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.

The expanding use of multi-processor supercomputers has made a significant impact on the speed and size of many problems. The adaptation of standard Message Passing Interface protocol (MPI) has enabled programmers to write portable and efficient codes across a wide variety of parallel architectures. Sorting is one of the most common operations performed by a computer. Because sorted data are easier to manipulate than randomly ordered data, many algorithms require sorted data. Sorting is of additional importance to parallel computing because of its close relation to the task of routing data among processes, which is an essential part of many parallel algorithms. In this paper, sequential sorting algorithms, the parallel implementation of man

Recently, all over the world mechanism of cloud computing is widely acceptable and used by most of the enterprise businesses in order increase their productivity. However there are still some concerns about the security provided by the cloud environment are raises. Thus in this our research project, we are discussing over the cloud computing paradigm evolvement for the large business applications like CRM as well as introducing the new framework for the secure cloud computing using the method of IT auditing. In this case our approach is basically directed towards the establishment of the cloud computing framework for the CRM applications with the use of checklists by following the data flow of the CRM application and its lifecycle. Those ch

يهدف البحث الى دراسة وتحليل الهندسة المتزامنة (CE) وتحسين التكلفة(CO)، واستعمال مخرجات الهندسة المتزامنة كمدخلات لتحسين التكلفة، وبيان دور الهندسة المتزامنة في تحسين جودة المنتوج، وتحقيق وفورات في وقت التصميم والتصنيع والتجميع وتخفيض التكاليف، فضلاً عن توظيف بعض النماذج لتحديد مقدار الوفورات في الوقت ومنها نموذج(Lexmark) ونموذج (Pert) لتحديد الوفورات في وقت التصميم وقت لتصنيع والتجميع.      ولتحقيق اهداف 

This investigation was carried out to study the treatment and recycling of wastewater in the Battery industry for an effluent containing lead ion. The reuse of such effluent can only be made possible by appropriate treatment method such as electro coagulation.
The electrochemical process, which uses a cell comprised aluminum electrode as anode and stainless steel electrode as cathode was applied to simulated wastewater containing lead ion in concentration 30 – 120 mg/l, at different operational conditions such as current density 0.4-1.2 mA/cm2, pH 6 -10 , and time 10 - 180 minute.
The results showed that the best operating conditions for complete lead removal (100%) at maximum concentration 120 mg/l was found to be 1.2 mA/cm2 cur

The study deals with the issue of multi-choice linear mathematical programming. The right side of the constraints will be multi-choice. However, the issue of multi-purpose mathematical programming can not be solved directly through linear or nonlinear techniques. The idea is to transform this matter into a normal linear problem and solve it In this research, a simple technique is introduced that enables us to deal with this issue as regular linear programming. The idea is to introduce a number of binary variables And its use to create a linear combination gives one parameter was used multiple. As well as the options of linear programming model to maximize profits to the General Company for Plastic Industries product irrigation sy

This paper investigated the fatigue life behavior of two composite materials subjected to different times of shot peening (2, 4 and 6 min).The first material prepared from unsaturated polyester with E-glass reinforcement by 33% volume fraction. While, the second one was prepared from unsaturated polyester with aluminum powder by2.5% volume fraction. The experimental results showed that the improvement in endurance limit was obtained (for the first material) at 2, 4 and 6 min shot peening times where the percentage of maximum improvement was 25% at shot peening time of 6 min. While, the endurance limit of the second material decreased at shot peening times of 2, 4 and 6 min where the percentage of maximum reduction was 29 % at shot peenin

Now-a-days the Flexible AC Transmission Systems (FACTS) technology is very effective in improving the power flow along the transmission lines and makes the power system more flexible and controllable. This paper deals with the most robust type of FACTS devices; it’s a Unified Power Flow Controller (UPFC). Many cases have been taken to study how the system behaves in the presence and absence of the UPFC under normal and contingency conditions. The UPFC is a device that can be used to improve the bus voltage, increasing the loadability of the line and reduce the active and reactive power losses in the transmission lines, through controlling the flow of real and reactive power. Both the magnitude and the phase angle of th

Numerical study has been conducted to investigate the thermal performance enhancement of flat plate solar water collector by integrating the solar collector with metal foam blocks.The flow is assumed to be steady, incompressible and two dimensional in an inclined channel. The channel is provided with eight foam blocks manufactured form copper. The Brinkman-Forchheimer extended Darcy model is utilized to simulate the flow in the porous medium and the Navier-Stokes equation in the fluid region. The energy equation is used with local thermal equilibrium (LTE) assumption to simulate the thermofield inside the porous medium. The current investigation covers a range of solar radiation intensity at 09:00 AM, 12:00 PM, and 04:00