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 state constrained problem are stated and proved.
According to the theory of regular geometric functions, the relevance of geometry to analysis is a critical feature. One of the significant tools to study operators is to utilize the convolution product. The dynamic techniques of convolution have attracted numerous complex analyses in current research. In this effort, an attempt is made by utilizing the said techniques to study a new linear complex operator connecting an incomplete beta function and a Hurwitz–Lerch zeta function of certain meromorphic functions. Furthermore, we employ a method based on the first-order differential subordination to derive new and better differential complex inequalities, namely differential subordinations.
Rheumatoid arthritis (RA) is characterized by persistent joint inflammation, which is a defining feature of this chronic inflammatory condition. Considerable advancements have been made in the field of disease-modifying anti-rheumatic medicines (DMARDs), which effectively mitigate inflammation and forestall further joint deterioration. Anti-tumor necrosis factor-alpha (TNF-α) drugs, which are a class of biological DMARDs (bDMARDs), have been efficaciously employed in the treatment of RA in recent times Adalimumab, a TNF inhibitor, has demonstrated significant efficacy in reducing disease symptoms and halting disease progression in patients with RA. However, its use is associated with major side effects and high costs. In addition,
... Show MoreBackground: The oral cavity is considered as a complex ecological niche, its complex microbial community is reflected to it. Streptococcus mutans has been implicated as one of the major etiological factor of dental caries. Tooth surfaces colonized with Streptococcus mutans are at a higher risk for developing caries, while lactobacilli are considered as the secondary invaders, not initiators of the carious lesion. The main purpose of this study was to correlate the dental caries (for primary and permanent teeth) in the upper jaw with the streptococcus mutans and lactobacilli count in the dental plaque and saliva, also to correlate the dental caries (for primary and permanent teeth) in the lower jaw with the streptococcus mutans and lactobaci
... Show MoreThe aim of the research was designing a nutritional program with amino acids well as designing exercises for muscular strength training for youth female badminton players. In addition to that the researcher aimed at identifying the effect of amino acid accompanied with muscular training on some physiological indicators in youth female badminton players. The researcher used the experimental method. The subjects were (7) youth female badminton players from the Armenian badminton club. Many physiological tests were conducted including PWC170 and Vo2Max. The data was collected and treated using proper statistical operations to conclude that amino acid accompanied with muscular ability training have a positive effect on some physiological indica
... Show MoreIn The Name of Allah Most Gracious Most Merciful
The fundamentals of jurisprudence have a great role in facilitating the ways to know the Shari’a rulings for everything that takes place between people in terms of relationships, and the actions that are issued by them, because without it, the sources from which the rulings were taken are not known, and the methods used by the imams of ijtihad in taking these rulings from those sources are not understood. The foundations on which they followed in the interpretation of texts and its rules, and Muslim scholars in different eras celebrated this science and gave it great care: with what they wrote in it from the works of different directions, but of course the complexity printed many
... Show MoreIn this paper, the effect of temperature on the charge transfer rate of dye (N3) in contact with ZnS semiconductors is discussed and studied when electrons move from the excited N3 dye to the conduction band of ZnS based on quantum shift theory. In a heterogeneous system, the energy levels are assumed to be continuous, and the N3-ZnS system is surrounded by a variety of polar solvent media. The transition energy of the N3/ZnS heterojunction was calculated using seven different solvents at room temperature, considering the refractive index and dielectric constant of the solvents and the ZnS semiconductor, respectively. The charge-transport reaction rate was calculated over different te