This paper deals with the continuous classical optimal control problem for triple partial differential equations of parabolic type with initial and boundary conditions; the Galerkin method is used to prove the existence and uniqueness theorem of the state vector solution for given continuous classical control vector. The proof of the existence theorem of a continuous classical optimal control vector associated with the triple linear partial differential equations of parabolic type is given. The derivation of the Fréchet derivative for the cost function is obtained. At the end, the theorem of the necessary conditions for optimality of this problem is stated and is proved.

The sun which is all energy sources, in today's society, hot water is used for various purposes starting from household to power production. People are adopting various ways to accomplish these goals, such as firewood heat and electrical power, so solar energy is an alternative to the dwindling resources of fossil fuels. Conversion of solar radiation into heat is one of the simplest and most direct applications of this energy, it can be used to heat water systems. A widely used flat-plate solar collector. In this study we have come to heat water using solar energy. This research presents the design and experimental analysis for using Spiral Flow Solar Water Heater (SFSWH) to enhance the thermal efficiency of a flat plate solar collector.

The aerodynamic characteristics of general three-dimensional rectangular wings are considered using non-linear interaction between two-dimensional viscous-inviscid panel method and vortex ring method. The potential flow of a two-dimensional airfoil by the pioneering Hess & Smith method was used with viscous laminar, transition and turbulent boundary layer to solve flow about complex configuration of airfoils including stalling effect. Viterna method was used to extend the aerodynamic characteristics of the specified airfoil to high angles of attacks. A modified vortex ring method was used to find the circulation values along span wise direction of the wing and then interacted with sectional circulation obtained by Kutta-Joukowsky the

Gold nanoparticles (Au NPs) have been synthesized via reduction of sodium tetrachloroaurate dihydrate (NaAuCl4.2H2O) with 2-(2-methyl-5-amino -1H-imidazol-1-yl) ethanol (2-MAE) in presence and absence of ascorbic acid as reducing and stabilizing agents. The resulting Au NPs were characterized by UV–Vis spectroscopy, scanning electron microscopy (SEM), atomic force microscopy (AFM), X-ray diffraction (XRD), FT-IR spectroscopy. The absorption spectra of gold nanoparticles solutions in the uv-visible and near IR regions were studied at different amine concentrations and pH media.

Gold nanoparticles (Au NPs) have been synthesized via reduction of sodium tetrachloroaurate dihydrate (NaAuCl4.2H2O) with 2-(2-methyl-5-amino -1H-imidazol-1-yl) ethanol (2-MAE) in presence and absence of ascorbic acid as reducing and stabilizing agents. The resulting Au NPs were characterized by UV–Vis spectroscopy, scanning electron microscopy (SEM), atomic force microscopy (AFM), X-ray diffraction (XRD), FT-IR spectroscopy. The absorption spectra of gold nanoparticles solutions in the uv-visible and near IR regions were studied at different amine concentrations and pH media.

The interplay of predation, competition between species and harvesting is one of the most critical aspects of the environment. This paper involves exploring the dynamics of four species' interactions. The system includes two competitive prey and two predators; the first prey is preyed on by the first predator, with the former representing an additional food source for the latter. While the second prey is not exposed to predation but rather is exposed to the harvest. The existence of possible equilibria is found. Conditions of local and global stability for the equilibria are derived. To corroborate our findings, we constructed time series to illustrate the existence and the stability of equilibria numerically by varying the different values

Experienced organizations in recent years, significant challenges , especially with the spread of economic globalization, making it required to provide new and better through experience , creativity and innovation to achieve the quality and high-quality products of all kinds , in order to achieve the objectives of the study and to answer its questions tested the study in the woolen Industries sector in Baghdad . The study was applied to a sample of 30 people in the senior management and the middle and lower in the company (managers of sections  , and  managers of people , and managers of the units , and office managers ) and for the processing of data and information used several statistical methods and extracted result

creating unique exercises utilizing a teaching approach that works with the research sample, determining how special exercises affect the development of torso flexibility, and determining how special exercises affect the development of bow ability. Activate the search The results of the pre- and post-tests for the control and experimental research groups show a statistically significant association that is favoring the post-test in the development of bow skill performance Using the experimental technique, the researcher set up one group and gave them two tests (pre and post) based on scientific theories that made sense for the topic at hand. Forty adolescent wrestlers from the Adhamiya Club in the Baghdad Governorate were recognized