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 research dealt with desalting of East Baghdad crude oil using pellets of either anionic, PVC, quartz, PE, PP or
nonionic at different temperature ranging from 30 to 80 °C, pH from 6 to 8, time from 2 to 20 minutes, volume percent
washing water from 5 to 25% and fluid velocity from 0.5 to 0.8 m/s under voltage from 2 to 6 kV and / or using additives
such as alkyl benzene sulphonate or sodium stearate. The optimum conditions and materials were reported to remove
most of water from East Baghdad wet crude oil.

This paper presents a newly developed method with new algorithms to find the numerical solution of nth-order state-space equations (SSE) of linear continuous-time control system by using block method. The algorithms have been written in Matlab language. The state-space equation is the modern representation to the analysis of continuous-time system. It was treated numerically to the single-input-single-output (SISO) systems as well as multiple-input-multiple-output (MIMO) systems by using fourth-order-six-steps block method. We show that it is possible to find the output values of the state-space method using block method. Comparison between the numerical and exact results has been given for some numerical examples for solving different type

This paper is concerned with the quaternary nonlinear hyperbolic boundary value problem (QNLHBVP) studding constraints quaternary optimal classical continuous control vector (CQOCCCV), the cost function (CF), and the equality and inequality quaternary state and control constraints vector (EIQSCCV). The existence of a CQOCCCV dominating by the QNLHBVP is stated and demonstrated using the Aubin compactness theorem (ACTH) under appropriate hypotheses (HYPs). Furthermore, mathematical formulation of the quaternary adjoint equations (QAEs) related to the quaternary state equations (QSE) are discovere  so as its weak form (WF) . The directional derivative (DD) of the Hamiltonian (Ham) is calculated. The necessary and sufficient conditions for

  In this paper we shall generalize fifth explicit Runge-Kutta Feldberg(ERKF(5)) and Continuous explicit Runge-Kutta (CERK) method using shooting method to solve second order boundary value problem  which can be reduced to order one.These methods we shall call them as shooting Continuous Explicit Runge-Kutta method, the results are computed using matlab program.

The reactive yellow azo dye (λmax = 420 nm) is widely utilized for textile coloring due to its low-cost stability and tolerance properties. Treatment of dye-containing wastewater by traditional methods is usually inadequate because of its resistance to biological and chemical degradation. From this research, the continuous reactor of an advanced oxidation method supported the use of H₂O₂/TiO₂/UV to remove the coloration of the reactive yellow dye from the discharge. At constant best conditions obtained from the batch reactor tests pH=7, H₂O₂ dosage = 400 mg/l and TiO₂=25mg/l , the aqueous solutions were tested in the continuous reactor at different dye concentration and d

Adsorption techniques are widely used to remove certain classes of pollutants from waters, especially those that are not easily biodegradable. Dyes represent one of the problematic groups. The removal of methyl green from waste water using bamboo was studied in batch and continuous system. In batch system equilibrium time and adsorption isotherm was studied at different concentrations (5, 10, 15, 20, 25 and 30 ppm) and 50 mg weight of adsorbent.
Langmuir and Freundlich equations were applied for adsorption isotherm data. Langmiur equation was fitted better than Freundlich equation (R2=0.984 for Langmuir equation).The maximum percentage dye removal obtained 79.4% and adsorption capacity was 15.5 mg/g. For continuous system the breakthr

This research deals with leverage and its impact on the profitability of Islamic banks in Iraq for the years (2015-2018), the research variables of leverage have been analyzed and measured as an independent variable, profitability as a dependent variable, and the research is based on a main hypothesis: there is a moral relationship of statistical significance. Between leverage and profitability at The Islamic Cooperation Bank for the period (2015-2018). The results of the research showed that there are moral (exorcist) relationships between the ratio of leverage and profitability indicators, as the higher the leverage ratio, the higher the profitability indicators. In addition, The Islamic Cooperation Bank has adopted a conservative poli

The high mobility group A1 gene (HMGA1) rs139876191 variant has been related to metabolic syndrome and type 2 diabetes, but data are lacking in Middle Eastern populations. The study aimed to assess whether the HMGA1 rs139876191 variant is associated with metabolic syndrome risk and whether this variant predicts the risk of insulin resistance. This case-control study was carried out at single center in Kirkuk city/ Iraq from February to August 2022. Polymorphisms in HMGA1 and genotyping were identified by Sanger sequencing of genomic DNA obtained from 91 Iraqi participants (61 patients with metabolic syndrome and 30 control). Lipid profile, serum (glucose and insulin), glycated hemoglobin, blood pressure, body mass index, and waist circumfer