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 associated with the quaternary linear hyperbolic boundary value problem is formulated and studied. The directional derivative for the cost functional is derived. Finally, the necessary optimality theorem for the optimal classical continuous control quaternary vector is proved.
The research aims to highlight the significance and composition and the diversity of meanings and the Quranic context in the necessary and transgressive verbs in Surat (Abs).
This research consists of : a preamble , and two studies . The researcher addressed in the preliminary the importance of the phenomenon of necessity and infringement, the signs of the necessary action , the structure and controls of the act , the methods of infringement , its sections and signs.
As for the first topic : The researcher addressed the necessary verbs in Surat Abs , an applied study in terms of grammati
... Show MoreThis research studies the effect of adding micro, nano and hybrid by ratio (1:1) of (Al2O3,TiO2) to epoxy resin on thermal conductivity before and after immersion in HCl acid for (14 day) with normality (0.3 N) at weight fraction (0.02, 0.04, 0.06, 0.08) and thickness (6mm). The results of thermal conductivity reveled that epoxy reinforced by (Al2O3) and mixture (TiO2+Al2O3) increases with increasing the weight fraction, but the thermal conductivity (k) a values for micro and Nano (TiO2) decrease with increasing the weight fraction of reinforced, while the immersion in acidic solution (HCl) that the (k) values after immersion more than the value in before immersion.