The paper is concerned with the state and proof of the existence theorem of a unique solution (state vector) of couple nonlinear hyperbolic equations (CNLHEQS) via the Galerkin method (GM) with the Aubin theorem. When the continuous classical boundary control vector (CCBCV) is known, the theorem of existence a CCBOCV with equality and inequality state vector constraints (EIESVC) is stated and proved, the existence theorem of a unique solution of the adjoint couple equations (ADCEQS) associated with the state equations is studied. The Frcéhet derivative derivation of the "Hamiltonian" is obtained. Finally the necessary theorem (necessary conditions "NCs") and the sufficient theorem (sufficient conditions" SCs") for optimality of the stat

Reliability analysis methods are used to evaluate the safety of reinforced concrete structures by evaluating the limit state function 𝑔(𝑋𝑖). For implicit limit state function and nonlinear analysis , an advanced reliability analysis methods are needed. Monte Carlo simulation (MCS) can be used in this case however, as the number of input variables increases, the time required for MCS also increases, making it a time consuming method especially for complex problems with implicit performance functions. In such cases, MCS-based FORM (First Order Reliability Method) and Artificial Neural Network-based FORM (ANN FORM) have been proposed as alternatives. However, it is important to note that both MCS-FORM and ANN-FORM can also be time-con

The mixed-spin ferrimagnetic Ising system consists of two-dimensional sublattices A and B with spin values and respectively .By used the mean-field approximation MFA of Ising model to find magnetism( ).In order to determined the best stabile magnetism , Gibbs free energy employ a variational method based on the Bogoliubov inequality .The ground-state (Phase diagram) structure of our system can easily be determined at , we find six phases with different spins values depend on the effect of a single-ion anisotropies .these lead to determined the second , first orders transition ,and the tricritical points as well as the compensation phenomenon .

Mycobacterium tuberculosis is the cause of the major world health issue, tuberculosis (TB). The cytokine, tumor necrosis factor alpha (TNF-α) has been implicated in protection against TB in the early stages of the disease. TNF-α is an effective cytokine in the killing of intracellular M. tuberculosis. This study inducted to investigate whether there is any relationship between levels of TNF-α in sera of TB patients and their recovery, and is there any difference in the level of this cytokine in sera of female and male TB patients. This study included 29 patients with pulmonary TB (18 female and 11 male), their ages ranging from 37 to 59 years. All of them received first line TB therapy. They were consulted at Pasture Center during Septem

Children who have a health problem need special requirements for their clothes. The purpose of the study is to design functional and aesthetic clothes to meet their needs. The research used the applied descriptive approach. The research sample comprised 120 women whose children suffered from hip dislocation. Designs for injured children presented and submitted to the arbitrators for evaluation regarding the functional and aesthetic aspects. The finding was achieving the design solutions. The most important recommendations are to increase attention to designing clothes to suit all the needs of society.