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 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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726 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
686 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
408 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
371 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
620 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
117 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
106 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
256 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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3k views

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
175 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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175 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
345 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
326 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
181 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
625 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
154 views

How to model multi-step cell differentiation

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

Conditional Expectation and the floor function

I have a piece of code the produces random integers. ...
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111 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
340 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
256 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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564 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
497 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 ...
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1answer
370 views

What is a 4-8 mesh?

A paper I'm reading uses this classification for a mesh, but I'm not sure what the numbers 4 and 8 signify. Could someone clarify? Here's an image from the paper of a 4-8 mesh.
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1answer
222 views

Social network representation: graphs or sets?

for social network representation, what is better, sets or graphs ? What kind of feature the first gives that the second doesn't and viceversa?
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1answer
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How to make simple iteration in Mathematica

How to make simple iteration in Mathematica for this three equations and save $q$ for each step. If we define $q'=dq/dx$, $q''=dq'/dx$ we have two equations (1) ...
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514 views

How to make iteration for Newmark method in Mathematica 8

How to make iteration method for solving differential equations by Newmark method? There are just three equations which describe the Newmark method. I need q for time step for example 0.01. Also, for ...
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160 views

How to model server load?

I want to model the server under load. I'm using following assumptions: The server serves only one request at a time, and all requests take him exactly 100ms to process. All requests that came ...
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2answers
503 views

Conserved Quantities in Dynamical Systems

A simple pendulum is modeled by the (nondimensionalized) differential equation $$\frac{d^{2}\theta}{dt^2} = -\sin(\theta)$$ With the auxiliary variable $w$, this is equivalent to the first-order ...
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2answers
144 views

Choosing set of best estimators for linear least squares

I have a measured experimental dataset which is well approximated by the sum of several basis functions in linear combinations. Linear least squares of course gives me the optimal weight for each ...
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1answer
156 views

Competition Models

Need help getting started on this homework problem and I am really lost. The notes given on this subject are really sparse and I haven't found anything online that was useful. Sorry about the lack of ...
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0answers
179 views

Modeling propositional formulas in integer programming

Say I have an binary integer programming problem: \begin{equation*} \begin{aligned} & \underset{\mathbf{x,y}}{\text{minimize}} & & f_0(\mathbf{x,y}) \\ & \text{subject to} & ...
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Operational research: group n items in x groups according to measure/constraints

I am searching for a consolidated model to group n items in x groups. Do you know how to find on the web some resources on the above subject? In my idea it can be something like: I have 4 persons and ...
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3answers
506 views

Dollar Cost Averaging and Gas Prices

Dollar cost averaging says the if you invest a set dollar amount at the fixed frequency, you will come out better than purchasing a set number of shares at the same frequency. While filling up the gas ...
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2answers
4k views

What is a “free parameter” in a computational model?

In many articles regarding computational models of some particular phenomenon, there seems to be a consensus: "the smaller the number of 'free parameters' in the model, the better". So, what is meant ...
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265 views

Legendre Polynomials

I was given a "generic" matrix that I was told was constructed using Legendre Polynomials. ...
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1answer
312 views

Is all acclimatization modeled by Newton’s Law of Cooling?

I have in mind things like language learning (native or foreign), and growth to adulthood. Is acclimatization the same thing as saturation? Can the logistic function be regarded as simply an ...
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2answers
776 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 ...
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1answer
545 views

Automation of 3D Paper Modeling

I recently saw this creative paper contraption online this prior weekend and wanted to see if I could automate the process of creating all ~35 layers of an equation. Essentially what I would want the ...
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34 views

How can I learn to create and solve Rational Choice models?

I have some scenarios I would like to model using rational choice theory (i.e. utility maximizing agents). For example, a two population type (I suspect this means two representative agents), two ...