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

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 ...
0
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12 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
9 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
26 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 ...
2
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1answer
24 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
13 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
19 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 ...
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1answer
36 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
43 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 ...
0
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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 ...
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0answers
31 views

Can a process be both chaotic and stochastic?

I have been reading about processes like evolution in biology. As the environmental variables that effect an individual's fitness and its survival, are stochastic, they effect the individuals in an ...
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
36 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
13 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) ...
0
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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, $A$ = ...
0
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1answer
29 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 ...
0
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0answers
32 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 ...
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5answers
152 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
35 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. ...
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0answers
19 views

How do display matrix A,b,c when using AMPL for a Linear Optimization's problem?

When solving a linear program in the form max/min c^T subject to Ax=b in AMPL is there a way to display just the matrix A, b, and c. I am using the following model file and read in matrices for the ...
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 ...
0
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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 ...
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0answers
25 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 ...
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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 ...
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0answers
15 views

Fourier transform used for time series prediction?

For a given time series data set $(t=0,...T)$, we can use Fourier transform to data fitness $$ X(n) = \mu + \sum_{k}\left( A_k cos \frac{2\pi k n}{N} + B_k cos \frac{2\pi k n}{N} \right) +\varepsilon ...
0
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2answers
36 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 ...
0
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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 ...
1
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0answers
32 views

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
22 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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0answers
37 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 ...
1
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1answer
20 views

Assuming a solution to a PDE

I am working on exercise involving the PDE $\frac{1}{2}{\sigma}^2 S^2 \frac{\partial^2 P}{\partial S^2}-rP+r\frac{\partial P}{\partial S}=0$ The solution I am looking at says to assume ...
0
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1answer
88 views

probability density function, integral 1

Let (M,W) be a continous probability space (take M=(a,b)), and let $x:M \rightarrow \mathbb{R} $ be a random variable which is bounded. Prove that $ \inf_{t\in M} x(t) \le E(x) \le \sup_{t \in M} ...
1
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1answer
32 views

present value, continously compounded

Compute the present value of a payment of 10 000 Euro after 3 years, if the continuously compounded interest rate in the first year ist 4%, in the second year 6%, and in the third year 5%. For a ...
0
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0answers
27 views

Does the “truncation function” $\langle a,b\rangle : \mathbb{R} \rightarrow \mathbb{R}$ have an accepted name or notation? [duplicate]

Given real numbers $a$ and $b$ satisfying $a \leq b$, define: $$\langle a,b\rangle (x) = \mathrm{min}(b,\mathrm{max}(a,x)) = \mathrm{max}(a,\mathrm{min}(b,x))$$ (These numbers are equal because $a ...
1
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1answer
24 views

Different names for model with parameters specified and not?

Say I have a general model: $$y=\beta_{1}x_{1}+\beta_{0}$$ or $$y=\beta_{1}x_{1}+\beta_{2}x_{2}+\beta_{0}$$ I might be performing some operations to determine which general model to choose. Say I ...
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0answers
19 views

Disadvantages of particle swarm optimization method

I am using particle swarm optimization method. It has a lot of advantages, but I am looking for disadvantages of this method. Can you help me?
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0answers
17 views

Model linearly: What products to make, how much to make and in what plants to make them?

A company wants to make 3 new products for the upcoming week. We are given that: Each product can be made in 1 of 2 plants. At most 2 of the 3 new products should be chosen to be ...
1
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0answers
42 views

$4$ or more type $2$ implies $3$ or less type $1$

I'm having difficulties with the logic with the last part of the reformulation part of the problem below. Let $x_i$ be the the number of ships of type $i$ to purchase. For $4a:$ (the ...
0
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0answers
19 views

How to model the following scenario with an ODE if possible

Consider a cylinder, full of charged particles travelling through. From the perspective of looking through the tube, you would see a circle of particles and obviously this circle continues down the ...
0
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2answers
23 views

Are there alternatives to polygons in mathematical (computational) modelling?

So polygons are pretty standard in computer graphics, but from a mathematical perspective, one'd expect something more refined and sophisticated to be possible right? Polygons are not very ...
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0answers
12 views

Modelling a charged particle flowing travelling through a conductive pipe.

I'm on an internship and have a project to model how a charged particle might be affected by a conductive surface either side of it. Here's how I approached it: I assumed the particle had some charge ...
0
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1answer
50 views

behavior of the Linear system of an ODE model

I am working on a predator-prey model and the linearization about and equilibrium point $(0,e_2)$ has Jacobian matrix as follows $$\mathcal{J} = \begin{pmatrix} 0 & 0\\ b& -b ...
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0answers
30 views

Non-linear systems: Modelling the behavior of an oscillatory system when adding a perturbation.

I have a non-linear system of equations that describes an oscillatory system. the oscillations is generated by the interplay of two chemical species $A$ and $B$ Equation 1 \begin{align} ...
0
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0answers
12 views

show if L, R, E0, and r as in (sin r t) are constant, the amplitude of the steady-state current is a maximum when the capacitance is $C = 1/ Lr^2$.

Can anybody please tell me how to start this questions. im stuck at making a differnetial eq for it because $C$ isnt constant and i dont understand where to put $C = 1/ Lr^2$. This is a second ...