The investigation of determining solutions for the Diophantine equation  over the Gaussian integer ring for the specific case of  is discussed. The discussion includes various preliminary results later used to build the resolvent theory of the Diophantine equation studied. Our findings show the existence of infinitely many solutions. Since the analytical method used here is based on simple algebraic properties, it can be easily generalized to study the behavior and the conditions for the existence of solutions to other Diophantine equations, allowing a deeper understanding, even when no general solution is known.

Fullerene nanotube was synthesized in this research by pyrolysis of plastic waste Polypropylene (PP) at 1000 ° C for two hours in a closed reactor made from stainless steel using molybdenum oxide (MoO₃) as a catalyst and nitrogen gas. The resultant carbon was purified and characterized by energy dispersive X-ray spectroscopy (EDX), X-ray powder diffraction (XRD). The surface characteristics of C₆₀ nanotubes were observed with the Field emission scanning electron microscopy (FESEM). The carbon is evenly spread and has the highest concentration from SEM-EDX characterization. The result of XRD and FESEM shows that C₆₀ nanotubes are present in Nano figures, synthesized at 1000 ° C and with pyrolysis tempera

Abstract. Nano-continuous mappings have a wide range of applications in pure and applied sciences. This paper aims to study and investigate new types of mappings, namely nano-para-compact, completely nano-regular, nano-para-perfect, and countably nano-para-perfect mappings in nano-topological spaces using nano-open sets. We introduce several properties and basic characterizations related to these mappings, which are essential for proving our main results. Additionally, we discuss the relationships among these types of mappings in nano-topological spaces. We also introduce the concept of nano-Ti-mapping, where i = 0, 1, 2, nano-neighborhood separated, and nano-functionally separated, along with various other definitions. We explore the relat

Abstract. The purpose of this work is to introduce and investigate new concepts of mappings namely nano paracompactmappings, nano locally limited, nano h-locally limited and finally nano-perfect in nano topology by using nano-closed sets. As well as, the relation between these concepts of mappings have been study in nano topology. Additionally, the nano topology groups of the types and advances results which are introduces in this work are very vital. We also presented the type of nano Lindeloff mappings, and the relations of them was introduce and discussed with several characteristics related it. Nano morphism also introduce.

The main factors that make it possible to get the corrosion of reinforcing steel in concrete are chloride ions and the absorption of carbon dioxide from the environment, and each of them works with a mechanism which destroys the stable immunity of rebar in the concrete. In this work the effect of carbon dioxide content in the artificial concrete solution on the corrosion behavior of carbon steel reinforcing bar (CSRB) was studied, potentiostatically using CO₂ stream gas at 6 level of concentrations;  0.03 to 2.0  weight percent, and the effect of rising electrolyte temperature was also followed  in the range 20 to 50^ᴼ C. Tafel plots and cyclic polarization procedures were obeyed to investigate the c

From a large number of bacterial samples collected from different hospital in Iraq in central  health laboratory ,only ten isolates were identified primary as Vibrio. A number of  morphology and biochemical test were carried out to complete this identification that showed all bacterial isolates were related to Vibrio cholerae .In this study  all Vibrio isolates were investigated for Bio typing and the result showed that all (10) isolate were related to (Eltor biotypes) .Also, the susceptibility test towards eight antibiotics were carried  out .

Results shows that  ciprofloxacin , Norfloxacin, Erythromycin, Ampicillin,  ceftriaxone  and Amikacin were the most effective

The goal of the research is to find the optimization in the test of the appropriate cross-over design for the experiment that the researcher is carrying out (under assumption that there are carry-over effects of the treatments) to posterior periods after the application period (which is often assumed to be the first period). The comparison between the double cross-over design and the cross-over design with extra period. The similarities and differences between the two designs were studied by measuring the Relative Efficiency (RE) of the experiment.

The possible effect of the collective motion in heavy nuclei has been investigated in the framework of Nilson model. This effect has been searched realistically by calculating the level density, which plays a significant role in the description of the reaction cross sections in the statistical nuclear theory. The nuclear level density parameter for some deformed radioisotopes of (even- even) target nuclei (Dy, W and Os) is calculated, by taking into consideration the collective motion for excitation modes for the observed nuclear spectra near the neutron binding energy. The method employed in the present work assumes equidistant spacing of the collective coupled state bands of the considered isotopes. The present calculated results for f

The inhibitive power of Polyvinyl Alcohol (PVA) was investigated toward the corrosion of carbon steel in 0.2N H₂SO₄ solution in the temperature range of 30-60˚C and PVA concentration range of 150-2000 ppm.

   The corrosion rate was measured using both the weight loss and the electrochemical techniques. The weight loss results showed that PVA could serve as a corrosion inhibitor but its inhibition power was found to be low for the corrosion of carbon steel in the acidic media. Electrochemical analysis of the corrosion process of carbon steel in an electrochemical corrosion cell was investigated using 3-Electrode corrosion cell. Polarization technique was used for carbon steel corrosion in 0.2N H

Coblatcomplex has been prepared by reaction between C16H19N3O3S (L) as ligand and metal salt (II). The prepared complex were characterized by infrared spectra, electromic spectra, magnetic susceptibility, molar conductivity measurement and metal analysis by atomic absorption and (C.H.N) analysis. From these studies tetrahedral geometry structure for the complex was suggested. The photodegredation of complex were study using photoreaction cell and preparednanoTiO2 catalyst in different conditions (concentration, temperatures, pH).The results show that the recation is of a first order with activation energy equal to (6.6512 kJ /mol).