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 paper, the classical continuous triple optimal control problem (CCTOCP) for the triple nonlinear parabolic boundary value problem (TNLPBVP) with state vector constraints (SVCs) is studied.  The solvability theorem for the classical continuous triple optimal control vector CCTOCV with the SVCs is stated and proved. This is done under suitable conditions. The mathematical formulation of the adjoint triple boundary value problem (ATHBVP) associated with TNLPBVP is discovered. The Fréchet derivative of the Hamiltonian" is derived.  Under suitable conditions, theorems of necessary  and sufficient conditions for the optimality of the TNLPBVP with the SVCs are stated and proved.    

     Let R be a commutative ring with unity and an R-submodule N is called semimaximal if and only if

 the sufficient conditions of F-submodules to be semimaximal .Also the concepts of (simple , semisimple) F- submodules and quotient F- modules are  introduced and given some  properties .

In this work, two different structures are proposed which is fuzzy real normed space (FRNS) and fuzzy real Pre-Hilbert space (FRPHS). The basic concept of fuzzy norm on a real linear space is first presented to construct  space, which is a FRNS with some modification of the definition introduced by G. Rano and T. Bag. The structure of fuzzy real Pre-Hilbert space (FRPHS) is then presented which is based on the structure of FRNS. Then, some of the properties and related concepts for the suggested space FRN such as -neighborhood, closure of the set  named , the necessary condition for separable, fuzzy linear manifold (FLM) are discussed. The definition for a fuzzy seminorm on  is also introduced with the prove that a fuzzy seminorm on

The results show the inability to apply the Taylor rule within inflation and GDP Gaps because the monetary behave is elated from the Iraqi economy.

When applying the Taylor rule to exchange rate with the inflation and the output gap, the results do not match the nominal price announced by the central thing, which proves the lack of commitment by the Central Bank by using the Taylor rule, whether short-run interest rate or exchange rate (Nominal Anchor),  so it did not stay to the Iraqi Central Bank only using the principle of Taylor with the expected inflation rate below the level of output (Macro activity) for the separation of monetary behavior from the real one o

      Let  be a ring with identity and let  be a left R-module. If is  a proper submodule of  and  ,  is called --semi regular element in  , If there exists a decoposition  such that  is projective submodule of  and  . The aim of this paper is to introduce properties of F-J-semi regular module. In particular, its characterizations are given. Furthermore, we introduce the concepts of Jacobson hollow semi regular module and --semiregular module. Finally, many results of Jacobson hollow semi regular module and --semiregular module are presented.

The aim of this paper is adopted to give an approximate solution for advection dispersion equation of time fractional order derivative by using the Chebyshev wavelets-Galerkin Method . The Chebyshev wavelet and Galerkin method properties are presented. This technique is used to convert the problem into the solution of linear algebraic equations. The fractional derivatives are described based on the Caputo sense. Illustrative examples are included to demonstrate the validity and applicability of the proposed technique.

In this work, we will combine the Laplace transform method with the Adomian decomposition method and modified Adomian decomposition method for semi-analytic treatments of the nonlinear integro-fractional differential equations of the Volterra-Hammerstein type with difference kernel and such a problem which the kernel has a first order simple degenerate kind which the higher-multi fractional derivative is described in the Caputo sense. In these methods, the solution of a functional equation is considered as the sum of infinite series of components after applying the inverse of Laplace transformation usually converging to the solution, where a closed form solution is not obtainable, a truncated number of terms is usually used for numerical

This paper aims to study the fractional differential systems arising in warm plasma, which exhibits traveling wave-type solutions. Time-fractional Korteweg-De Vries (KdV) and time-fractional Kawahara equations are used to analyze cold collision-free plasma, which exhibits magnet-acoustic waves and shock wave formation respectively. The decomposition method is used to solve the proposed equations. Also, the convergence and uniqueness of the obtained solution are discussed. To illuminate the effectiveness of the presented method, the solutions of these equations are obtained and compared with the exact solution. Furthermore, solutions are obtained for different values of time-fractional order and represented graphically.

     The inefficient use of spectrum is the key subject to overcome the upcoming spectrum crunch issue. This paper presents a study of performance of cooperative cognitive network via hard combining of decision fusion schemes. Simulation results presented different cooperative hard decision fusion schemes for cognitive network. The hard-decision fusion schemes provided different discriminations for detection levels. They also produced small values of Miss-Detection Probability at different values of Probability of False Alarm and adaptive threshold levels. The sensing performance was investigated under the influence of channel condition for proper operating conditions. An increase in the detection performance was achi