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 investigation, the mechanical properties and microstructure of Metal Matrix Composites (MMCs) of Al.6061 alloy reinforced by ceramic materials SiC and Al₂O₃ with different additive percentages 2.5, 5, 7.5, and 10 wt.% for the particle size of 53 µ_m are studied. Metal matrix composites were prepared by stir casting using vortex technique and then treated thermally by solution heat treatment at 530 ⁰C for 1 hr. and followed by aging at 175 ⁰C with different periods. Mechanical tests were done for the samples before and after heat treatment, such as impact test, hardness test, and tensile test. Also, the microstructure of the metal matrix composites was examine

The high viscosity of heavy oil is a crucial factor that strongly affects its up-stream recovering, down-stream surface transporting and refining processes. Economical methods for recovering the heavy oil and reducing is very important and related to capital and/or operating cost. This research studies the treatment of Iraqi heavy crude oil, which characterize with high viscosity and low API which makes transportation of heavy crude oil a difficult mission, needs for treatment to reduce viscosity for facilitating transportation and processing. Iraqi heavy crude oil was used Sharqi Baghdad, which obtained from Baghdad east oil fields with API 22.2º.Many kinds of additives were used to reduce the viscosity, experiments were performed o

A simple, accurate and rapid method for separation and determination of most commonly usedinsecticides in Iraq [thiamethoxam (Thi), imidacloprid (Imi), indoxacarb (Ind), and abamectin (Aba)] ispresented. The separation was performed by gradient reversed-phase high performance liquidchromatography on a C18 stationary phase column. The method was developed and validated. The-1mobile phase was a mixture of acetonitrile and water using gradient flow. The flow rate was 1.0 mL min .The optimum temperature of separation was 25 ºC. The detection was performed at multiple wavelengths.The analysis time was up to 10.5 minutes with retention times of 3.221, 3.854, 6.385, and 9.452 min for-1the studied insecticides. The linearity was in the range of 0.

This study focuses on studying the effect of reinforced steel in detail, and steel reinforcement (tensile ratio, compression ratio, size, and joint angle shape) on the strength of reinforced concrete (compressive strength) Fc' and searching for the most accurate details of concrete divisions, their behavior, and corner resistance of reinforced concrete joint. The comparison of this paper with previous studies, especially in the studied properties. The conclusions of the chapter are summarized that these effects had a clear effect and a specific effect on the behavior and resistance of the reinforced concrete corner joints under the negative moments and under their influence and the resulting stress conditions. The types of defects that can

The influence and hazard of fire flame are one of the most important parameters that affecting the durability and strength of structural members. This research studied the influence of fire flame on the behavior of reinforced concrete beams affected by repeated load. Nine self- compacted reinforced concrete beams were castellated, all have the same geometric layout (0.15x0.15x1.00) m, reinforcement details and compressive strength (50 Mpa). To estimate the effect of fire flame disaster, four temperatures were adopted (200, 300, 400 and 500) oC and two method of cooling were used (graduated and sudden). In the first cooling method, graduated, the tested beams were leaved to cool in air while in the second method, sudden, water splash was use

The influence and hazard of fire flame are one of the most important parameters that affecting the durability and strength of structural members. This research studied the influence of fire flame on the behavior of reinforced concrete beams affected by repeated load. Nine self- compacted reinforced concrete beams were castellated, all have the same geometric layout (0.15x0.15x1.00) m, reinforcement details and compressive strength (50 Mpa).

To estimate the effect of fire flame disaster, four temperatures were adopted (200, 300, 400 and 500) ^oC and two method of cooling were used (graduated and sudden). In the first cooling method, graduated, the tested beams were leaved to cool in air while in the seco

The study of green colour in glass has a special importance on the glass quality, specially the effect of ferrous oxides content of the limestone. Results obtained that there was a reduction in green colour when different ferrous oxide contents in the limestone were added in glass production, limestone sources from two quarries, and the first contains 0.67% ferrous oxide and the second posses less ferrous oxide.

Reduction of green colour showed higher transmittance12% and it could be suggested that reduction of ferrous oxides content in the limestone is of special importance on the optical properties of glass.

Background: In recent years, the immediate loading of dental implants has become more accepted as a standard protocol for the treatment of the edentulous area. Success in implant dentistry depends on several parameters that may improve phenomenon of osseointegration and new bone formation in close contact with the implant. The aim of study was to evaluate the effect of strontium chloride coating of screw shape commercially pure titanium dental implant osseointegration at bone - implant interface by histomorphometric analysis and compare with hydroxyapatite coating at 2 time periods (2 weeks and 6 weeks). Materials and methods: Electrophoretic Deposition Technique (EPD) was used to obtain a uniform coating layer on commercially pure titanium