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.

Pure nano Ferro fluid was synthesized by chemical co-precipitation method. The composite of polyaniline with nano sized Ferro fluid was prepared by In-situ–chemical oxidation polymerization method with ammonium per sulphate as an oxidant in aqueous hydrochloric acid under constant stirring at room temperature. The optical properties, absorption, transmission, optical energy gap (Eg) and optical constant refractive index (n) have been investigated. The value of the Eg decreased with increasing Ferro fluid concentration.

Among the different passive techniques heat pipe heat exchanger (HPHE) seems to be the most effective one for energy saving in heating ventilation and air conditioning system (HVAC). The applications for nanofluids with high conductivity are favorable to increase the thermal performance in HPHE. Even though the nanofluid has the higher heat conduction coefficient that dispels more heat theoretically but the higher concentration will make clustering .Clustering is a problem that must be solved before nanofluids can be considered for long-term practical uses. Results showed that the maximum value of relative power is 0.13 mW at nanofluid compared with other concentrations due to the low density of nanofluid at this concentration. For highe

Alloys of GaxSb1-x system with different Ga concentration (x=0.4, 0.5, 0.6) have been prepared in evacuated quartz tubes. The structure of the alloys were examined by X-ray diffraction analysis (XRD) and found to be polycrystalline of zincblend structure with strong crystalline orientation (220). Thin films of GaxSb1-x system of about 1.0 μm thickness have been deposited by flash evaporation method on glass substrate at 473K substrate temperature (Ts) and under pressure 10-6 mbar. This study concentrated on the effect of Ga concentration (x) on some physical properties of GaxSb1-x thin films such as structural and optical properties. The structure of prepared films for various values of x was polycrystalline. The X-ray diffraction analy

The research aims to apply one of the techniques of management accounting, which is the technique of the quality function deployment on the men's leather shoe product Model (79043) in the General Company for Textile and Leather Industries by determining the basic requirements of the customer and then designing the characteristics and specifications of the product according to the preferences of the customer in order to respond to the customer's voice in agreement With the characteristics and technical characteristics of the product, taking into account the products of the competing companies to achieve the maximum customer satisfaction, the highest quality and the lowest costs. Hence, the importance of research has emerged, which indicat

يحتل موضوع الاستهلاك اهمية كبيرة في الدراسات الاقتصادية في حالتي السلم والحرب وذلك لارتباط هذا الموضوع بالانسان والمجتمع ولكونه احد مؤشرات مستوى الرفاهية الاقتصادية والاجتماعية وتزداد اهمية ضبط حركة هذا المتغير السلوكي والكمي في زمن الحرب اكثر مما هو عليه في حالة السلم، في هذا البحث تم استخدام بيانات احصائية عن الانفاق الاستهلاكي الخاص ونصيب الفرد من الدخل القومي اضافة الى الرقم القياسي لاسعار المس

This research studies the effect of addition of some nanoparticles
(MgO, CuO) and grain size (30,40nm) on some physical properties
(impact strength, hardness and thermal conductivity) for a matrix
blend of epoxy resin with SBR rubber. Hand –Lay up method was
used to prepare the samples. All samples were immersed in water for
9 weeks.
The Results showed decreased in the values of impact strength and
hardness but increased the coefficient of thermal conductivity.

There are many problems facing the economic entities  as a result of its mass production &variation of its products  , the matter which had  increased the need & importance of cost accounting which is regarded a main tool for the managerial control.

The actual costing system is unable to meet the contemporary management needs ,so the Standard costing system appear to provide the management  with required information to perform its functions by the best use& way.

This research aims to determine  the standard cost for the  direct material for oil extraction activity by applying it in the north oil company.