In this paper the Galerkin method is used to prove the existence and uniqueness theorem for the solution of the state vector of the triple linear elliptic partial differential equations for fixed continuous classical optimal control vector. Also, the existence theorem of a continuous classical optimal control vector related with the triple linear equations of elliptic types is proved. The existence of a unique solution for the triple adjoint equations related with the considered triple of the state equations is studied. The Fréchet derivative of the cost function is derived. Finally the theorem of necessary conditions for optimality of the considered problem is proved.

In this paper, our purpose is to study the classical continuous optimal control (CCOC)  for quaternary nonlinear parabolic boundary value problems (QNLPBVPs). The existence and uniqueness theorem (EUTh) for the quaternary state vector solution (QSVS) of the weak form (WF) for the QNLPBVPs with a given quaternary classical continuous control vector (QCCCV) is stated and proved via the Galerkin Method (GM) and the first compactness theorem under suitable assumptions(ASSUMS). Furthermore, the continuity operator for the existence theorem of a QCCCV dominated by the QNLPBVPs is stated and proved under suitable conditions.

This work presents a design for a pressure swing adsorption process (PSA) to separate oxygen from air with approximately 95% purity, suitable for different numbers of columns and arrangements. The product refill PSA process was found to perform 33% better (weight of zeolite required or productivity) than the pressure equalization process. The design is based on the adsorption equilibrium of a binary mixture of O₂ and N₂ for two of the most commonly used adsorbents, 5A & 13X, and extension from a single column approach. Zeolite 13X was found to perform 6% better than zeolite 5A. The most effective variables were determined to be the adsorption step time and the operational pressure. Increasing the adsorption step

The Child's theatre was and still is the most investing art for masks of all kinds (partial and total) for suspense, aesthetic and artistic purposes that meet the requirements of those performances. Here the actor's performance is associated with two tools, i.e. the body and the mask, where it has become a must to search for the performance transformations required in order to achieve the highest level of the right performance through this dualism. This urged the researcher to address this problem. Thus, the researcher has put forward an objective to identify the transformations of the character's performance between the body and the mask in the child's theatre shows. The research consists of a methodological framework and a theoretical

To evaluate impact the difference in stages ofage and related incidence of hemodialysis patients.Two hundred and fifty patients undergoing hemodialysis were collected from general hospital in Baghdad city /Iraq. The samples with renal failure before hemodialysis were divided into (138) male,( 112)female. The sera were separated from samples to physiological investigation. We found that renal failure was more predominant among the patients ages group ranging from (51-70) years old. The results shows A significant increase in the levels of urea, creatinine, in younger patients (≤ 30 years) when compared with older patients (>70 years). Furthermore a significant decrease in serum levels of total protein in patients in older patients (>7

  The present study was conducted on sixty five pregnant women that infected with    acute toxoplasmosis, serum samples were tested for detection specific anti-Toxoplasma gondii IgM using the rapid Toxo IgG/IgM Chromatographic immune assay test cassette and ELISA, and fifty healthy married women (not pregnant)  as  was considered as control group.       The level of serum IL-6, IL-8, IL-12, TNF-α, TGF-β1, IP-10, MIP-1, MIG and ICAM were significantly increased (P <0.005) in pregnant patients infected with acute toxoplasmosis, while serum level of MCP-1(14.46 ± 1.38pg/ml) was not significantly increased when compared to controls(11.25 ± 0.24pg/ml)  , these levels can be used as i