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.

في 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

Objective: Evaluation of the poly ether keton keton polymer (PEKK) coating material on the commercial pure titanium disks (CP Ti) with or without laser surface structuring. Design: In vitro experimental study of PEKK polymer coated material on the CP Ti disks with or without laser surface structuring. Materials and methods: coating the surface of the commercial pure titanium (CP Ti) disks with PEKK polymer was performed via using frictional mode CO2 laser, then the samples disks analyzed by using FESEM. Results: the FESEM reveal good adherence and distribution of the PEKK coated material over the CP Ti substrate by using the frictional mode CO2 laser at 2 watt and 6 ms pulse duration. Conclusion: the frictional mode CO2 laser considered an

This study was aimed to director wheat production's technical efficiency grown under two irrigation systems(fixed and pivot sprinkler irrigation systems)using random border analysis.Samples were collected randomly from267farmers from Salah Al-Din Governorate/Iraq.The samples were divided into two groups;187farmers used a pivot sprinkler irrigation system with three categories of possession(80,60and120dunums),while the other group used a fixed sprinkler irrigation system with four categories of possession(40,30,20and10dunums).Transcendent production function was used to study the effect of production factors on wheat yield. The results indicated that the mechanization work and the amount of added irrigation water increased by 1% whil

Buckling analysis of a laminated composite thin plate with different boundary conditions subjected to in-plane uniform load are studied depending on classical laminated plate theory; analytically using (Rayleigh-Ritz method). Equation of motion of the plates was derived using the principle of virtual work and solved using modified Fourier displacement function that satisfies general edge conditions. The eigenvalue problem generated by using Ritz method, the set of linear algebraic equations can be solved using MATLAB for symmetric and anti-symmetric, cross and angle-ply laminated plate considering some design parameters such as aspect ratios, number of layers, lamination type and orthotropic ratio. The results obtained g

In the present work, the behavior of thick-walled cylinder of elasto-plastic material (polymeric material) has been studied analytically. The study is based on modified Von-Mises yield criterion (for non metallic material). The equations of stress distribution are obtained for the cylinder under general cases of elastic expansion, plastic initiation and elastic-plastic expansion.

        A computer program is developed for evaluating the stress distribution. The solution is carried out for worst boundary conditions when the cylinder is subjected to the combination of pressure load, inertia load, and temperature gradient.

        The results are presente

An atomic force microscope (AFM) technique is utilized to investigate the polystyrene (PS) impact upon the morphological properties of the outer as well as inner surface of poly vinyl chloride (PVC) porous fibers. Noticeable a new shape of the nodules at the outer and inner surfaces, namely "Crater nodules", has been observed. The fibers surface images have seen to be regular nodular texture at the skin of the inner and outer surfaces at low PS content. At PS content of 6 wt.%, the nodules structure was varied from Crater shape to stripe. While with increasing of PS content, the pore density reduces as a result of increasing the size of the pore at the fiber surface. Moreover, the test of 3D-AFM images shows that the roughness of both su

The analysis of the root cause techniques is a reasonable option to be made to assess the root causes of the funding of construction projects. There are a variety of issues related to financing in construction industries in Iraq. The root,cause analysis is the impact of security and social conditions on financial funding. Variety tools of root cause analysis have originated from literature, as common methods for the detection of root causes. The purpose of this study was to identify and diagnose causes that lead to obstruction of financial funding in the construction projects in the republic of Iraq from the contractors' point of view and their interaction with a number of variables. The study diagnosed nine causes of fi

Recording an Electromyogram (EMG) signal is essential for diagnostic procedures like muscle health assessment and motor neurons control. The EMG signals have been used as a source of control for powered prosthetics to support people to accomplish their activities of daily living (ADLs). This work deals with studying different types of hand grips and finding their relationship with EMG activity. Five subjects carried out four functional movements (fine pinch, tripod grip and grip with the middle and thumb finger, as well as the power grip). Hand dynamometer has been used to record the EMG activity from three muscles namely; Flexor Carpi Radialis (FCR), Flexor Digitorum Superficialis (FDS), and Abductor Pollicis Brevis (ABP) with different le