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 research seeks to clarify the problems related to the aspects of the financial and accounting process resulting from entering into contractual arrangements with a period of more than 20 years, among which is the research problem represented by the lack of clarity of the foundations and procedures for the recognition of oil costs and additional costs borne by foreign invested companies, which led to a weakening of their credibility and reflection. Negatively "on the measurement and accounting disclosure of financial reports prepared by oil companies, and the research aims to lay down sound procedures for measuring and classifying oil costs and additional costs paid to foreign companies, and recognizing and recording them in th
... Show MoreThe research aims to develop physical exercises with auxiliary training tools that work to develop the explosive power of the arms and legs, and then find out their effect on the accuracy of shooting from free throw and correction from jumping of advanced basketball players, as the researchers found a problem that these players have weakness in the skill of throwing Free throwing and shooting by jumping calculated with two points as a result of adopting unhealthy physical and technical positions, which led to a lack of focus and accuracy, and thus negatively affected the performance technique of free throw and jump shot, as most teams use traditional exercises without the use of auxiliary training tools, and this topic gave researchers the
... Show MoreBackground: Crohn's disease (CD) is an immunological disorder associated with chronic inflammatory process of several unspecific regions of gastrointestinal tract but frequently detected in the terminal Ilium and proximal colon or both. This disease frequently presented with various oral manifestations as a consequence of inflammatory process of the disease, nutritional deficiency or medications side effects. Several therapeutic approaches have been developed for CD management that are targeting the inflammatory process and directed at controlling the host immune response. Immunosuppressants such as Azathioprine and anti-TNF α agents as well as the combination of them have been widely used as an effective therapeutic modality with a bett
... Show MoreThe aim of this paper is to investigate the effects of Nd:YAG laser shock processing (LSP) on micro-hardness and surface roughness of 86400Cu-Zn alloy. X-ray fluorescence technique was used to analyze the chemical composition of this alloy. LSP treatment was performed with a Q-switched Nd: YAG laser with a wavelength of 1064 nm. The results show that laser shock processing can significantly increase. The micro-hardness and surface roughness of the LSP-treated sample. Vickers diamond indenter was used to measure the micro-hardness of all samples with different laser pulse energy and the different number of laser pulses. It is found that the metal hardness can be significantly increased to more than 80% by increasing the laser energy and t
... Show MoreIn this paper, the delay integral equations in population growth will be described,discussed , studied and transfered this model to integro-differential equation. At last,we will solve this problem by using variational approach.
Relation on a set is a simple mathematical model to which many real-life data can be connected. A binary relation on a set can always be represented by a digraph. Topology on a set can be generated by binary relations on the set . In this direction, the study will consider different classical categories of topological spaces whose topology is defined by the binary relations adjacency and reachability on the vertex set of a directed graph. This paper analyses some properties of these topologies and studies the properties of closure and interior of the vertex set of subgraphs of a digraph. Further, some applications of topology generated by digraphs in the study of biological systems are cited.
Background: Maxillary first premolar with wide MOD cavity more susceptible to fracture. The aim of this study was to assess the influence of cavity design for cusp coverage on the fracture resistance of weakened maxillary first premolar restored with CAD/CAM hybrid ceramic versus nanohybide composite. Materials and Methods: Fifty six intact maxillary first premolars of approximately comparable sizes were divided into seven groups eight for each: Group A: Intact teeth (control group); Group B: teeth prepared for MOD inlay; Group C: teeth prepared for MOD onlay covering the lingual cusp; Group D: teeth prepared for MOD covering buccal and lingual cusps ,the previous three groups indirectly restored with nanohybrid composite (3M ESPE Z 250 X
... Show MoreIn the cuurent article, the photophysical properties of 3,6-bis(5-bromothiophen-2-yl)-2,5-bis(2-ethylhexyl)-2,5-dihydropyrrolo[3,4-c]pyrrole-1,4-dione were investigated. The visible absorption bands at 527, 558 and 362 nm in propylene carbonate and the compound was found to be fluorescent in solution and in the plastic film with emission wavelengths between 550- 750 nm. The Stokes Shift of P.C., acetonitrile, diethyl ether, Tetrahydrofuran THF, cyclohexane, dibutyl ether, and dichloromethane DCM are 734, 836, 668, 601, 601, 719, and 804 cm-1 in respectively. The Stokes Shift Δ was less in THF and cyclohexane, than the solvents, which indicates that the energy loss is less between the excitation and fluorescence states. The
... Show More