In this paper, the continuous classical boundary optimal control problem (CCBOCP) for triple linear partial differential equations of parabolic type (TLPDEPAR) with initial and boundary conditions (ICs & BCs) is studied. The Galerkin method (GM) is used to prove the existence and uniqueness theorem of the state vector solution (SVS) for given continuous classical boundary control vector (CCBCV). The proof of the existence theorem of a continuous classical boundary optimal control vector (CCBOCV) associated with the TLPDEPAR is proved. The derivation of the Fréchet derivative (FrD) for the cost function (CoF) is obtained. At the end, the theorem of the necessary conditions for optimality (NCsThOP) of this problem is stated and prov

The -mixing of  - transition in Er 168 populated in Er)n,n(Er 168168  reaction is calculated in the present work by using a2- ratio method. This method has used in previou studies [4, 5, 6, 7] in case that the second transition is pure or for that transition which can be considered as pure only, but in one work we applied this method for two cases, in the first one for pure transition and in the 2nd one for non pure transitions. We take into accunt the experimental a2- coefficient for p revious works and -values for one transition only [1]. The results obtained are, in general, in agood agreement within associated errors, with those reported previously [1], the discrepancies that occur are due to inaccuracies existing

The study deals with the issue of multi-choice linear mathematical programming. The right side of the constraints will be multi-choice. However, the issue of multi-purpose mathematical programming can not be solved directly through linear or nonlinear techniques. The idea is to transform this matter into a normal linear problem and solve it In this research, a simple technique is introduced that enables us to deal with this issue as regular linear programming. The idea is to introduce a number of binary variables And its use to create a linear combination gives one parameter was used multiple. As well as the options of linear programming model to maximize profits to the General Company for Plastic Industries product irrigation sy

Water quality planning relies on Biochemical Oxygen Demand BOD. BOD testing takes five days. The Particle Swarm Optimization (PSO) is increasingly used for water resource forecasting. This work designed a PSO technique for estimating everyday BOD at Al-Rustumiya wastewater treatment facility inlet. Al-Rustumiya wastewater treatment plant provided 702 plant-scale data sets during 2012-2022. The PSO model uses the daily data of the water quality parameters, including chemical oxygen demand (COD), chloride (Cl-), suspended solid (SS), total dissolved solids (TDS), and pH, to determine how each variable affects the daily incoming BOD. PSO and multiple linear regression (MLR) findings are compared, and their performance is evaluated usin

    A new Schiff base complex was prepeard and characterized: Chloro –Oxo (bis(Ohydroxy benzaldehyde) O-phenylene di imination ) Vanadium (V) with general  formula (VOLCL). Complex was studied by using Three different organics Organic The photo chemistry of this  solvent with different polarity . These solvents were ( Acetone,pyridinest chloro form) . It was found that the chelate Vanadium (V) complex decomposed photochemically in these solvents during . In the tra oxidation –reduction reaction leading to free radical derived in the ligand of shiff base â„“ .Vanadium IV chelate complex . It was also found that the quantum yield of photo decomposition (Ñ„d) and Activity ratio did  not de

The improvement in Direction of Arrival (DOA) estimation when the received signals impinge on Active-Parasitic Antenna (APA) arrays will be studied in this work. An APA array consists of several active antennas; others are parasitic antennas. The responses to the received signals are measured at the loaded terminals of the active element. The terminals of the parasitic element are shorted. The effect of the received signals on the parasites, i.e., the induced short-circuit current, is mutually coupled to the active elements. Eigen decomposition of the covariance matrix of the measurements of the APA array generates a third subspace in addition to the traditional signal and noise subspaces generated by the all-active ante

Water quality planning relies on Biochemical Oxygen Demand BOD. BOD testing takes five days. The Particle Swarm Optimization (PSO) is increasingly used for water resource forecasting. This work designed a PSO technique for estimating everyday BOD at Al-Rustumiya wastewater treatment facility inlet. Al-Rustumiya wastewater treatment plant provided 702 plant-scale data sets during 2012-2022. The PSO model uses the daily data of the water quality parameters, including chemical oxygen demand (COD), chloride (Cl^-), suspended solid (SS), total dissolved solids (TDS), and pH, to determine how each variable affects the daily incoming BOD. PSO and multiple linear regression (MLR) findings are compared, and their perfor

            Spectrophotometric method was developed for the determination of copper(II) ion. Synthesized (2,2[O-Tolidine-4,4-bis azo]bis[4,5-diphenyl imidazole]) (MBBAI) was used as chromogenic reagent at pH=5. Various factors affecting complex formation, such as, pH effect, reagent concentration, time effect and temperature effect, have been considered and studied. Under optimum conditions concentration ranged from (5.00-80.00) µg/mL of copper(II) obeyed Beer`s Low. Maximum absorption of the complex was 409nm with molar absorpitivity 0.127x10⁴ L mol^-1 cm^-1. Limit of detection(LOD) and Limit of quantification were 1.924 and 6.42 μg/mL, respectively.

Background: Bone density is a major factor that affect mini implant primarily stability; no Iraqi studies have evaluated bone density related to mini-implant placement for orthodontic anchorage at age 13 -15 years. The present research aims to evaluate gender, side and site differences in the bone density at various orthodontic implant sites for the maxillary alveolar bone. Materials and methods: Twenty nine individuals (16 males and 13 females) had subjected to clinical examination, then 64-multislice computed tomography scan data were evaluated and bone density was measured in Hounsfield unit at 21 points (9 points for each side and 3 points between the right and left central incisors) . Results: The results obtained showed that there ar