This paper is concerned with the numerical solutions of the vorticity transport equation (VTE) in two-dimensional space with homogenous Dirichlet boundary conditions. Namely, for this problem, the Crank-Nicolson finite difference equation is derived.  In addition, the consistency and stability of the Crank-Nicolson method are studied. Moreover, a numerical experiment is considered to study the convergence of the Crank-Nicolson scheme and to visualize the discrete graphs for the vorticity and stream functions. The analytical result shows that the proposed scheme is consistent, whereas the numerical results show that the solutions are stable with small space-steps and at any time levels.

Abstract
The use of electronic valves is commonly available. yet, the most
common is the techniques of communications as prod casting transmitter that
are used by these valves in addition to their use in communication tools as far
distance telephone, electronic measuring techniques , and others.
In this study, an attempt is endeavored for improving the efficiency of the
vacuum micro- valves(GI-19b) through activating their internal surfaces by the
use of ionic pumping which is used for treating valves which are out of order
(because of sedimentation some materials and oxide on its poles). The
existence of these materials and oxide increase the sum of current leakage
moving in between. The use of ionic pumpin

This investigation reports application of a mesoporous nanomaterial based on dicationic ionic liquid bonded to amorphous silica, namely nano-N,N,N′,N′-tetramethyl-N-(silican-propyl)-N′-sulfo-ethane-1,2-diaminium chloride (nano-[TSPSED][Cl]2), as an extremely effectual and recoverable catalyst for the generation of bis(pyrazolyl)methanes and pyrazolopyranopyrimidines in solvent-free conditions. In both synthetic protocols, the performance of this catalyst was very useful and general and presented attractive features including short reaction times with high yields, reasonable turnover frequency and turnover number values, easy workup, high performance under mild conditions, recoverability and reusability in 5 consecutive runs without lo

In recent decades, the identification of faces with and without masks from visual data, such as video and still images, has become a captivating research subject. This is primarily due to the global spread of the Corona pandemic, which has altered the appearance of the world and necessitated the use of masks as a vital measure for epidemic prevention. Intellectual development based on artificial intelligence and computers plays a decisive role in the issue of epidemic safety, as the topic of facial recognition and identifying individuals who wear masks or not was most prominent in the introduction and in-depth education. This research proposes the creation of an advanced system capable of accurately identifying faces, both with and

This paper proposes a new method to tune a fractional order PID controller. This method utilizes both the analytic and numeric approach to determine the controller parameters. The control design specifications that must be achieved by the control system are gain crossover frequency, phase margin, and peak magnitude at the resonant frequency, where the latter is a new design specification suggested by this paper. These specifications results in three equations in five unknown variables. Assuming that certain relations exist between two variables and discretizing one of them, a performance index can be evaluated and the optimal controller parameters that minimize this performance index are selected. As a case study, a third order linear time

In this research, Haar wavelets method has been utilized to approximate a numerical solution for Linear state space systems. The solution technique is used Haar wavelet functions and Haar wavelet operational matrix with the operation to transform the state space system into a system of linear algebraic equations which can be resolved by MATLAB over an interval from 0 to . The exactness of the state variables can be enhanced by increasing the Haar wavelet resolution. The method has been applied for different examples and the simulation results have been illustrated in graphics and compared with the exact solution.

     In this article, we aim to define a universal set consisting of the subscripts of the fuzzy differential equation (5) except the two elements  and , subsets of that universal set are defined according to certain conditions. Then, we use the constructed universal set with its subsets for suggesting an analytical method which facilitates solving fuzzy initial value problems of any order by using the strongly generalized H-differentiability. Also, valid sets with graphs for solutions of fuzzy initial value problems of higher orders are found.