In this work, we prove that the triple linear partial differential equations (PDEs) of elliptic type (TLEPDEs) with a given classical continuous boundary control vector (CCBCVr) has a unique "state" solution vector (SSV)  by utilizing the Galerkin's method (GME). Also, we prove the existence of a classical continuous boundary optimal control vector (CCBOCVr) ruled by the TLEPDEs. We study the existence solution for the triple adjoint equations (TAJEs) related with the triple state equations (TSEs). The Fréchet derivative (FDe) for the objective function is derived. At the end we prove the necessary "conditions" theorem (NCTh) for optimality for the problem.

     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.

This paper is illustrates the sufficient conditions of the uniformly asymptotically stable and the bounded of the zero solution of fifth order nonlinear differential equation with a variable delay τ(t)

The aesthetic and technical expertise help  in producing the artistic work and achieving results in aesthetic formulations that reflect the aesthetic and  expressive dimensions and the reflective dimensions of the pottery, surpassing its traditions, asserting  its active presence in life, cherishing it  even when it  breaks  or get damaged   by employing techniques that are originated  from  the Japanese environment.

                       The research problem is to study how ( Kintsugi) technique and similar techniques are used to create  new rebirths of pottery piec

       There are many techniques for face recognition which compare the desired face image with a set of faces images stored in a database. Most of these techniques fail if faces images are exposed to high-density noise. Therefore, it is necessary to find a robust method to recognize the corrupted face image with a high density noise. In this work, face recognition algorithm was suggested by using the combination of de-noising filter and PCA. Many studies have shown that PCA has ability to solve the problem of noisy images and dimensionality reduction. However, in cases where faces images are exposed to high noise, the work of PCA in removing noise is useless, therefore adding a strong filter will help to im

The aim of this paper is prove a theorem on the Riesz mean of expansions with respect to Riesz bases, which extends the previous results of Loi and Tahir on the Schrodinger operator to the operator of 4-th order.

  The aim of this paper is to prove a theorem on the Riesz means of expansions with respect to Riesz bases, which extends the previous results of [1] and [2] on the Schrödinger operator and the ordinary differential operator of 4-th order to the operator of order 2m by using the eigen functions of the ordinary differential operator. Some Symbols that used in the paper:     the uniform norm. <,>   the inner product in L2. G   the set of all boundary elements of G. ˆ u   the dual function of u.