In this work, the classical continuous mixed optimal control vector (CCMOPCV) problem of couple nonlinear partial differential equations of parabolic (CNLPPDEs) type with state constraints (STCO) is studied. The existence and uniqueness theorem (EXUNTh) of the state vector solution (SVES) of the CNLPPDEs for a given CCMCV is demonstrated via the method of Galerkin (MGA). The EXUNTh of the CCMOPCV ruled with the CNLPPDEs is proved. The Frechet derivative (FÉDE) is obtained. Finally, both the necessary and the sufficient theorem conditions for optimality (NOPC and SOPC) of the CCMOPCV with state constraints (STCOs) are proved through using the Kuhn-Tucker-Lagrange (KUTULA) multipliers theorem (KUTULATH).

The Iraqi culture faced a set of challenges that can be diagnosed with the most prominent features as follows:

1. The dominance of authoritarian political systems which entails authoritarian regimes with the absence of contemporary political concepts of human rights.
2. The prevalence of non- informed cultural systems which have the shortage of capabilities that enable them to activate cultural elements in positive references, historical, or seclusion on itself and not be able to interact with the current active cultures.
3. Stagnant economic conditions have not had a decent life for individuals, or a certain level of well-being, as well as poor services and others.
4. Social life controlled by the prevai

An experiment in the semester, the second semester of the academic year (2022-2023), and the data used was not processed (the second test for two independent, inaccurate samples, the Bermon correlation coefficient, and the Spearman correlation coefficient), and the following results were reached: There is a statistically significant difference at the level of ( 0) average, 05) between the third grade who studied the plan for asking cluster questions, and between the average of those who studied the special feature according to the traditional method of selecting achievement, and enjoyed completing the specialization, choosing the experimental group, because the strategy of asking cluster questions is one of the externalities that... Lear

Background: One of the major problems in endodontics is micro-leakage of root canal fillings which might contribute to the failure of endodontic treatment. To avoid this problem, a variety of sealers have been tested. The objective of this, in vitro, study was to evaluate the shear bond strength of four resin based sealers (AH plus, silver free AH26, RealSeal SE and Perma Evolution permanent root canal filling material) to dentin. Materials and Methods: Forty non-carious extracted lower premolars were used. The 2mm of the occlusal surfaces of teeth were sectioned, to expose the dentin surface. The exposed dentin surfaces of teeth were washed with 5ml of 2.5% NaOCl solution followed by 5ml of 17 % EDTA then rinsed by deionized water to remov

Background: Neural tube defects (NTDs) are said to be inherited in a multifactorial fashion, i.e. genetic-environmental interaction. Maternal nutritional deficiencies had long been reported to cause NTDs, especially folate deficiency during early pregnancy. More attention had been paid to the exact mechanism by which this deficiency state causes these defects in the developing embryo. The most significant of all researches was that connecting reduced folate and increased homocysteine level in maternal serum on one hand and the risk of developing a NTD baby on the other hand. Objectives : to determine the significance of homocysteine level in Iraqi mothers who gave birth to babies with NTDs as compared to normal controls. Patients, Materials

Globally, breast cancer is the common malignancy affecting women and understanding its associated molecular events could help in disease prevention and management strategies. The present study was set to investigate an association between total antioxidant capacity (TAC) and endothelial nitric oxide synthase (eNOS) polymorphisms with breast cancer. For this purpose, 100 subjects were participated in this work, including 50 female patients diagnosed with breast cancer recruited from Oncology hospital, Baghdad - Iraq and 50 healthy women as a control group. The concentration of antioxidants was measured in the serums collected from blood samples of breast cancer patients and healthy controls. While eNOS SNPs (rs1799983, G894T and rs2070744, T

The aim of this paper is to demonstrate the effect of Na2[Fe(CN)5.NO].2H2O impurity (0.1 M) concentration on the dielectrical properties of poly (P-Aminobenzaldehyde) terminated by pheneylenediamine in the frequency and temperature ranges (1-100)KHz and (283-348) K respectively.These properties include dissipation factor, series and parallel resistance, series and parallel capacitance, real and imaginary part of the dielectric constant, a.c conductivity and impedance (real and imaginary) part, that have been deduced from equivalent circuit. The investigation shows that adding Na2[Fe(CN)5.NO].2H2O as additive to the polymer lead to increase of the dielectric constant with increasing temperature and it is decreasing with increasing the freq

Density functional theory (DFT) with B3LYP level and 6-311G[Formula: see text] basis sets for light atoms like N and O and SDD basis sets for heavy atoms like Sn is used to examine the interaction of tin dioxide nanocrystals with nitrogen dioxide as a function of temperature from 273[Formula: see text]K to 373[Formula: see text]K through a Gaussian 09W software program. Gibbs free energy, enthalpy, and entropy of activation and reaction are calculated. The situation of transition of SnO₂ clusters toward nitrogen dioxide is investigated. According to the findings, the activation energy of SnO₂ clusters with nitrogen dioxide increases as the temperature rises (in negative value). Gauss view 0

Several methods have been developed for routing problem in MANETs wireless network, because it considered very important problem in this network ,we suggested proposed method based on modified radial basis function networks RBFN and Kmean++ algorithm. The modification in RBFN for routing operation in order to find the optimal path between source and destination in MANETs clusters. Modified Radial Based Neural Network is very simple, adaptable and efficient method to increase the life time of nodes, packet delivery ratio and the throughput of the network will increase and connection become more useful because the optimal path has the best parameters from other paths including the best bitrate and best life link with minimum delays. The re