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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Future Space Opportunities for a Mathematician [on hold]

I don't know if this question should be asked here or on "Mathematics Educators", however I'll post it here for the moment. I've just finished my first year of Mathematics and I do really like maths. ...
2
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1answer
24 views

Problem of Linear Programming, Scilab or Octave

I have to solve this with Octave or Scilab. There's an airplane company with airplanes flying to 3 different destinations (London, Paris, Rome). Schedule of flights ...
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26 views

Model for headphone quality as a function of price

I've looked for any mathematical model that shows headphone quality as a function of the price of the headphones, but have not found anything yet. Of course, "quality" is quite subjective, which could ...
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0answers
27 views

Prediction for time series

Suppose we have several weeks (say, 30) in a row and number of advertisements sent on e-mails on each week and number of the following orders of the product. How can I estimate the necessary number ...
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29 views

tangent space in a moving coordinate frame

I've got a problem in some geometry of flow. For the sake of completeness I will give the complete derivation of the equation of interest, but I will seperate it into derivation part and question ...
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0answers
21 views

Interesting/emerging research topics in mathematical modelling? [closed]

I get the privilege of doing an undergrad research project next year, and I've decided to go in an applied/computational maths route. The problem is, I have no idea where to start and despite looking ...
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0answers
27 views

Make a mathematical model from the given temperature problem

Find the temperature $u(x,t)$ in a laterally insulated bar of length $L=3.14$ $m$ having the material property $k=c\rho$ whose ends are kept at temperature $0$ degree Celsius, assuming that the ...
7
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1answer
197 views

Is there any probability model for multi-stage motion of an object such as this.

I have this following case (please refer to attached pic below) where a particle is resting on the ground and it needs a minimum amount of force (Fmin) to reach from one level to the next level. But ...
6
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3answers
848 views

Probability sum of 5 before sum of 7

Pair of fair die are rolled (independently I hope) infinitely. Find probability sum of 5 appears before sum of 7. 2 approaches: $$P(\text{sum of 5 appears before sum of 7})$$ $$= P(\text{roll 1 ...
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0answers
38 views

What constitutes sensitivity to initial conditions for a system of continuous ODEs?

I am currently working on a disease model (5 dimensions) which seems to exhibit sensitivity to initial conditions. I have used numerical analysis following the method described in Wolf's paper (link ...
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1answer
38 views

Books on mathematical biology

Can someone recommend good books on mathematical biology for self study. Especially to understand SIR models and stochastic models such as branching process. For SIR models I want more of beginner ...
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18 views

SIR model parameter notation

I am reading on SIR models and I found this article In the article it has three groups as one without vaccination, one with only whole cell(wP) vaccination, and one with only acelluar(aP) vaccination....
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1answer
15 views

Poisson Mean Term reduce with time

I've had a search for the answer to this problem but I can't find a solution anywhere. I am using a Poisson model and estimating the average time of a potential insurance claim arising in the future. ...
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1answer
16 views

Finding equation of a bent sufficiently flexible cardboard of length $l$ fitting into a gap of width $m<l$

I was thinking about how the walls of a barrel is made then I realized it is someone like fitting a piece of wood of length $l$ in between some "gap" of length $m<l$. This would cause the piece of ...
0
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1answer
24 views

Increase Profit sale car with respect to rebate

Tesla makes $ 1,500 $ dollars on sale of model 3. It is estimated for every $100$ dollars of rebate, sales increase by $15$%. Use one variable optimization to maximize profits. I did pass my calc ...
0
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1answer
15 views

How to denote the aggregation of values into a vector?

How do I denote that I am aggregating values into a vector? For example, I have a set of values $F$ in which a function $fun$ will be applied. Finally, a vector is build with the results. For ...
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0answers
23 views

Do you know an operation in which the order of elements does not matter but repetitions is allowed?

In order to present a concept in an article, I need an operation in which the order of elements does not matter but repetitions is allowed. For example, if a have some vectors [1 2 3], [2 3 1], [1 2 ...
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2answers
51 views

How do I develop a formula to find the height of a male using his femur? [closed]

I'm a grade eleven math student and I need a formula to find the height of a 15/16 year old male subject using only the length of his femur. I'm very confused on how to do this, please help, it's for ...
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0answers
13 views

What is the mathematical model for a Parallel Machine Scheduling with multi-processes?

Parallel machine scheduling is a problem contains $i$ jobs and each job have $j$ processes and each processes can be processed on $k$ different machine. Processes can not be interrupt and have to be ...
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0answers
10 views

Bounds on the divisor of Webster's apportionment method

I am currently in the process of studying various apportionment methods in a summer class, and while learning about Webster's apportionment method (also known as Webster-Willcox or method of major ...
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1answer
29 views

Solving functional equation $\frac{f(s, t)}{f(s, m)} = \frac{1}{1+s(m-t)}$

I want to find a functional equation $f(s,x)$ such that $$\frac{f(s, t)}{f(s, m)} = \frac{1}{1+s(m-t)}$$ If it helps the context I need this in is where $t$ is a member of a set of real number and $m$...
2
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1answer
27 views

What model should I use for judging a dimension given only composed data with another?

I am attempting to upgrade a modeling system using a limited type of statistical information, but with the sample covering the entire system. The problem is how to use the additional information in ...
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0answers
14 views

Analysis of incomplete system of diferential equations

I need to find information about the kinetics of a reaction. I tried to solve this problem first generalizing the equations for the different kind of reactions yielding an equation like: $$ \dot{x} =...
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0answers
20 views

Simple example of “Spike-and-Slab Prior” for Bayesian Inference

I would really like to understand how Spike-and-Slab Priors work in relation to Linearized Models. Can somebody provide a toy example of a Spike-and-Slab Prior with a Bernoulli spike and a Gaussian ...
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0answers
11 views

How to model a point force with uncertain concentration point?

I consider a beam which is bent under influence of a point force concentrated at some point $\xi$ of the beam. The exact co-ordinate of $\xi$ is not known, but it is known a neighbourhood $(l_0,l_1)\...
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1answer
38 views

Can anyone answer this equation or tell me what it is? [closed]

I have been sent an image, and have no idea what it means. Think this is the best site to try. The image is of the equation $$W_T=\sum_{i=1}^nW_i\;.$$
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0answers
18 views

Which of the following is more efficient?

In an auditorium where 100 people are sitting, with 10 people in each of the 10 rows. What will be the most efficient way of increasing the distance between the first row and the stage: by making the ...
0
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2answers
53 views

asymmetrical sine wave

How do you model a sine wave that begins to shift over asymmetrically (like a ocean swell approaching a beach)? Is sine even the right function for this model, or is some other type of function better?...
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0answers
12 views

Match harmonics while decoding the speech signal

There is a matlab's program. In the input parameters is a wav file. After executing a program there are appearing an array of frames. Frames partially recover each other. In each frame there are ...
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0answers
18 views

function to model breaking wave

What is a good parametric function to model a breaking wave (im ok with something complicated)? More specifically, I am looking for a general form, such that it looks like a normal swell and then as a ...
0
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0answers
14 views

Modeling population density with PDE

If we know that the population density $u(x,t)$ in some lake varies as a function of $x>0$ and time $t$, where $x$ increases downwards with depth, and that the population diffuses with constant $D$ ...
0
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1answer
38 views

Conditioning Poisson on Poisson [closed]

There is a bus, whose departure at a stop is distributed as poisson(mu). People arriving to the same stop is distributed as poisson(lambda). Find the PMF of the number, N, of people on any given bus. ...
2
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2answers
106 views

Model for spread of infection, with vaccination

I'm trying to solve following problem: $N = 10^6$ ... number of people $ir = 8\% $ ... infection rate time unit - 1 day And when there are 3% of population infected, vaccination begins. Its effect ...
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1answer
15 views

Using a continuous function to describe discrete data

I've always been told to use discrete functions with discrete data and continuous functions with continuous data. This especially comes to light when talking stats and people emphasize the difference ...
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0answers
20 views

Modeling simple linear equations

This should be pretty simple but I'm blanking on this. I need to model (graph) how path 1 becomes equally as efficient as path 2 as the distance of path 2 increases. distance of path 1 (from A to B) =...
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0answers
25 views

how do I resolve equations that are both dependant on each other

I'm working on a project concerning the ideal power equation of aerodynamic bodies seen here: $$P = \frac{1}{2}C A D v^3 + \frac{W^2}{Db^2v}$$ where $P$ = power, $C$ = coefficient of drag, $A$ = ...
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1answer
30 views

How can I adduce the mathematical model in my master thesis?

Please explain how to adduce and describe the mathematical model obtained by neural network modeling, if the model contains 50 inputs and five neurons in the hidden layer. How to show values of ...
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36 views

Curve fitting on non-linear ODE data

Background The graph below was generated by a set non-linear ODEs. For those of you who might want to know: It shows the maximum distance achieved by a cylinder when fired at a specified initial ...
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5answers
154 views

Can we abuse traffic patterns to get home earlier?

I had a heated discussion with my co-worker today, and was wondering if someone here could shed some light on this situation. The post is a bit lengthy, but I wanted to put all my intuition down in ...
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0answers
36 views

How can I correctly catalog this partition problem?

Studying the partition problems, I tried to do an special version to apply it to a kind of model of "orbits and energy levels" (explained below), but I am having problems to properly catalog this. ...
0
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1answer
12 views

Diffusion model - sign of boundary condition

I'm trying to compute the concentration of some pollutant in the rectangular pool. The pool is isolated from two sides (hatching in the picture), on the third side there is some cleaner which ...
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0answers
7 views

The difference between Linear Regression and SLR?

I can't find any videos or pages online explaining this in a straightforward way. Here's my understanding of it. The SLR model uses a Linear Regression Model (Y = B_0_ + B_1_X + ε). It becomes "...
0
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0answers
26 views

linear, homogeneous recursion, biological interpretation

Given the recursion $u_{k+1}=\frac{1}{2}(3 u_k - u_{k-1})$ find the expression of $u_k$ in dependence on the values $u_0$ and $u_1$. What is the limit as $ k\rightarrow \infty$ of $\{u_k\}_{k}$? Give ...
0
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1answer
53 views

Max $z = x_1(1-x_2)x_3$ s.t. $x_1 - x_2 + x_3 \le 1$

Using dynamic programming, Maximise $$z = x_1(1-x_2)x_3$$ subject to $$x_1 - x_2 + x_3 \le 1$$ $$x_1, x_2, x_3 \ge 0$$ Here's the outline of my solution 1. How is it? Let $y_2=...
0
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2answers
37 views

Find the price of the bond using its book value

A n year 1000 par-value bond with 8% annual coupons has an annual effective yieled of i, 1+i >0 . The book value of the bond at the end of the third year is 990.92 and the book value of the bond at ...
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1answer
26 views

Solving a differential equation for a cyclic model?

I am trying to figure out how to solve this differential equation for the initial condition, but I am completely lost and the book doesn't cover anything like this in the same section. So can anyone ...
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Models for Probability Density Functions with unknown parameters and given mean and variance

The PDF $f(x)$ of a non-negative random variable $x$ has the structure $$f(x)=\exp (a-bx-cx^{2})$$ where $a$, $b$ and $c$ are any model parameters. It is assumed that $c\ge 0$ so that $f(x)$ does not ...
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0answers
23 views

Finding equilibrium points of a system of nonlinear differential equations

I am currently working on a spatially explicit ODE model with dispersion to study the population dynamics of mosquitoes. I wish to compute the equilibrium values of the populations as functions of the ...
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41 views

Does anyone known the parametric equations for Cloud Gate?

I would like to use Mathematica to plot the famous Chicago "Bean." I couldn't find parametric equations anywhere and was wondering if anyone knew them. Thanks!
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28 views

How to analyse infinite equilibrium points?

I'm work in a predator-prey model, and for some values of parameters, the system of equations is: $x'=-(1+x)^3xy$ (prey) $y'=-P(x-1)^2y$ (predator) with $P>0$ constant. Only equilibrium ...