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

In this paper the concept of (m, n)- fully stable Banach Algebra-module relative to ideal (F − (m, n) − S − B − A-module relative to ideal) is introducing, we study some properties of F − (m, n) − S − B − A-module relative to ideal and another characterization is given

Grapes and grape seeds are important samples employed for environmental medical studies . The air of this work was to identify and concentration calculation of the elements in grapes fruit and thier seeds by using X-Ray fluoresces technique (XRF) . Samples were collected from Abo Ghraib of Baghdad city ,the grape seeds were obtained from those samples . Both samples were taken under experimental procedure to obtain the sample which were ready for analysis . The samples were then submitted to experimental conditions using a radiation source and then samples were applied for counting analysis shows the elements Na , Mg , Al , Si , P , S , Cl , K , Ca , and Sr as major components of the samples. Fe , Sr , I , Ba and V were

Objective: The antimicrobial efficacy of three disinfection solutions: 5.25% sodium hypochlorite (NaOCl), 2% chlorhexidine (CHX) and Listerine mouthwash were investigated as routine chair-side gutta-percha (GP) disinfection reagents. Design: four groups of gutta percha points were contaminated with E. faecalis bacteria then disinfected by immersion in different solutions (5.25% sodium hypochlorite, 2% chlorhexidine gluconate, Listerine mouth wash and distilled water as control) after 1 and 7 days culturing periods. The antibacterial efficacy of these disinfection solutions was evaluated by using colonies per units (CPU) Methods: Forty GP cones (F3 Dentsply) were sterilized with ethylene oxide gas before immersed contamination within broth m