In this paper the Galerkin method is used to prove the existence and uniqueness theorem for the solution of the state vector of the triple linear elliptic partial differential equations for fixed continuous classical optimal control vector. Also, the existence theorem of a continuous classical optimal control vector related with the triple linear equations of elliptic types is proved. The existence of a unique solution for the triple adjoint equations related with the considered triple of the state equations is studied. The Fréchet derivative of the cost function is derived. Finally the theorem of necessary conditions for optimality of the considered problem is proved.

The research aims to determine the required rate of return according to the Fama and French five-factor model, after strengthening it by adding the indebtedness factor to build the Fama and French six-factor model FF6M-DLE. The effect of the indebtedness factor on the company's profitability and the real value of the ordinary shares calculated according to the (equivalent ascertainment) model and its suitability with the company's situation, and an analysis of the fluctuation between the market value and the real value of the ordinary stocks.

       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.

     The aim of this paper is to study the quaternary classical continuous optimal control for a quaternary linear parabolic boundary value problems(QLPBVPs). The existence and uniqueness theorem of the continuous quaternary state vector solution  for the weak form of the QLPBVPs with given quaternary classical continuous control vector (QCCCV)  is stated and proved via the Galerkin Method. In addition, the existence theorem of a quaternary classical continuous optimal control vector governinig by the QLPBVPs is stated and demonstrated. The Fréchet derivative for the cost function is derived. Finally, the necessary conditions for the optimality theorem  of the proposed problem is stated and  demonstrated.

The importance of the research lies in knowing the effect of the exercises of the reciprocal method in developing some physical abilities in learning the performance of the players for the effectiveness of the long jump in an economical manner in terms of time and effort and knowing their positive impact and the extent of their impact in creating the required learning for students, and the research aims to prepare reciprocal style exercises in developing some abilities The researchers used the experimental method in the pre and post test for the experimental and control groups to suit the nature of the research, and the research community was identified for the long jump players, the Specialized School for Talent Care in the 2022 sports sea

In this research, study the effect of sunspots on electromagnetic radio signals when it passed through F layer. The evaluation for this effect is carried out on radio Jove telescope frequency (20.1MHz) observations result. Radio emission for Jupiter storm burst observations over 11 years (1999-2009) from Hawaii, USA station (about 37611observations must be attended), are used in this research.
Two data limitations are applied on number of observation for Hawaii station, first due station location, second due to the reception of telescope antenna. The number of observations are reduced to 337 due to these limitation, but the actual number that be detected by station telescope is only 20.A model for ionospherical effect ,only due to sun

      This research evaluates the optical properties of an inhomogeneous and non-paraxial system using a solar ball lens (SBL) as a new thermal solar concentrated collector. This evaluation is based on detecting a diacaustic curve in a straightforward and accurate manner, with the diagnostic relying on image processing as a computational tool using the MATLAB program rather than a complicated numerical analytic procedure. The circle of least confusion (CLC) of the (SBL), (Fluorinated ethylene propylene (FEP) polymer – water core), was calculated. Furthermore, the study evaluated the maximum geometrical concentration ratio (G C) of refracted solar radiation that can be captured by a receiver of the (SBL). Without energy losses due

Bacteria could produce bacterial nanocellulose through a procedure steps: polymerization and crystallization, that occur in the cytoplasm of the bacteria, the residues of glucose polymerize to (β-1,4) lineal glucan chains that produced from bacterial cell extracellularly, these lineal glucan are converted to microfbrils, after that these microfbrils collected together to shape very pure three dimensional pored net. It could be obtained a pure cellulose that created by some M.O, from the one of the active producer organism like Acetic acid bacteria (AAB), that it is a gram -ve, motile and live in aerobic condition. The bacterial nanocellulose (BNC) have great consideration in many fields because of its flexible properties, features

The aim of the research is to clarify the measurement of the impact regarding financial value of human resources on investors' decisions by considering that the human element is one of the assets of the company. Therefore, a set of criteria must be available to determine the applicability of these standards in the human resource because it has an effective role in the success for the company. Is to measure the value of human resources in a financial format according to the first two methods depends on the value and the second depends on the cost.

In order to achieve the objectives of the study, a questionnaire was designed to survey the views of a number of employees of the General Company for Leather Industries in order to arriv