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

Abstract

Anaerobic digestion process of organic materials is biochemical decomposition process done by two types of digestion bacteria in the absence of oxygen resulting in the biogas production, which is produced as a waste product of digestion. The first type of bacteria is known as acidogenic which converts organic waste to fatty acids. The second type of bacteria is called methane creators or methanogenic which transforms the fatty acids to biogas (CH₄ and CO₂). The considerable amounts of biodegradable constitutes such as carbohydrates, lipids and proteins present in the microalgae biomass make it a suitable substrate for the anaerobic digestion or even c

A series of lanthanide metal (???) complexes have been prepared from the new azo ligand, 3-(1-methyl-2-benzimidazolylazo)-Tyrosine (MBT). The structural feature were confirmed on the basis of their elemental analysis, metal content, molar conductance, magnetic measurement, FTIR, 1 HNMR and UV-Vis spectra studies. The isolated complexes were found to have a mole ratio (1:2) (metal:ligand) stoichiometry with the general formula [Ln(MBT)2]Cl (Ln(???) = La, Ce, Pr, Nd, Sm, Eu and Gd). The chelates were found to have octahedral structures. The FTIR spectra shows that the ligand (MBT) is coordinated to lanthanide ions as a N, N, O-tridentate anion via benzimidazole nitrogen, azo nitrogen and oxygen of hydroxyl after deprotonation. Com

New (pentulose-?-lactone-2,3-enedibenzoate barbituric acid) (L) have been synthesized by reaction of (5-C-dimethyl malonyl-pentulose-?-lactone-2,3-enedibenzoate) with urea in alkaline media (sodium methoxide). (Ca+2, Co+2, Ni+2, Cu+2, Zn+2, Cd+2 and Hg+2) complexes of (pentulose-?-lactone-2,3-enedibenzoate barbituric acid) (L) have been prepared and characterized by (1H and 13CNMR), FTIR, (U.V-Vis) spectroscopy, Atomic absorption spectrophotometer (A.A.S), Molar conductivity measurements and Magnetic moment measurements, and the following general formula has been given for the prepared complexes [MLCl2(H2O)].XH2O, where M = (Ca+2, Co+2, Ni+2, Cu+2, Zn+2, Cd+2, Hg+2), X = five molecules with (Cd+2) complex, L = (pentulose-?-lactone-2,3

The aim of the work is the synthesis and characterization of the tridentate Schiff base (HL) containing (N and O) as donor atoms type (ONO). The ligand is: (HL) phenyl 2-(2-hydroxybenzylidenamino)benzoate This ligand was prepared by the reaction of (phenyl 2-aminobenzoate) with salicylaldehyde under reflux in ethanol and few drops of glacial acetic acid which gave the ligand (HL). The prepared ligand was characterized by (FT IR,UV–Vis) spectroscopy, Elemental analysis of carbon, hydrogen and nitrogen (C.H.N.) and melting point. The ligand was reacted with some metal ions under reflux in ethanol with (1 metal :2 ligand )mole ratio which gave complexes of the general formula: Pr III , Cr and III La III [M(L)2]Cl , M = Products were found to

(phen) (L(M [formula general a with complexes ligand-mixed new of series A methods analyses different by characterised and synthesised been have ,ligand arysecond as phenanthroline1,10- = phen and ligand primary as dithiocarbamate-1-azolebenzoimid-H-1)sulfinyl)methyl)yl-”-2pyriden)trifluroethoxy2,2,2- “(-4-methyl3-(((2-Sodium = L,ZnIIandCdII,CuII,NiII,CoII= M where,Cl)]phen)(L(Pd [Cland]2)O2H( ligands to metal ,moments magnetic and ,elementalanalysis ,spectrum mass ,surementsmea conductivity ,analysis thermal ,spectroscopy Vis-UV ,IR-FT ,NMR-C,13 H1 such dithiocarbamate the with formed coordination anisobidentate that showed spectra IRFT The.)phen:dithiocarbamate:M) (1:1:1(be to found been has complexes all in ratio nitrogen th

This research deals with the study of top soil electrical conductive regions located within Baghdad City. The research included measuring the dissolved soil material extraction Electrical Conductivity (EC) with an aqueous solution for the top (0-30 cm) soil layer of the study area. As the electrical conductivity values increase by increasing the amount of dissolved salts in principle, we can consider that the aim of this research is to predict the amount and distribution of (soil contamination with salts) which is represented by the (Salt Index), this factor calculated for each soil representative sample taken from the region with a depth of (30 cm). Laboratory (EC) test values measured by the use of solutions (EC) digital meter for the ex

New metal ions complexes of tridentate ligand (1-((dicyclohexylamino) methyl)-3-(1,5-dimethyl-3-oxo-2-phenyl-2,3-dihydro-1H-pyrzol-4-ylimino) indolin-2-one) have been synthesized and characterized by chemical-physical analysis. The ligand acts as a tridentate for the complexation reaction with all metal ions. The new complexes, possessing the general formula [M(L)Cl]Cl where M=[Ni(II), Cu(II), Zn(II), Pd(II), Cd(II), Pt(IV) and Hg(II) ] ,show tetrahedral geometry. All complexes ,except Pd(II) complex which has a square planar geometry and Pt(IV) which show an octahedral geometry. The geometry of the prepared compounds has been proposed in another method theoretically by using one of the calculation molecular programs (Hype