Tagged Questions

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 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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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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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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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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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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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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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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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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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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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 made. ...
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$4$ 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 ...
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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 ...
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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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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 ...
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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 $$\mathcal{J} = \begin{pmatrix} 0 & 0\\ b& -b \end{pmatrix},$$...
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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} \frac{d[B]}{...
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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 ...
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Does mathematical modeling assist in learning how to derive equations?

I am hoping someone can provide a starting point to the question: Would mathematical modeling be a good place to start learning how to derive equations and functions from a set of data? For example, ...
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Optimisation/Control in lieu of knowing the future …

I’m interested to hear about the methods that would be best applied to an optimization/control problem. Context: I’m looking at the concept of ‘peak shaving’ in power networks, which are achieved by ...
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3rd order polynomial with a covariate?

I'm a physiologist by profession. I've conducted a research study that examines the effect of altitude on sustainable power output (let's call this variable CP) in cycling. A 3rd order polynomial ...
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Root mean square function (RMS) in the ODEs of a dynamical system

I am trying to obtain the differential equations of a dynamic system in which one of the blocks calculates the RMS of a signal. When arranging the ODEs I see that the differential version of the RMS ...
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Prove that taking the inverse Fourier transform of frequency returns time.

If we evaluate the inverse Fourier transform of X(w) how do we know we get x(t) back? Link to X(w) and x(t) equations I know that integrating in the frequency domain results in getting information ...
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Important subjects for biological systems modelling

which subjects and tools are important for a person who wants to start modelling biological systems? For example, everyone knows that calculus is really important to step in any mathematical ...
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Determine the optimal number and location of the plants and pipelines in the 7 cities.

There are 7 cities, up to 4 plants to be made in them and up to 18 pipelines to be made connecting them. Determine the optimal amount of plants and pipelines to be made, the optimal locations of the ...
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Help finding TF from a mechanical system

I have been working on this past for a bit and I keep running into the same roadblock where I am having problems approximating the third order polynomial I get in the denominator of the transfer ...
I tried using Runge-Kutta methods to approximate motion equations in matlab but it turn out wrong. $$M\left(\frac{d^2x}{dt^2}\right)=F_n(\cosΦ - u\sinΦ) \\ M\left(\frac{d^2z}{dt^2}\right)=F_n(\sinΦ + ... 1answer 27 views How to compute Simple Linear Regression equation not using Least Squares Estimators? I know how to compute the Simple Linear Regression (SLR) equation using Least Squares Estimators, b_0 and b_1. But I was given the following table:$$ \begin{array}{c|lcr} & \text{mean} &...
For the solution: Just wanted to ask for $V_{3}(HTH)$ I get $S_{1}(H)$ and $S_{3}(HTH)$ to give me the same maximum value of $16$ so would it also be right if I used $S_{1}(H)$ nstead of $S_{3}(HTH)$?...