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

A new ligand [N-(4-methoxy benzoyl amino)-thioxo methyl ] leucine (MBL) was prepared from the reaction of (4-methoxy benzoyl isothiocyanate with leucine acid in molar ratio (l:l), it was characterized by elemental analysis (C.H.N.S), FT-IR, UV-Vis, 1H and 13C-NMR. The complexes of the bivalent ions (Mn, Fe, Co, Ni, Cu, Zn, Cd and Hg ) have been prepared and characterized too. The structural was established by elemental analysis (C.H.N.S), FT-IR, UV-Vis spectra, conductivity measurements atomic absorption and magnetic susceptibility and determination of molar ration (M:L). The complexes showed characteristic behavior of tetrahedral geometry around the metal ions except with (Cu) complex showed square planer.

This research deals with unusual approach for analyzing the Simple Linear Regression via Linear Programming by Two - phase method, which is known in Operations Research: “O.R.”. The estimation here is found by solving optimization problem when adding artificial variables: Ri. Another method to analyze the Simple Linear Regression is introduced in this research, where the conditional Median of (y) was taken under consideration by minimizing the Sum of Absolute Residuals instead of finding the conditional Mean of (y) which depends on minimizing the Sum of Squared Residuals, that is called: “Median Regression”. Also, an Iterative Reweighted Least Squared based on the Absolute Residuals as weights is performed here as another method to

Objective: To assess the role of tumour necrosis factor alpha level and genotyping in susceptibility to leishmaniasis.Method: The case-control study was conducted from March to July 2021 at Baqubah Teaching Hospital, Diyala, Iraq,and comprised patients of cutaneous leishmaniasis in group A and healthy controls in group B. The serum level andsingle nucleotide polymorphisms of tumour necrosis factor-alpha rs41297589 and rs1800629 were compared betweenthe groups. Data was analysed using SPSS 28.Results: Of the 150 subjects, there were 75(50%) in group A; 39(52%) males and 36(48%) females with mean age23.91±13.14 years. The remaining 75(50%) subjects were in group B; 38(50.7%) males and 37(49.3%) females withmean age 22.84±4.35 years.

tA novel synthesis procedure is presented for preparing triethanolamine-treated graphene nanoplatelets(TEA-GNPs) with different specific areas (SSAs). Using ultrasonication, the covalently functionalizedTEA-GNPs with different weight concentrations and SSAs were dispersed in distilled water to prepareTEA-GNPs nanofluids. A simple direct coupling of GNPs with TEA molecules is implemented to synthesizestable water-based nanofluids. The effectiveness of the functionalization procedure was validated by thecharacterization and morphology tests, i.e., FTIR, Raman spectroscopy, EDS, and TEM. Thermal conduc-tivity, dispersion stability, and rheological properties were investigated. Using UV–vis spectrometer, ahighest dispersion stability of 0.876