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.

Radiotherapy is the branch of clinical medicine concerned with the application of ionizing radiation in the treatment of disease. And it is used to killing of cancer cells in a tissue using ionizing radiation while keeping the sparing of healthy cells at acceptable level. X-ray beams are used to deposit absorbed dose at depth within a patient at the site of the tumor. The aim of this work is studying the relationship between the depth dose and the field size in water phantom and homogenous actual planning. In our work, the dose distribution at different depths (zero-18 cm) deep at1cm interval treated with field size (10×10 and 20×20) cm2 were studied.
Results show that high similarity between water phantom and actual planning for th

The main function of a power system is to supply the customer load demands as economically as possible. Risk criterion is the probability of not meeting the load. This paper presents a methodology to assess probabilistic risk criteria of Al-Qudus plant before and after expansion; as this plant consists of ten generating units presently and the Ministry Of Electricity (MOE) is intending to compact four units to it in order to improve the performance of Iraqi power system especially at Baghdad region. The assessment is calculated by a program using Matlab programming language; version 7.6. Results show that the planned risk is (0.003095) that is (35 times) less than that in the present plant risk; (0.1091); which represents respectable imp

     University Campuses, as any lively physical entity, is subject to continuous variation due to . growth, development and change. This reality covers the existing or futuristic additives or  additions, consecutively these changes may have a strong sensation of disorientation as a result of formatic changes in buildings, or in movement paths. And it epitomized the research problem to "the need for knowledge to clarify the impact of intellectual and executive policy in achieving coherence, functional and space organization of the elements of the university urban environment and in the stages of future growth and change,"  the search targeted "to highlight the study of constraction politics on campus Bmqomad

This paper aims to propose a hybrid approach of two powerful methods, namely the differential transform and finite difference methods, to obtain the solution of the coupled Whitham-Broer-Kaup-Like equations which arises in shallow-water wave theory. The capability of the method to such problems is verified by taking different parameters and initial conditions. The numerical simulations are depicted in 2D and 3D graphs. It is shown that the used approach returns accurate solutions for this type of problems in comparison with the analytic ones.

            Diabetes mellitus caused by insulin resistance is prompted by obesity. Neuropeptide Nesfatin-1 was identified in several organs, including the central nervous system and pancreatic islet cells. Nesfatin-1 peptide appears to be involved in hypothalamic circuits that energy homeostasis and control food intake. Adiponectin is a plasma collagen-like protein produced by adipocytes that have been linked to the development of insulin resistance (IR), diabetes mellitus type 2 (DMT2), and cardiovascular disease (CVD). Resistin was first identified as an adipose tissue–specific hormone that was linked to obesity and diabetes.  The aim of this study was to estimate the relationship between human serum nesfatin-1, adiponect

The necessary optimality conditions with Lagrange multipliers  are studied and derived for a new class that includes the system of Caputo–Katugampola fractional derivatives to the optimal control problems with considering the end time free. The formula for the integral by parts has been proven for the left Caputo–Katugampola fractional derivative that contributes to the finding and deriving the necessary optimality conditions. Also, three special cases are obtained, including the study of the necessary optimality conditions when both the final time  and the final state  are fixed. According to convexity assumptions prove that necessary optimality conditions are sufficient optimality conditions.

The current research is a spectroscopic study of Coumarin 334 dissolved in methanol. The range of concentrations of the prepared stock solution was (3.39x10^-9 to 2.03x10^-8) M. Some optical characteristics of this dye were investigated such as absorbance and transmission spectra, absorption coefficient, refractive and extinction coefficients, oscillation and dispersion energies, and energy band gap. The absorbance spectra were recorded at 452 nm using Broad Band Cavity Enhanced Absorption Spectroscopy (BBCEAS) which depends on increasing the path length of the traveling light from the source to the detector. The minimum absorbance amount was 0.07 with a low concentration of 3.39x10^-9 M. As a result, the ot

After the success of the reforms Keynesian save the capitalist system from collapse and to apply the concepts of state intervention in economic activity in order to revive aggregate demand to achieve the purposes of macro-economic policies which draw their scope of economic (John Keynes) theory of effective demand, which created the new role of the state away from the classical concepts. Valley transmission role of the State of (State Guardian) to the process of state overlapping that increased and social functions have become responsible for raising the standard of living of classes with limited incomes, in particular, and the rest of the classes in general, through the expansion of the delivery of public servic