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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Euler angle in ellipsoid rotation

I am modeling an ellipsoid tumbling in a flow field. I have derived an expression for the Euler angle $\phi(t)$ of the rotation in the $x$-$y$ plane as a function of time, but its range is only $\pi$, ...
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38 views

Predicting time t given time t-n

..Hi, Everyone! I'm having a bit of trouble with a statistics/forecasting problem and I could use some help. I have temperature measurements for each hour of each day for the past 10 years. Given the ...
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23 views

simplifying equations from model

I'm using the community land model (CLM) to do some university work and I'm trying to understand some of the equations that go into the model, one example is: $$ ...
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5k views

Examples of types of mathematical models

I am a student currently doing a course on modelling and simulation. I came across the classifications of mathematical models and studied that they can classified as static or dynamic, deterministic ...
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41 views

Linear Fit Issue

Consider a quantity $Q$ that changes as a function of time. The function $Q(t)$ is not explicitly known. We know that $Q(t_{0})=Q_{0}$. Assume for $t-t_{0}\le\epsilon$, we have a method to estimate ...
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153 views

Request for reference and technical support [closed]

I am going to write my master thesis in order to become a teacher of mathematics (with second subject business management). Supported by the ERASMUS program I have the opportunity to do this in ...
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110 views

Math model - constrain GDP given different growth rates of industries

ideas needed to model national GDP given different sector growth rates subject to some contraints Given: GDP equations for $n$ industries depend on growth rates and time i.e. $g(r_1,t), g(r_2, t), ...
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164 views

Statistics on three variables/factors

I have what is probably a simple problem. I'm trying to say something about sells of candy bars. I got data of sells for a population of children. There are three parameters (factors) to this data: ...
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311 views

Edge weight function for graph instance of scheduling and allocation problem

I have difficulties developing a proper (non-scalar) edge cost function $c_e$ for my resource scheduling problem, which I mapped into a graph problem. Processes $P_i$ need resources $R_i \in ...
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58 views

is possible to deduce a formula for vaccination coverage from Whittle threshold theorem?

I am reading the article Application of Whittle’s stochastic threshold theorem to a chickenpox outbreak and I can't understand the meaning of the term "intensity" in the Whittle threshold theorem. In ...
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2k views

True Velocity and Heading

An airplane flies at $670$ MPH directly northwest. Wind blows at $70$ MPH from the west (i.e the wind is blowing towards the east). Determine the true velocity and heading of the plane. Steps: ...
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97 views

Modeling gravity field with finite elements

Well, my question is rather from applied maths area, not pure mathematics, so I am not sure that it's a place on this board for one. I want to solve a direct gravity gradiometry problem on 3D ...
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70 views

Acceleration of series convergence

everyone! I am currently struggling with following problem: compute the series $$ \sum\limits_{m=1}^{+\infty}\frac{1}{m}\sin(m\alpha)(\cos(m\beta_1) - \cos(m\beta_2)) $$ and $$ ...
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77 views

How to define an objective function that conveys the concept of selecting the best elements in a set

Consider a set of tasks $\mathcal{T} = \{t_1, \ldots, t_I\}$. Consider also a set of workers $\mathcal{W} = \{w^1, \ldots, w^J\}$, where each worker $w^j \in \mathcal{W}$ is associated with a value ...
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Question regarding the projective models of the anti-de-Sitter spaces and good online references for learning them from the scratch? (Specifics below)

As my title says above, I am trying to find answers to and also good online reference where I can find complete description of projective models of hyperbolic space, de-Sitter space and anti-de-Sitter ...
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235 views

Water Systems: When can I use buckets of water to simulate an ODE.

It is quite common to use physical systems to perform calculations (see here and here). This is for a number of reasons: sometimes the physical system is efficient, sometimes it helps us understand ...
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642 views

Relationship between Turing bifurcation, saddle-node bifurcation, and Hopf bifurcation?

Quoting from http://jxshix.people.wm.edu/2009-harbin-course/mississippi-bifurcation-2.pdf a Turing bifurcation occurs when for an ODE and related PDE $u' = f(u,v), v' = g(u,v)$ $u_t = d_1 \nabla ...
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55 views

Approximation of beam

Assume that there is a simply supported beam subjected to concentrated moments $M_0$ at each end. The governing equation is $$EI\frac{d^2y}{dx^2}-M(x)=0$$ with the boundary conditions $y(0)=0$ and ...
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112 views

Mathematical Modelling Homework

Considering a situation in which two motorists, person A and B, share the same driving route but own different sized vehicles. Person A fills up the vehicle’s tank at a station along normal route for ...
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87 views

How do you set up a system of ODE's for this problem?

The problem is as follows: Black and White balls are being created inside an arbitrary volume at rates of $Q_{B}$ and $Q_{W}$. They also disappear from the volume at rates $\lambda_{B}$ and ...
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1answer
49 views

What method or subject deals with the following?

Can you point me to areas and methods that deals with modeling output from input data? Say we think our output depends on certain parameters, and say we have samples of this output versus time and ...
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106 views

Differential Equations & Sinusoidal Functions

I am developing a model for sales forecasting, the basic premise of which is that the rate of change of sales is proportional to the number of possible buyers. In developing this model, I came up with ...
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1k views

Sine and Cosine Models

This is a general question about modeling the seasons using sine and cosine functions; I am trying to use sine and cosine to model cyclic behavior in sales due to the seasons (spring, summer, fall and ...
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128 views

How can I model a rotating system which does not have constant acceleration?

I've sampled a rotating system to come up with a list of positions and velocities at certain times. I want to be able to predict how long it will take to reach a certain speed and how far it will have ...
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36 views

Model selection with different error distributions

I have three different models for a given set of data. Each of the models has a different error distribution. These error distributions are known. How can I decide what is the best model?
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65 views

matrix question - help needed

I am doing revision on matrices and came across this question. The solution (the matrix provided below the question) is there. I am not sure how or why 180 is in the position (1,4) (row and column ...
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93 views

Tensor compact/matrix form.

I have got this tensor $S_{ij} = \frac{1}{2}(\frac{\partial u_i}{\partial x_j} + \frac{\partial u_j}{\partial x_i})$ Anyway I solve it for my problem and get $$ S_{ij} = \left( \begin{array}{ccc} 0 ...
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306 views

What kinds of sets are reasonable to place on the continuum?

Warning: I don't know anything about set theory so I wouldn't really know how to spot an existing answer if it were around. Suppose I want to model some economic good or product. I would like to ...
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1answer
347 views

How to classify equilibrium points

I have the two differential equations: $$\frac{dN_1}{dt} = N_1(2 - N_1 - 2N_2)$$ $$\frac{dN_2}{dt} = N_2(3 - N_2 - 3N_1).$$ I worked out the equilibrium points to be at $N_1 = 0, \frac{4}{5}$ and ...
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154 views

special matrix in terms of its covariance matrix

How can we find a matrix $S\in \mathcal{M}_{n,n}$ and $Z\in \mathcal{M}_{n,m}$ whose $n$ entries of the $i^{th}$ column $Z_i$ are correlated $Z_i \sim \mathcal{N}(0,S)$ where $S \in \mathcal{M}_{n,n}$ ...
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278 views

Pursuit curves and arc length question

I am studying pursuit curves where a fast pirate ship which pursues a heavily laden treasure ship which tracks along a straight line. The ratio of the speeds of the ships is r > 1 (which is fixed) and ...
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49 views

Solving a form of the logistic equation to arrive a given solution

I am writing my bachelor thesis on modelling of city growth and using the book Cities and Complexity by Michael Batty. On page 394, while modelling the growth as spatial epidemic, he writes: ...
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139 views

Shape of a Kite String

A kite is flown at some angle and elevation. Without wind, the string takes the shape of a catenary curve. But the wind is crucial. Is there a name for the shape of a kite string -- is it some ...
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86 views

Boltzmann machines - motivation for the energy function

I've been studying Boltzmann machines lately and was wondering if anyone could give me a "high-level" explanation or motivation for the energy function used: $$E = -\sum_{i<j} w_{ij} \, s_i \, s_j ...
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1answer
823 views

Python numerical solution for a nonlinear second order ODE with two boundary conditions

I want to solve numerical the next equation, in Python $$u''(x) = \left( a - \Big(b\big(u(x)^{2}\big)\Big) \right) \big(u'(x)\big)^{3}$$ it is a nonlinear second order $ODE$ with two $B.C$. ...
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479 views

How to find the length of a curved path.

We have to find a continuous model for a curved path which you then solve. A woman is running in the positive y-direction starting at x=50 (50,0) which is orthogonal to the x axis. At this point a dog ...
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2k views

Calculating equilibrium point of non-linear ODE with free parameter

I have two ordinary differential equations equations: $$ \dot{x}=1+x^{2}y-(1+A)x $$ $$ \dot{y}=Ax-yx^{2} $$ I need to find the single equilibrium point in terms of $A$. So set $\dot{x}$ and ...
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1answer
65 views

Amount of information a hidden state can convey (HMM)

In this paper (Products of Hidden Markov Models, http://www.cs.toronto.edu/~hinton/absps/aistats_2001.pdf), the authors say that: The hidden state of a single HMM can only convey log K bits of ...
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1answer
43 views

Trouble understanding a part of the book Cities and Complexity

I am writing my bachelor thesis or whatever it is called about modelling of city growth, using a book called Cities and Complexity by Michael Batty. It is not that mathematical, to be honest, it has ...
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65 views

Curvature of surface

So lets say I have a mesh and for each face I have the position of its $3$ vertices and the area of the face. So let's say I have a point $p$ on this face and a vector $v$ that goes from $p$ to the ...
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222 views

Looking for a Lyapunov function for the next system

I am really stuck looking for a Lypaunov candidate for the next system (which in simulation is stable). $$ \dot{x} = -(A+A^T)x + Ay \\ \dot{y} = K(x-y) $$ where x and y are vectors in R^3, A is a ...
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390 views

Slide Puzzle logic??

say there is an image made into a slide puzzle in a grid of sections 4 wide and 6 high, the missing piece that is missing so you can slide the other pieces of the puzzle around is always the bottom ...
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3answers
961 views

I need a differentiable function whose plot is a plateau and the steepness and width can be varied arbitrarily and easily

I need to model the solar radiation incident on a solar panel. I tried using $$\tanh(b*(x-a))-\tanh(b*x)$$ but it does not give me a lot of flexibility with the characteristics of the curve, namely ...
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25 views

Is there a trade model which takes in account credulity?

I have to admit I'm not to familiar with mathematical economics but, as a student in mathematics, I was trying to play a bit with a toy trade model I'm try to build over a finite population. My ...
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111 views

how to estimate a variable's upper limit with 95% confidence level?

Suppose I have a variable, $S(t)$, for stock price. So always have $S(t) > 0$. $S(t)$ is a random variable, with some volatility $\sigma$ and trend. Now the requirement is to estimate $\hat ...
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78 views

Computing the length of a path

The rectangular grounds at Hillingham University is going to have a new path built which takes the curved shape of $y=2.2x^2$, starting from the south-west corner - (taken as the origin in a graph) ...
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81 views

Calculating the expected number of items shared by chance in a Venn Diagram

I have a Venn Diagram that looks like this: $$A) \, 213 \quad B) \, 160 \quad A\cap B) \, 100$$ The items from $A$ come from a population where their probability to be selected is ...
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201 views

How large initial angular velocity is needed for pendulum to go completely around?

If a pendulum is initially at its unstable equilibrium position, how large an initial angular velocity is necessary for it to go completely around?
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134 views

Are there rigorous mathematical definitions for these waves?

My friend linked this .gif to me tonight, and asked me if I knew of any equations that might model these bottom two waves (the blue and green waves). Unfortunately, I am not far enough in my education ...
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55 views

a line perpendicular to a given line

I am confused now, I have a 2D line. If its equation is $r = x\cos(\theta) + y\sin(\theta)$, then what will be the line which is perpendicular to that line? Where $r, \theta$ is described ...