In this paper the Galerkin method is used to prove the existence and uniqueness theorem for the solution of the state vector of the triple linear elliptic partial differential equations for fixed continuous classical optimal control vector. Also, the existence theorem of a continuous classical optimal control vector related with the triple linear equations of elliptic types is proved. The existence of a unique solution for the triple adjoint equations related with the considered triple of the state equations is studied. The Fréchet derivative of the cost function is derived. Finally the theorem of necessary conditions for optimality of the considered problem is proved.

This paper provides a four-stage Trigonometrically Fitted Improved Runge-Kutta (TFIRK4) method of four orders to solve oscillatory problems, which contains an oscillatory character in the solutions. Compared to the traditional Runge-Kutta method, the Improved Runge-Kutta (IRK) method is a natural two-step method requiring fewer steps. The suggested method extends the fourth-order Improved Runge-Kutta (IRK4) method with trigonometric calculations. This approach is intended to integrate problems with particular initial value problems (IVPs) using the set functions  and   for trigonometrically fitted. To improve the method's accuracy, the problem primary frequency  is used. The novel method is more accurate than the conventional Runge-Ku

     In this work, new di-acid monomers 4, 4’-di-carboxillic-2”-chloro-4”- nitro triphenylamine (Di-CO2H-1), 4, 4’- di-carboxylic -2”,4”,6”-trichloro-triphenylamine (Di-CO2H-2) were synthesized by reaction of p-cyanobenzofluride with two aromatic amines (2-chloro 4-nitro aniline and 2,4,6-trichloro aniline by aromatic nucleophilc substitution method to produce two di cyano intermediates compounds 4, 4’-Dicyano-2”-chloro-4”- nitro triphenylamine (Di-CN1) and 4, 4’-dicyano-2”,4”,6”-trichloro-triphenylamine (Di-CN2) which form final di-carboxylic monomers after alkaline hydrolysis. Finally, these monomers react with two different arom

Several attempts have been made to modify the quasi-Newton condition in order to obtain rapid convergence with complete properties (symmetric and positive definite) of the inverse of  Hessian matrix (second derivative of the objective function). There are many unconstrained optimization methods that do not generate positive definiteness of the inverse of Hessian matrix. One of those methods is the symmetric rank 1( H-version) update (SR1 update), where this update satisfies the quasi-Newton condition and the symmetric property of inverse of Hessian matrix, but does not preserve the positive definite property of the inverse of Hessian matrix where the initial inverse of Hessian matrix is positive definiteness. The positive definite prope

Giardiasis is an infection caused by the protozoan flagellate parasite Giardia spp. in the intestine. G duodenalis, a species complex of diverse genotypes that tend to demonstrate host specificity, is responsible for most veterinary health related infections; production animals, companion animals, and wildlife can all be infected. Abdominal pain and diarrhea, typically accompanied by steatorrhea, are the most common symptoms of Giardiasis. Cysts or antigens in feces are commonly used to diagnose the disease. Treatment regimens vary and are dependent on the indication. Control methods must include hygiene measures. Despite direct evidence of Giardia sp transmission to humans via polluted water supplies, our analysis will focus on some r

The calculation of the oil density is more complex due to a wide range of pressuresand temperatures, which are always determined by specific conditions, pressure andtemperature. Therefore, the calculations that depend on oil components are moreaccurate and easier in finding such kind of requirements. The analyses of twenty liveoil samples are utilized. The three parameters Peng Robinson equation of state istuned to get match between measured and calculated oil viscosity. The Lohrenz-Bray-Clark (LBC) viscosity calculation technique is adopted to calculate the viscosity of oilfrom the given composition, pressure and temperature for 20 samples. The tunedequation of state is used to generate oil viscosity values for a range of temperatu

The study showed flow rates and the interaction between the settlements served by applying the model of gravity theory to measure depending on the number of the population between city Najaf and the rest of the other settlements served and using three functions of disability, time and cost, as recorded an increase in the interaction index with some settlements like them Kufa, Abbasid and Manathira, while the indicator contrast was in other settlements, either when the application of the gravity model depending on trips and socio-economic characteristics accuracy rate was more pronounced.