In this research, we study the classical continuous Mixed optimal control vector problem dominated by couple nonlinear elliptic PDEs. The existence theorem for the unique state vector solution of the considered couple nonlinear elliptic PDEs for a given continuous classical mixed control vector is stated and proved by applying the Minty-Browder theorem under suitable conditions.  Under suitable conditions, the existence theorem of a classical continuous mixed optimal control vector associated with the considered couple nonlinear elliptic PDEs  is stated and proved.

This paper has the interest of finding the approximate solution (APPS) of a nonlinear variable coefficients hyperbolic boundary value problem (NOLVCHBVP).  The given boundary value problem is written in its discrete weak form (WEFM) and proved  have a unique solution, which is obtained via the mixed Galerkin finite element with implicit method that reduces the problem to solve the Galerkin nonlinear algebraic system  (GNAS). In this part, the predictor and the corrector techniques (PT and CT, respectively) are proved at first convergence and then are used to transform  the obtained GNAS to a linear GLAS . Then the GLAS is solved using the Cholesky method (ChMe). The stability and the convergence of the method are stud

    This work is concerned with studying the solvability for optimal classical continuous control quaternary vector problem that controls by quaternary linear hyperbolic boundary value problem. The existence of the unique quaternary state vector solution for the quaternary linear hyperbolic boundary value problem  is studied and demonstrated by employing the method of Galerkin, where the classical continuous control quaternary vector  is Known. Also, the existence theorem of an optimal classical continuous control quaternary vector related to the quaternary linear hyperbolic boundary value problem is demonstrated. The existence of a unique solution to the adjoint quaternary linear hyperbolic boundary value problem a

In this paper, the nonclassical approach to dynamic programming for the optimal control problem via strongly continuous semigroup has been presented. The dual value function VD ( .,. ) of the problem is defined and characterized. We find that it satisfied the dual dynamic programming principle and dual Hamilton Jacobi –Bellman equation. Also, some properties of VD (. , .) have been studied, such as, various kinds of continuities and boundedness, these properties used to give a sufficient condition for optimality. A suitable verification theorem to find a dual optimal feedback control has been proved. Finally gives an example which illustrates the value of the theorem which deals with the sufficient condition for optimality.

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Abstract

This research’s goal is to  restore and to revive the jurisprudence of  Mother of Believers (Um alMuaamineen) “Um Salmah” "may God bless her", and to highlight her outstanding assimilation and understanding of religion and her conscious thought.  The current research is a comparative scientific theoretical study  represented in the comparison of  jurisprudence of “Um Salamah” with Hadiths  of  fasting  and pilgrimage rules as well as the duration  mentioned in jurisprudence  of  for doctrines( 4 schools of thought )to identify these hadiths with the inclusion and discussion of their evidence.

The current research included two topics: the first one is to identify and introduce

Grey system theory is a multidisciplinary scientific approach, which deals with systems that have partially unknown information (small sample and uncertain information). Grey modeling as an important component of such theory gives successful results with limited amount of data. Grey Models are divided into two types; univariate and multivariate grey models. The univariate grey model with one order derivative equation GM (1,1) is the base stone of the theory, it is considered the time series prediction model but it doesn’t take the relative factors in account. The traditional multivariate grey models GM(1,M) takes those factor in account but it has a complex structure and some defects in " modeling mechanism", "parameter estimation "and "m

The Korteweg-de Vries equation plays an important role in fluid physics and applied mathematics. This equation is a fundamental within study of shallow water waves. Since these equations arise in many applications and physical phenomena, it is officially showed that this equation has solitary waves as solutions, The Korteweg-de Vries equation is utilized to characterize a long waves travelling in channels. The goal of this paper is to construct the new effective frequent relation to resolve these problems where the semi analytic iterative technique presents new enforcement to solve Korteweg-de Vries equations. The distinctive feature of this method is, it can be utilized to get approximate solutions for travelling waves of 

The Korteweg-de Vries equation plays an important role in fluid physics and applied mathematics. This equation is a fundamental within study of shallow water waves. Since these equations arise in many applications and physical phenomena, it is officially showed that this equation has solitary waves as solutions, The Korteweg-de Vries equation is utilized to characterize a long waves travelling in channels. The goal of this paper is to construct the new effective frequent relation to resolve these problems where the semi analytic iterative technique presents new enforcement to solve Korteweg-de Vries equations. The distinctive feature of this method is, it can be utilized to get approximate solution

This paper aims to study the quaternary classical continuous optimal control problem consisting of the quaternary nonlinear parabolic boundary value problem, the cost function, and the equality and inequality constraints on the state and the control. Under appropriate hypotheses, it is demonstrated that the quaternary classical continuous optimal control ruling by the quaternary nonlinear parabolic boundary value problem has a quaternary classical continuous optimal control vector that satisfies the equality constraint and inequality state and control constraint. Moreover, mathematical formulation of the quaternary adjoint equations related to the quaternary state equations is discovered, and then the weak form of the quaternary adjoint