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

The principal aim of this research is to use the definition of fuzzy normed space
to define fuzzy bounded operator as an introduction to define the fuzzy norm of a
fuzzy bounded linear operator then we proved that the fuzzy normed space FB(X,Y)
consisting of all fuzzy bounded linear operators from a fuzzy norm space X into a
fuzzy norm space Y is fuzzy complete if Y is fuzzy complete. Also we introduce
different types of fuzzy convergence of operators.

    In this paper, the concepts of -sequence prime ideal and -sequence quasi prime ideal are introduced. Some properties of such ideals are investigated. The relations between -sequence prime ideal and each of primary ideal, -prime ideal, quasi prime ideal, strongly irreducible ideal, and closed ideal, are studied. Also, the ideals of a principal ideal domain are classified into quasi prime ideals and -sequence quasi prime ideals.

Thermal and catalytic pyrolysis of waste plastics in an inert atmosphere has been regarded as a creative method, since pyrolysis can convert plastics waste into hydrocarbons that can be used either as fuels or as a source of chemicals.

Natural Iraqi kaolin clay was used to synthesis the NaX nano- zeolite by hydrothermal conditions with average particle size equal to 77.63nm.Thermal decomposition kinetics of high-density polyethylene (HDPE) in the absence and presence of catalysts nano NaX Zeolite was investigated. Thermal and catalytic degradation of HDPE was performed using a thermogravimetric analyzer in nitrogen atmosphere under non-isothermal conditions 4, 7 and 10 °C/min heating rates were employed in thermogravimetric anal

The new Schiff base, namely (2-Amino-phenylimino)-acetic acid (L) was prepared
from condensation of glyoxylic acid with o-phenylene diamine. The structure (L) was
characterized by, IR,
1
H,
13
C-NMR and CHN analysis. Metal complexes of the ligand (L)
were synthesized and their structures were characterized by Atomic absorption, IR and UV-Visible spectra, molar conductivity, magnetic moment and molar ratio determination (Co
+2
,
Cd
+2
) complexes. All complexes showed octahedral geometries.

In this research, the effect of multi-walled carbon nanotubes (MWCNTs) on the alumina/chromia (Al₂O₃/Cr₂O₃) nanocomposites has been investigated. Al₂O₃/Cr₂O₃-MWCNTs nanocomposites with variable contents of Cr₂O₃ and MWCNTs were fabricated using coprecipitation process and followed by spark plasma sintering. XRD analysis revealed a good crystallinity of sintered nanocomposites samples and there was only one phase presence of Al₂O₃-Cr₂O₃ solid solution. Density, Vickers microhardness, fracture toughness and fracture strength have been measured in the sintered samples. The results show tha

This research presents a study in ultra-desulfurization of diesel fuel produced from conventional hydro desulfurization process, using oxidation and solvent extraction techniques. Dibenzothiophene (DBT) was the organosulfur compound that had been detected in sulfur removal. The oxidation process used hydrogen peroxide as an oxidant and acetic acid as homogeneous catalyst . The solvent extraction process used acetonitrile (ACN) and N-methyl – 2 - pyrrolidone (NMP) as  extractants . Also the effect of five parameters (stirring speed :150 , 250 , 350 , and 450) rpm, temperature (30 , 40 , 45 , and 50) ^oC, oxidant/simulated diesel fuel ratio (0.5 , 0.75 , 1 , and 1.5) , catalyst/oxidant ratio(0.125,0.25,0.5

The Wheat husk is one of the common wastes abundantly available in the Middle East countries especially in Iraq. The present study aimed to evaluate the Wheat husk as low cost material, eco-friendly adsorbents for the removal of the carcinogenic dye (Congo red dye) from wastewater by investigate the effect of, at different conditions such as, pH(3-10), amount of adsorbents (1-2.3gm/L),and particle size (125-1000) μm, initial Congo red dye concentration(10, 25 , 50 and 75mg/l)  by batch experiments. The results showed that the removal percentage of dye increased with increasing adsorbent dosage, and decreasing particle size. The maximum removal and uptake reached (91%) , 21.5mg/g, respectively for 25 initial concent

     In this research, we prepared a polymer blend of polyvinylalcohol (PVA)/carrageenan/kaolinite by means of the solution cast approach. The composition of the blend was PVA in 1 gm by weight with 0.2 gm carrageenan as a plasticizer. The ratio of nanoclay varied between 1 and 5 wt%. Different properties were investigated in this study such as water vapor permeability, hardness, tear strength, color stability, thermal stability, and antibacterial activity. Water vapor permeability was decreased with increasing the ratio of nanoclay, while the values of hardness, tear strength, color stability, and thermal stability were increased. Also, the antibacterial activity examination with two types of bacteria, e.g.

This paper concerned with development of a spectrophotometric method for the determination of paracetamol, based on the diazotisation and coupling reaction with anthranilic acid in basic medium, to form an intense yellow coloured, water-soluble and stable azo-dye which shows a maximum absorption at 421nm. Beer’s law is obeyed over the concentration range of 1.0-10 µg/ml; with molar absorptivity of 2.1772×104 L.mol -1.cm-1 and Sandell’s sensitivity index 6.9446 µg.cm-2. The method has been applied successfully for the determination of paracetamol in pharmaceutical formulation.