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.
We study the physics of flow due to the interaction between a viscous dipole and boundaries that permit slip. This includes partial and free slip, and interactions near corners. The problem is investigated by using a two relaxation time lattice Boltzmann equation with moment-based boundary conditions. Navier-slip conditions, which involve gradients of the velocity, are formulated and applied locally. The implementation of free-slip conditions with the moment-based approach is discussed. Collision angles of 0°, 30°, and 45° are investigated. Stable simulations are shown for Reynolds numbers between 625 and 10 000 and various slip lengths. Vorticity generation on the wall is shown to be affected by slip length, angle of incidence,
... Show Moreفي هذا البحث نحاول تسليط الضوء على إحدى طرائق تقدير المعلمات الهيكلية لنماذج المعادلات الآنية الخطية والتي تزودنا بتقديرات متسقة تختلف أحيانا عن تلك التي نحصل عليها من أساليب الطرائق التقليدية الأخرى وفق الصيغة العامة لمقدرات K-CLASS. وهذه الطريقة تعرف بطريقة الإمكان الأعظم محدودة المعلومات "LIML" أو طريقة نسبة التباين الصغرى"LVR
... Show Moreالتعددية الثقافية هي مفهوم يتعلق بالمجتمعات التي تضم ثقافات عده، أو العالم الذي يتضمن ثقافات متنوعة؛ فالتعددية هي التنوع الثقافي والفكري؛ وبالتالي هي عنصر إثراء للإنسانية وأساس لوجودها؛ فالتعددية الثقافية تتضمن القبول بالثقافات والافكار الانسانية كلها، وإفساح المجال أمامها للمشاركة في بنا ء الثقافة والفكر العالمي؛ وهكذا فإنها تتمثل في التسامح مع الثقافات والافكار المختلفة الاعتراف بالهويات والخصوصيات
... Show MoreThe blade pitch angle (BPA) controller is key factor to improve the power generation of wind turbine (WT). Due to the aerodynamic structural behavior of the rotor blades, wind turbine system performance is influenced by pitch angle and environmental conditions such as wind speed, which fluctuate throughout the day. Therefore, to overcome the pitch angle control (PAC) problem, high wind speed conditions, and due to type-1 and type-2 fuzzy logic limitations for handling high levels of uncertainty, the newly proposed optimal hybrid type-3 fuzzy logic controller has been applied and compared since type-3 fuzzy controllers utilize three-dimensional membership functions, unlike type-2 and type-1 fuzzy logic controllers. In this paper six differen
... Show MoreThis study aims to test ceramic waste's capacity to remove nickel from aqueous solutions through adsorption. Ceramic wastes were collected from the Refractories Manufacturing Plant in Ramadi. Through a series of lab tests, the reaction time (5, 10, 15, 20, 25, 30, 35, 40, 45, and 50 minutes, and Ni concentrations (20, 40, 60, and 80) were tested using ceramic wastes with a solid to liquid ratio of 2g/30ml. At a temperature of 30ºC, the pH, total dissolved solids (TDS), and electrical conductivity (EC) were all measured. The equilibrium time was set at 30 min. Thereafter, the sorption (%) somewhat increased positively with the Ni concentration. Freundlich's equation showed that the adsorption intensity is 1.1827 and the Freundlich c
... Show MoreThe federal state is usually based on a number of regions because it is based on the multiplicity of political entities. The federal experiments were based on the existence of two or more regions and each federal system has its own peculiarities. Administrative authority between the federal government and local elected bodies of local people of absolute relative independence does not threaten the entity of the state according to the Constitution and the law and on a regional or reformer basis and exercise its powers within the legal scope prescribed The relationship between the federal authority and the Kurdistan region is the first level of the relationship on the real level, especially since no other region in Iraq has been formed exce
... Show MoreBackground: Irrigation has a central role in endodontic treatment. Several irrigating solutions have the antimicrobial activity and actively kill bacteria and yeasts when introduced in direct contact with the microorganisms. The purpose of this study was to evaluate the antimicrobial effectiveness of Dandelion (Taraxacum officinale) root and leaf extracts as possible irrigant solutions, used during endodontic treatments, and both were compared to Sodium hypochlorite, Propolis and Ethyl alcohol. Materials and Method: Forty seven human extracted single rooted teeth were selected. The teeth were decoronated using a diamond disk to have a length of 15 mm ±1 mm and they were instrumented using the hybrid technique. All roots were sterilized
... Show MoreAcademic achievement is a professional standard for measuring student levels in the first stages. Therefore, any indication of the level of achievement makes us in an attempt to employ students in evening schools. The researcher has developed a closed questionnaire of (36) paragraphs. A total of (164) male and (24) female students were chosen from evening schools. The result of this research revealed that the number of students was a reason for the low level of their achievement, the lack of laboratories, educational methods, and techniques of the most prominent problems confirmed by students in these schools. In addition, to support educational institutions with their necessary needs. The most important conclusion in this research is th
... Show More