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.

In this work ,pure and doped(CdO)thin films with different concentration of V2O5x (0.0, 0.05, 0.1 ) wt.% have been prepared on glass substrate at room temperature using Pulse Laser Deposition technique(PLD).The focused Nd:YAG laser beam at 800 mJ with a frequency second radiation at 1064 nm (pulse width 9 ns) repetition frequency (6 Hz), for 500 laser pulses incident on the target surface At first ,The pellets of (CdO)1-x(V2O5)x at different V2O5 contents were sintered to a temperature of 773K for one hours.Then films of (CdO)1-x(V2O5)x have been prepared.The structure of the thin films was examined by using (XRD) analysis..Hall effect has been measured in orded to know the type of conductivity, Finally the solar cell and the effici

A real method of predication brake pad wear ,could lead to substantiol economies of time and money. This paper describes how such a procedure has been used and gives the results to establish is reliability by comparing the predicted wear with that which actually occurs in an existing service. The experimental work was carried out on three different commercial samples ,tested under different operation conditions (speed,load,time...etc)using a test ring especially modified for this purpose. Abrasive wear is mainly studied , since it is the type of wear that takes place in such arrangements. Samples wear tested in presences of sand or mud between the mating surfaces under different operational conditions of speed, load and braking time .Mec

The thermal properties (thermal transfer and thermal expansion coefficient) of the enhanced epoxy resin (MWCNT / x-TiO₂) were studied by weight ratios with the values (0%, 3%, 5%, 7% and 10%) and a constant ratio of 3% of MWCNT. The ultrasonic technology was used to prepare the neat and composites which were then poured into Teflon molds according to standard conditions. Thermo-analyzer sensor technology was used to measure thermal transfer (thermal conductivity, thermal flow, thermal diffusion, thermal energy and heat resistance). The thermal conductivity, flow, and thermal conductivity values were increased sequentially by increasing the weight ratio of the filler while the results of stored energy values an

The effect of substitution of Ni on Cu in (Bi0.8Pb0.2)2(Sr0.9Ba0.1)2 Ca2Cu3-x Nix O10+? for (x=0,0.1….1,2,3) superconductor system and sintering time has been investigated .The samples were prepared by solid-state reaction methods. The results show that the optimum sintering temperature is equal to 850 ºC, and the sintering time is equal to 140 h. The highest transition temperature (Tc) obtained for (Bi0.8Pb0.2)2(Sr0.9Ba0.1)2 Ca2Cu3-x NixO10+? composition was 113 with x=0.8 Phase analyses of the samples by X-ray diffraction (XRD) analysis showed an orthorhombic structure with a high Tc phases (2223) as a dominant phase and low Tc phase (2212) in addition to some impurity phases.

Ferrite with general formula Ni1-x Cox Fe2O4(where x=0.0.1,0.3,0.5,0.7, and 0.9), were prepared by standard ceramic technique. The main cubic spinel structure phase for all samples was confirmed by x-ray diffraction patterns. The lattice parameter results were (8.256-8.299 ^°A). Generally, x -ray density increased with the addition of Cobalt and showed value between (5.452-5.538gm/cm³). Atomic Force Microscopy (AFM) showed that the average grain size and surface roughness was decreasing with the increasing cobalt concentration. Scanning Electron Microscopy images show that grains had an irregular distribution and irregular shape. The A.C conductivity was found to increase with the frequency and the addition of Cobal

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

This study investigates the possibility of using waste plastic as one of the components of expired lead-acid batteries to produce lightweight concrete. Different percentages of lead-acid battery plastic were used in the production of lightweight concrete. The replacements were (70, 80 and 100%) by volume of the fine and coarse aggregate. Results demonstrated that a reduction of approximately 23.6% to 35% in the wet density was observed when replacement of 70% to 100% of the natural aggregate by lead-acid battery plastic. Also, the compressive strength decreased slightly with the increase in plastic content at different curing ages of 7, 28, 60, 90, 120 days. The lowest value of compressive strength was (20.7 MPa) for (wa