Does Fokker-Planck equation give us the exact measure of the statistical ensemble of the trajectories of the stochastic differential equation?

It is known that the FPE gives the time evolution of the probability density function of the stochastic differential equation. I could not see any reference that relates the PDF obtain by the FPE...

09 October 2019 9,834 6 View

Is it possible to stabilize an Infinite-dimensional system by stabilization of the corresponding approximated finite-dimensional system?

we can approximate an infinite-dimensional system with a finite-dimension system, (for example by proper orthogonal decomposition) If we stabilize the approximate finite dimension of an...

09 October 2019 223 6 View

Is it necessary for engineers to know the definitions of mathematical spaces?

We know that mathematicians study different mathematical spaces such as Hilbert space, Banach space, Sobolev space, etc... but as engineers, is it necessary for us to understand the definition of...

09 October 2019 4,950 4 View

In stochastic systems(SDEs), Most of the time we assumed that the disturbance and noise vanish at the equilibrium point, is it reasonable assumption?

One of the main stability theories for stochastic systems is stochastic Lyapanuv stability theory, it is the same as Lyapanuv theory for deterministic systems. the main idea is that for the...

31 December 2018 4,292 4 View

Under which condition it is possible to change the dynamics of a nonlinear system to an arbitrary dynamic with feedback control input?

Imagine we have an ODE system x_dot=[f1(x,u), f2(x,u), f3(x,u),....fn(x,u)] where f1,..,fn are nonlinear functions of control input u and states x, x is member of R^n and u is member of...

31 December 2018 7,430 6 View

Is there a general framework to compute the reachability set of nonlinear affine-control systems?

for linear control systems x_dot=Ax+Bu the reachability set can be calculated using the Image of the controllability matrix, i.e R=([B AB A^2B,....,]) and reachability set=Im(R) when rank(R)=n,...

31 December 2018 1,854 3 View

Is it possible to prove the stability of a continuous time system from its corresponding discrete version?

In a simplest case imagine we have a continuous finite-dimensional dynamic system described by and ODE x_dot=f(x) (1) , Is it possible to prove the asymptotic stability of (1) by...

11 December 2018 5,264 30 View

Which one is a stronger stability condition? Lyapunov stochastic stability or detailed balance?

in most cases for continuous time stochastic systems which are modeled by SDE, the Lyapunov stability conditions can guarantee the stochastic stability of the system, another definition In...

11 December 2018 3,911 4 View

Is it possible to establish the stability results based on pseudo-spectra for a linear differential operator?

In the theory of the stability of the differential operators, one could prove the stability results based on spectra of an operator, (all eigenvalues must be negative for example). one problem...

10 November 2018 2,847 7 View

What is the best method for generating a data-set for training in high dimensional function approximation with neural network?

Imagine we have an 7-D function f(P_i), i=1,...,7. Fortunately, we can create our own data sets for training, i.e we can choose as many samples from the sample space of each P_i (the sample space...

07 August 2018 6,717 5 View

What is the most Operating System (OS) which can be INSTALL on Tiny hard devices like Raspberry Pi (RPi) hardware ?

I'm targeting to deploy a mesh network and manually configure MANET routing protocols. I'm preparing scenarios, architectures, and hard devices needed to do that. Are there some step-by-step...

03 March 2021 1,931 5 View

Could you recommend any books about Number Theory?

Beginner level books. High level books. Analytical Number Theory. Algebraic Number Theory. Combinatorical Number Theory. Books about partitions. Books about primes.

03 March 2021 7,174 5 View

Can we classify HV and LV lines based on line length?

I have dataset which shows the length of power lines. I need to classify the lines based on the line length. Is there a rule to classify the High voltage (HV) and low voltage (LV) lines based on...

03 March 2021 4,116 4 View

Is there a classification scheme for rock cavities or caverns with respect to their size and shape?

The range of forms and sizes of cavities in rock is very big. Is there a classification scheme for rock cavities regarding their size and shape?

02 March 2021 4,511 3 View

Arena simulation - how do i model the following model in ARENA (see description) (new to ARENA)?

Hello, I'm fairly new to ARENA and I have the following problem: I have two queues in which, in each queue, a different order type arrives (both having an arrival rate of exponential 10). Order...

02 March 2021 2,431 3 View

Is there a powerful system for the security of the systems distributed on IoT systems?

Is there a powerful system for the security of the systems distributed on IoT systems?

02 March 2021 3,858 10 View

Which is suitable for use with Python? MySQL or SQL Server?

Which is suitable for use with Python? MySQL or SQL Server? What is your suggestion?

01 March 2021 3,422 3 View

How to choose ANN number of hidden layers and nodes?

Hello, Could you please share any interesting research explaining how to choose the number of hidden layers and nodes per layer in case of regression problems using ANN? Thank you, any help would...

01 March 2021 6,200 3 View

How to Eliminate cosine error and abbe error in LASER measurement system(for example Rhenishaw XL80)?

I like to do project in laser measurement system. My objective is to eliminate or reduce the cosine error, abbe error in Laser measurement system. I have Rhenishaw XL80 system. Please tell the...

28 February 2021 4,890 3 View

What is Flat Lens Antenna?

28 February 2021 5,433 3 View