This paper deals with finding an approximate solution to the index-2 time-varying linear differential algebraic control system based on the theory of variational formulation. The solution of index-2 time-varying differential algebraic equations (DAEs) is the critical point of the equivalent variational formulation. In addition, the variational problem is transformed from the indirect into direct method by using a generalized Ritz bases approach. The approximate solution is found by solving an explicit linear algebraic equation, which makes the proposed technique reliable and efficient for many physical problems. From the numerical results, it can be implied that very good efficiency, accuracy, and simplicity of the pre

In this study, the photodegradation of Congo red dye (CR) in aqueous solution was investigated using Au-Pd/TiO₂ as photocatalyst. The concentration of dye, dosage of photocatalyst, amount of H₂O₂, pH of the medium and temperature were examined to find the optimum values of these parameters. It has been found that 28 ppm was the best dye concentration. The optimum amount of photocatalyst was 0.09 g/75 mL of dye solution when the degradation percent was ~ 96 % after irradiation time of 12 hours, while the best amount of hydrogen peroxide was 7μl/75 mL of dye solution at degradation percent ~97 % after irradiation time of 10 hours, whereas pH 5 was the best value to carry out the reaction at the highest deg

In this study, the photodegradation of Congo red dye (CR) in aqueous solution was investigated using Au-Pd/TiO2 as photocatalyst. The concentration of dye, dosage of photocatalyst, amount of H2O2, pH of the medium and temperature were examined to find the optimum values of these parameters. It has been found that 28 ppm was the best dye concentration. The optimum amount of photocatalyst was 0.09 g/75 mL of dye solution when the degradation percent was ~ 96 % after irradiation time of 12 hours, while the best amount of hydrogen peroxide was 7μl/75 mL of dye solution at degradation percent ~97 % after irradiation time of 10 hours, whereas pH 5 was the best value to carry out the reaction at the highest degradation percent. In additio

The simulation of passively Q-switching is four non – linear first order differential equations. The optimization of passively Q-switching simulation was carried out using the constrained Rosenbrock technique. The maximization option in this technique was utilized to the fourth equation as an objective function; the parameters, γa, γc and β as were dealt with as decision variables. A FORTRAN program was written to determine the optimum values of the decision variables through the simulation of the four coupled equations, for ruby laser Q–switched by Dy +2: CaF2.For different Dy +2:CaF2 molecules number, the values of decision variables was predicted using our written program. The relaxation time of Dy +2: CaF2, used with ruby was

 The present study introduces description of a new species of class Ostracoda genus Hemicypris Sars, 1903. External morphological characters particularly shape, size and structure of left and right valves of carapace and body appendages were discussed and illustrated. Locality and date of collection were given.

This research aims to identify the effect of numbered heads strategy on developing oral expression skills among fifth-grade primary students in Bisha Province. To achieve this, the researcher prepared a research tool represented in the observation card which consists of (27) statements distributed in four axes. The tool was sent to (5) experts in the field to verify their validity. In light of their corrections, the tool was developed to be valid for gathering field information. To verify the validity of the content and the reliability of the tool, the researcher applied it to a sample consists of (20) students from outside the research group. The overall coefficient of correlation between the statements of the tool is as follows: (.95,

    The adsorption study of thymol, was carried out at (25±0.1) ^°C, using granulated surfactant modified Iraqi Na – montmorillonite clay (initiated modified bentonite); in a down-flow packed column, the modified mineral was characterized by FT-IR spectroscopy.  A linear calibration graph for thymol was obtained, which obey Beer's law in the concentration range of 5-50 mg/L at 274 nm against reagent blank. Single-factor-at-a-time approach; showed that the equilibrium time required for complete adsorption was 45 minute with flow rate (4.0drop/ mint). The adsorption of thymol increased with rising pH of the adsorbate solution, increase of solute uptake when  the initial adsor

       Field experiment was conducted during 2018- 2019 in loam soil at the research field of the Department of Biology, College of Science, Baghdad University, Baghdad, Iraq, to study the effect of bio-fertilizers and two levels of chemical fertilization ( 50% and 100%) in some agronomic traits of wheat Triticum aestivum L. cultivar IPA 99  by the genus Azotobacter chroococum and AMF Glomus mosseae singly or in combination under drought condition. The experimental design was a Completely Randomized Block Design (CRBD)with three replications. The results revealed that the application of bio-fertilizers reduced the negative impacts of water deficit. However, &nbsp