although elzaki transform is stronger than sumudu and laplace transforms to solve the ordinary differential equations withnon-constant coefficients, but this method does not lead to finding the answer of some differential equations. in this paper, a method is introduced to find that a differential equation by elzaki transform can be ‎solved?‎

The extreme precision requirements in semiconductor manufacturing drive the need for an active vibration isolation system in a laser pattern generator. Optimizing the controller would not only improve isolation performance, but could also reduce the cost of ownership by extending lifetime of consumables and stretch service intervals. The optimization has been performed and evaluated in a model ...

A given monoid usually admits many presentations by generators and relations the notion of Tietze equivalence characterizes when two describe same monoid: it is case one can transform presentation into other using families so-called transformations. The goal this article to provide an abstract geometrical understanding well-known fact, constructing a model structure on category presentations, i...

We develop a method for calculating the eikonal function (or phase function) of light field, ensuring formation prescribed irradiance distribution in geometrical optics approximation. In proposed method, problem being solved is formulated semi-discrete form as maximization concave function. For finding solution to latter problem, gradient used, with analytical expressions obtained gradient. Usi...

Matrices equivariant under a group of permutation matrices are considered. Such matrices typically arise in numerical applications where the computational domain exhibits geometrical symmetries. In these cases, group representation theory provides a powerful tool for block diagonalizing the matrix via the Generalized Fourier Transform. This technique yields substantial computational savings in ...