 views

Is there a mathematical function giving an approximation to human breathing over time?

I want to animate something with the same frequency that a human breathes in and out, something like the Apple Macbook power light when it is in sleep mode. So basically an ease in ease out function ...
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1answer
182 views

Help with recursion/difference equation manipulation

I'm trying to reproduce the analysis of a simple biological model from an old paper. The model describes the frequency of two organism types in a population as: $p_{t+1} = \frac{p_t ( s + (1 - ...
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4answers
633 views

Biological processes described by the exponential function

What are biological or biochemical processes that are described (stochastically or deterministically) by exponential function $f(x) = e^{ax}$? Edit: What about examples that are not related to the ...
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2answers
156 views

How to model multi-step cell differentiation

Can I better explain cell lineages using PDEs or stochastic?
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1answer
349 views

Conditional Expectation and the floor function

I have a piece of code the produces random integers. ...
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3answers
112 views

Is there a formal name for a mathematical model that has an overly sensitive parameter

I'm a software engineer with a bit of mathematics expertise working with an NGO that has developed mathematical models for ecosystem services. It turns out that one of these models is overly ...
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1answer
343 views

Population Dynamics model

I am currently searching for population dynamics models. Concerning animal population growth, I have found the following so far : Growth models for fish Predator-prey : Lotka-Voltera and ...
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2answers
258 views

Do Ambivalent Axioms have a place in Mathematics?

I can't think of any examples of ambivalent axioms in mathematics (two ideas are ambivalent if there are sometimes conflicts between them), so please let me humor you with a strange example. Suppose ...
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573 views

How to approach mathematical modeling of the human heart problem?

I have to create a mathematical model of the human heart but it was quite a time ago I finished University and I experience some difficulties with the math behind the subject. What is the necessary ...
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1answer
511 views

Simplify water salinity equations

I recently became interested in calculating water salinity from conductivity and temperature. I failed to find any theoretical model to how this is done, only empirical models derived from fitting to ...
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1answer
76 views

How to model a problem to validate/improve an attempt at solving computer programming problem

I have attempted a solution to a beginners programming question which produces what I think is unexpected output. I need a way to validate it and was hoping to do that mathematically. Problem ...