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.

Studies on the flexural behavior of post-tensioned beams subjected to strand damage and strengthened with near-surface mounted (NSM) technique using carbon fiber-reinforced polymer (CFRP) are limited and fail to examine the effect of CFRP laminates on strand strain and strengthening efficiency systematically. Furthermore, a design approach for UPC structures in existing design guidelines for FRP strengthening techniques is lacking. Hence, the behavior of post-tensioned beams strengthened with NSM-CFRP laminates after partial strand damage is investigated in this study. The testing program consists of seven post-tensioned beams strengthened by NSM-CFRP laminates with three partial strand damage ratios (14.3% symmetrical damage, 14.3%

Alloys of InxSe1-x were prepared by quenching technique with
different In content (x=10, 20, 30, and 40). Thin films of these alloys
were prepared using thermal evaporation technique under vacuum of
10-5 mbar on glass, at room temperature R.T with different
thicknesses (t=300, 500 and 700 nm). The X–ray diffraction
measurement for bulk InxSe1-x showed that all alloys have
polycrystalline structures and the peaks for x=10 identical with Se,
while for x=20, 30 and 40 were identical with the Se and InSe
standard peaks. The diffraction patterns of InxSe1-x thin film show
that with low In content (x=10, and 20) samples have semi
crystalline structure, The increase of indium content to x=30
decreases degree o

The current research deals with practical studies that explain to the Iraqi consumer multiple instances about the phenomenon of water hammer which occur in the water pipeline operating with pressure. It concern a practical study of the characteristics of this phenomenon and economically harmful to the consumer the same time. Multiple pipe fittings are used aimed to reduce this phenomenon and its work as alternatives to the manufactured arresters that used to avoid water hammer in the sanitary installations, while the consumer did not have any knowledge as to the non-traded for many reasons, including the water pressure decreases in the networks and the use of consumer pumps to draw water directly from the network. Study found a number of

Topology and its applications occupy the interest of many researching centers in the advanced world. From this point of view and because the near open sets play a very important role in general topology and they are now the research topics of many topologists worldwide and its sets doesn’t enter in fibrewise topology yet. Therefore, we use some of the near open sets to be model for introduce results and new spaces in fibrewise topological spaces. Also, there is a very important role of closure operators in constructing a topological spaces, so we introduce a new closure operators on the power set of vertices on graphs and conclusion theorems and new spaces from it. Furthermore, we discuss the relationships of connectedness between some ty

The current research deals with practical studies that explain to the Iraqi consumer multiple instances about the phenomenon of water hammer which occur in the water pipeline operating with pressure. It concern a practical study of the characteristics of this phenomenon and economically harmful to the consumer the same time. Multiple pipe fittings are used aimed to reduce this phenomenon and its work as alternatives to the manufactured arresters that used to avoid water hammer in the sanitary installations, while the consumer did not have any knowledge as to the non-traded for many reasons, including the water pressure decreases in the networks and the use of consumer pumps to draw water directly from the network. Study found a numbe

Lithium–Manganese ferrites having the chemical formula (Li0.5-0.5x Mnx Fe2.5-0.5x O4), (0 ≤ x ≤ 1) were prepared by double sintering powder processing. The density of the ferrite increased with Mn content while the porosity was noticed to decrease. The dielectric constant was found to increase at high frequencies more rapidly than the low ones. The dielectric constant found to decrease with Mn content. The decrease in loss factor with frequency agreed with Deby’s type relaxation process. A maximum of dielectric loss factor was observed when the hopping frequency is equal to the external electric field frequency. Manganese substitution reduced the dielectric loss in ferrite. The variation of tanδ with frequency shows a similar na

This work illustrates an enhanced visible light photocatalytic degradation of methyl orange dye (M.O.) by employing BiOI / BiOCl composites prepared under room temperature and without any organic precursors. Various experimental parameters have been studied, namely; composition of the composite, irradiation time and cell material. Composition D which implied 75% BiOI and 25% BiOCl has shown the highest bleaching of M.O. dye. This confirms the optimum photo-sensitization phenomenon for this composition in comparison to others. In the optimum photo-sensitized composite the electron of the conduction band reveals better reducing power and the hole of the valence band exhibits more oxidative power than those of pure BiOI electron and hole. Acco

                The electrical characteristics of polyvinyl alcohol PVA doped with different concentrations (0, 1, 2, 3 and 4wt%) of sodium  iodide NaI powder were studied. The films are prepared using solution casting technique, in order to investigate the effect of sodium iodide NaI additions on the electrical properties of PVA host. The D.C conductivity measured by measuring the D.C electrical resistance using the Keithly Electrometer type 616C, and for different temperatures ranging from 30 – 70^oC.

          The dielectric properties measured by measuring the capacitor and the loss