This paper is concerned with the quaternary nonlinear hyperbolic boundary value problem (QNLHBVP) studding constraints quaternary optimal classical continuous control vector (CQOCCCV), the cost function (CF), and the equality and inequality quaternary state and control constraints vector (EIQSCCV). The existence of a CQOCCCV dominating by the QNLHBVP is stated and demonstrated using the Aubin compactness theorem (ACTH) under appropriate hypotheses (HYPs). Furthermore, mathematical formulation of the quaternary adjoint equations (QAEs) related to the quaternary state equations (QSE) are discovere  so as its weak form (WF) . The directional derivative (DD) of the Hamiltonian (Ham) is calculated. The necessary and sufficient conditions for

In this paper, our purpose is to study the classical continuous optimal control (CCOC)  for quaternary nonlinear parabolic boundary value problems (QNLPBVPs). The existence and uniqueness theorem (EUTh) for the quaternary state vector solution (QSVS) of the weak form (WF) for the QNLPBVPs with a given quaternary classical continuous control vector (QCCCV) is stated and proved via the Galerkin Method (GM) and the first compactness theorem under suitable assumptions(ASSUMS). Furthermore, the continuity operator for the existence theorem of a QCCCV dominated by the QNLPBVPs is stated and proved under suitable conditions.

In this paper, three approximate methods namely the Bernoulli, the Bernstein, and the shifted Legendre polynomials operational matrices are presented to solve two important nonlinear ordinary differential equations that appeared in engineering and applied science. The Riccati and the Darcy-Brinkman-Forchheimer moment equations are solved and the approximate solutions are obtained. The methods are summarized by converting the nonlinear differential equations into a nonlinear system of algebraic equations that is solved using Mathematica®12. The efficiency of these methods was investigated by calculating the root mean square error (RMS) and the maximum error remainder (𝑀𝐸𝑅n) and it was found that the accuracy increases with increasi

This paper is attempt to study the nonlinear second order delay multi-value problems. We want to say that the properties of such kind of problems are the same as the properties of those with out delay just more technically involved. Our results discuss several known properties, introduce some notations and definitions. We also give an approximate solution to the coined problems using the Galerkin's method.

In the present work, different thicknesses of CdS film were prepared by chemical bath deposition. Z-Scan technique was used to study the nonlinear refractive index and nonlinear absorption coefficients. Linear optical testing were done such as transmission test, and thickness of films were done by the interference fringes (Michelson interferometer). Z-scan experiment was performed at 650nm using CW diode laser and at 532nm wavelength. The results show the effect of self-focusing and defocusing that corresponds with nonlinear refraction n2. The effect of two-photon absorption was also studied, which correspond to the nonlinear absorption coefficient B.

The Research aims to determine role of The Intellectual capital in the performance of small and medium enterprises , to achieve this goal through a researcher from the theoretical literature and studies related to the construction of the scheme shows the hypothetical relationship between the variables, which was adopted by the independent variable intellectual capital, distributed four variable are:( human  capital, structure capital ,customer capital, innovation capital) as well as four variable (the financial perspective, the customer perspective, process perspective ,the learning & growth perspective) The  study were getting to  many results as bellow :the intellectual capital in the small and intermediate p

In this paper, the main work is to minimize a function of three cost criteria for scheduling n jobs on a single machine. We proposed algorithms to solve the single machine scheduling multiobjective problem. In this problem, we consider minimizing the total completion times, total tardiness and maximum tardiness criteria. First a branch and bound (BAB) algorithm is applied for the 1//∑Ci+∑Ti+Tmax problem. Second we compare two multiobjective algorithms one of them based on (BAB) algorithm to find the set of efficient (non dominated) solutions for the 1//(∑Ci ,∑Ti ,Tmax) problem. The computational results show that the algorithm based on (BAB) algorithm is better than the other one for generated the total number of