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

The study evaluated endophytic communities associated with five oil-bearing plants, including sesame, corn, sunflower, olives and castor, which were collected from Baghdad and Diyala (Iraq), evaluated their oil production capacity and identified metabolites from the lipid fraction. Out of 151 isolates were collected from 21 taxa. Aspergillus niger showed the highest frequency (6.62 %), while the genera Aspergillus and Fusarium were the most dominant endophytes. The highest oil yield was identified and recorded in Aspergillus terreus (24.12 %). While the lowest oil yield was observed in Sclerotinia spp. (3.96 %). Gas chromatography-mass spectrometry (GC-MS) analysis of A. terreus revealed a profile dominated by pentadecyl acrylate (2

Consuming of by-product or waste materials in highway engineering is significant in the construction of new roads and/or in renovations of the existing ones. Pulverised Fuel ash (PFA), which is a by-product material of burning coal in power stations, is one of these materials that might be incorporated instead of mineral filler in hot asphalt mixtures.

Two types of surface course mixtures have been prepared one with conventional mineral filler i.e. ordinary Portland cement (OPC) while the second was with PFA. Several testings have been conducted to indicate the mechanical properties which were Marshall Stability and Indirect Tensile Strength tests. On the other hand, moisture damage and ageing have been evaluated

This paper predicts the resilient modulus (Mr) for warm mix asphalt (WMA) mixtures prepared using aspha-min. Various predictor variables were analyzed, including asphalt cement types, asphalt contents, nominal maximum aggregate sizes (NMAS), filler content, test temperatures, and loading times. Univariate and multivariate analyses were conducted to examine the behavior of each predictor variable individually and collectively. Through univariate analysis, it was observed that Mr exhibited an inverse trend with asphalt cement grade, NMAS, test temperature, and load duration. Although Mr increased slightly with higher filler and asphalt content, the magnitude of this increase was minimal. Multivariate analysis revealed that the rate of change

The current Iraqi standard specifications for roads and bridges allowed the prepared Job-Mix Formula for asphalt mixtures to witness some tolerances with regard to the following: coarse aggregate gradation by ± 6.0 %, fine aggregate gradation by ± 4.0 %, filler gradation by ± 2.0 %, asphalt cement content by ± 0.3 % and mixing temperature by ± 15 ^oC. The objective of this work is to evaluate the behavior of asphalt mixtures prepared by different aggregates gradations (12.5 mm nominal maximum size) that fabricated by several asphalt contents (40-50 grade) and various mixing temperature. All the tolerances specified in the specifications are taken into account, furthermore, the zones beyond these tolerances

Accurate predictive tools for VLE calculation are always needed. A new method is introduced for VLE calculation which is very simple to apply with very good results compared with previously used methods. It does not need any physical property except each binary system need tow constants only. Also, this method can be applied to calculate VLE data for any binary system at any polarity or from any group family. But the system binary should not confirm an azeotrope. This new method is expanding in application to cover a range of temperature. This expansion does not need anything except the application of the new proposed form with the system of two constants. This method with its development is applied to 56 binary mixtures with 1120 equili

The durability of asphalt pavement is associated with the properties and performance of the binder. This work-study intended to understand the impact of blending Styrene-Butadiene-Styrene (SBS) to conventional asphalt concrete mixtures and calculating the Optimum Asphalt Content (OAC) for conventional mixture also; compare the performance between SBS modified with the conventional mixture. Two different kinds of asphalt penetration grades, A.C. (40-50) and A.C. (60-70), were improved with 2.5 and 3.5% SBS polymer, respectively. Marshall properties were determined in this work. Optimum Asphalt Content (OAC) was 4.93 and 5.1% by weight of mixture for A.C. (40-50) and (60-70), respectively. Marshall properties results show an increasem

Rutting is a crucial element of the mechanical performance characteristics of asphalt mixtures, which was the primary target of this study. The task involved substituting various portions of virgin coarse aggregate with recycled concrete aggregate materials that had been treated or left untreated at rates ranging from 25 to 100%, with a constant increase of 25%. The treatment process of recycled concrete aggregate involved soaking in acetic acid, followed by a mechanical process for a short time inside a Los Angeles machine without the balls. This research utilized two primary tests: the standard Marshall test to identify the optimal asphalt contents and the volumetric characteristics of asphalt mixtures. The other one w

Abstract :

      The research aims to Estimate the Strength of Strategic Innovation application in terms of application strength , and on the overall level in number of Iraqi Industrial business organizations . After wards determine whether their is differerences among those organizations in application process for the dimensions , and for the overall process .

      The Research revealed number of conclusions including that the process of strategic innovation is applied in a good Level , and demonstrates the desier of the industrial companies Leaders to Launch beyond the familiar products , and to provide new products that