In this research, our aim is to study the optimal control problem (OCP) for triple nonlinear elliptic boundary value problem (TNLEBVP). The Mint-Browder theorem is used to prove the existence and uniqueness theorem of the solution of the state vector for fixed control vector. The existence theorem for the triple continuous classical optimal control vector (TCCOCV) related to the TNLEBVP is also proved. After studying the existence of a unique solution for the triple adjoint equations (TAEqs) related to the triple of the state equations, we derive The Fréchet derivative (FD) of the cost function using Hamiltonian function. Then the theorems of necessity conditions and the sufficient condition for optimality of

The goal of this work is demonstrating, through the gradient observation of a   of type linear ( -systems), the possibility for reducing the effect of any disturbances (pollution, radiation, infection, etc.) asymptotically, by a suitable choice of related actuators of these systems. Thus, a class of  ( -system) was developed based on finite time  ( -system). Furthermore, definitions and some properties of this concept -system and asymptotically gradient controllable system ( -controllable) were stated and studied. More precisely, asymptotically gradient efficient actuators ensuring the weak asymptotically gradient compensation system ( -system) of known or unknown disturbances are examined. Consequently, under convenient hypo

The paper is concerned with the state and proof of the solvability theorem of unique state vector solution (SVS) of triple nonlinear hyperbolic boundary value problem (TNLHBVP), via utilizing the Galerkin method (GAM) with the Aubin theorem (AUTH), when the boundary control vector (BCV) is known. Solvability theorem of a boundary optimal control vector (BOCV) with equality and inequality state vector constraints (EINESVC) is proved. We studied the solvability theorem of a unique solution for the adjoint triple boundary value problem (ATHBVP) associated with TNLHBVP. The directional derivation (DRD) of the "Hamiltonian"(DRDH) is deduced. Finally, the necessary theorem (necessary conditions "NCOs") and the sufficient theorem (sufficient co

In this paper, a least squares group finite element method for solving coupled Burgers' problem in   2-D is presented. A fully discrete formulation of least squares finite element method is analyzed, the backward-Euler scheme for the time variable is considered, the discretization with respect to space variable is applied as biquadratic quadrangular elements with nine nodes for each element. The continuity, ellipticity, stability condition and error estimate of least squares group finite element method are proved.  The theoretical results  show that the error estimate of this method is . The numerical results are compared with the exact solution and other available literature when the convection-dominated case to illustrate the effic

In this study the Bauxite has been activated and used to prepare two complexes: Bauxite - urea and Bauxite - melamine, these complexes were merged and polymerized with formaldehyde to prepare the complex Bauxite polymer - urea - melamine - formaldehyde (modified Bauxite). In the Bauxite-urea complex XRD results indicate that the urea molecules penetrate among the layers of the crystal plane (110) of the Gibbsite mineral while in the Bauxite-melamine the interaction was at the outer surface of the Bauxite forming minerals because the relatively large volume of the melamine molecule. FT-IR results show the interaction of these two bases with Bauxite was mainly based on the hydrogen bonding and in less extent on the coordination between N l

One of the most important enhanced oil recoveries methods is miscible displacement. During this method preferably access to the conditions of miscibility to improve the extraction process and the most important factor in these conditions is miscibility pressure. This study focused on establishing a suitable correlation to calculate the minimum miscibility pressure (MMP) required for injecting hydrocarbon gases into southern Iraq oil reservoir.  MMPs were estimated for thirty oil samples from southern Iraqi oil fields by using modified Peng and Robinson equation of state. The obtained PVT reports properties were used for tunning the equation of state parameters by making a match between the equation of state results with experimenta

The two body model of (Core+n) within the radial wave functions of the cosh potential has been used to investigate the ground state features such as the proton, neutron and matter densities, the root mean square (RMS) nuclear proton, neutron, charge and mass radii of unstable neutron-rich 14B, 15C, 19C and 22N nuclei. The calculated results show that the two body model with the radial wave functions of the cosh potential succeeds in reproducing neutron halo in these nuclei.

In the present research a new test rig has been proposed to be suitable for different cyclic loads such as cyclic bending, cyclic torsion, proportional and non proportional loads. In this work the efforts were concentrated on the cyclic bending loads concerning cracked pipes with or without internal pulsing pressure to study crack propagation in small bore pipes (up to 1'') for transverse or inclined cracks. The rig simulates the real service conditions under different stresses by means the least dangerous case will be suggested, so the experiments were considered for copper pipe, and the results have been tabulated and drawn to demonstrate the crack growth behavior as well as to justify the outcomes practically, consequently the durabil

In the present study, activated carbon supported metal oxides was prepared for thiophene removal from model fuel (Thiophene in n-hexane) using adsorptive desulfurization technique. Commercial activated carbon was loaded individually with copper oxide in the form of Cu₂O/AC. A comparison of the kinetic and isotherm models of the sorption of thiophene from model fuel was made at different operating conditions including adsorbent dose, initial thiophene concentration and contact time. Various adsorption rate constants and isotherm parameters were calculated. Results indicated that the desulfurization was enhanced when copper was loaded onto activated carbon surface. The highest desulfurization percent for Cu₂O/AC and o

This research includes synthesis of new 5-Nitro isatin derivatives starting from 5-Nitro-3-(ethyl imino acetate)-2-oxo indole (1) namely 5-nitro-3-[(imino acetyl) semicarbazide]-2-oxo indole (2); 5-nitro-3-[(imino acetyl) phenylsemicarbazide]-2-oxo indole (3); 5-nitro-3-[(imino acetyl) thiosemicarbazide]-2-oxo indole (4); 5-nitro-3-[(iminoacetyl) phenylthiosemi carbazide]-2-oxo indole (5); 5-nitro-3-[(methyl imino)-4H-1, 2, 4-triazol-5-ol-3-yl]-2-oxo indole (6); 5-nitro-3-[(methyl imino) 4-phenyl-1, 2, 4-triazol-5-ol-3-yl]-2-oxo indole (7); 5-nitro-3-[(methyl imino) 4-phenyl-1, 2, 4-triazol-5-thiol-3-yl]-2-oxo indole (8) and 5-nitro-3-[(methyl imino) 4H-1, 2, 4-triazol-5-thiol-3-yl]-2-oxo indole (9). The derivatives were characterized us