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.

In this paper we prove the boundedness of the solutions and their derivatives of the second order ordinary differential equation x ?+f(x) x ?+g(x)=u(t), under certain conditions on f,g and u. Our results are generalization of those given in [1].

This research deals with the relationship between television advertising and buying random cosmetics, where we find that TV ads influence on the purchasing behavior of women, has conducted research in the field on a sample of women in the University of Baghdad, was a random sample taken from 150 different women in the age and social levels educational and cultural students and employees and teachers in order to sample representative be for the research community, and designed a questionnaire for this purpose form as a tool to collect data and information search and analyzed they answered the sample surveyed using a statistical program (spss) to extract percentages And correlation coefficients and testing square Kay , The study found Of w

Abstract

Electrical magnate  was designed and constructed,  the optimum Magnetic flux  and the effect of time on the physical properties of the alkaline (magnetic water) produced from the bottled drinking water [the total dissolved solids (TDS) or the electrical conductivity, and pH] were studied, to simulate ZamZam water in Mekka Saudi Arabia. Also, the efficiency of magnetic field from this designed electrical magnate in decreasing the TDS of sea water (of 1500 ppm NaCl Content), to convert it to water suitable for irrigation (TDS<1000 ppm) was investigated in this work.The results show that the magnetic flux from our designed electrical magnate in the range of (0.013- 0.08) Tesla and 30 minut

Praise be to God, Lord of the Worlds, and prayers and peace be upon the Master of Messengers and his family and companions.

The study of the jurisprudential opinions of scholars, their choices, or their weightings, sheds light on the approach they followed in their choices, and reveals the originality of the scholar or his influence on those who preceded him from among the scholars.

And the commentators of the noble hadith of the Prophet have their important contributions in this aspect, as they undertake the task of explaining the noble hadith, the second source of legislation

Contemporary commentators have their share in the service of the honorable hadith, and the statement of their choices and preferences, and am

Background: Waterpipe tobacco smoking has become common especially among young people, Waterpipe smoking misconcepted as a safer mean of smoking, so in this study we will highlight the effect of Waterpipe smoking ‎on periodontal and oral health.‎ Materials and method. The selected ‎‎‎100 male subjects of 30-40 years, ‎categorized into 4 groups (each group ‎‎25 subject): Waterpipe smoker ‎with ‎healthy periodontium, ‎Waterpipe smoker ‎‎with chronic periodontitis, Non-‎‎smoker ‎with healthy periodontium and Non-smoker ‎with chronic periodontitis. Whole ‎unstimulated ‎saliva was collected. Clinical measurements: plaque ‎index

This research has presented a solution to the problem faced by alloys: the corrosion problem, by reducing corrosion and enhancing protection by using an inhibitor (Schiff base). The inhibitor (Schiff base) was synthesized by reacting of the substrates materials (4-dimethylaminobenzaldehyde and 4-aminoantipyrine). It was diagnosed by infrared technology IR, where the IR spectrum and through the visible beams proved that the Schiff base was well formed and with high purity. The corrosion behavior of carbon steel and stainless steel in a saline medium (artificial seawater 3.5%NaCl) before and after using the inhibitor at four temperatures: 20, 30, 40, and 50 C° was studied by using three electrodes potentiostat. The corrosion behavior was

Anadara granosa is a species of the class bivalve commonly found on the east coast of South Sumatra as a fishery commodity. This species has not been widely studied as a source of new bioactive compounds that have antioxidant abilities. This study aims to analyze the antioxidant ability of A. granosa against DPPH radicals and its phytochemical profile qualitatively. Samples were taken at the fishing port of Sungsang Village, South Sumatra, Indonesia. Furthermore, the samples were extracted using ethanol as a solvent and tested for antioxidants against DPPH radicals, total phenol analysis, and preliminary phytochemical test. Based on the antioxidant test results, the IC₅₀ value of the ethanolic extract of

ABSTRACT Backgrounds: Maxillary canine impaction is complicated and time consuming to treat, for being highly diverse in inclination and location; it may be a companied by root resorption of the neighboring teeth. CBCT has been used for its' diagnostic reliability in localization of impacted canine and revealing its' serious local complications. Objectives: Localization of maxillary impacted canine using cone beam computed tomography for assessment of angulation, distance from occlusal plane, alveolar width and proximity to adjacent teeth. Subjects and Methods: The study sample was 33 subjects 16 females and 17 males attended to Al-Wasitti general hospital in Baghdad city-Oral and maxillofacial radiology department for CBCT scan investigati

In this paper, we study the growth of solutions of the second order linear complex differential equations  insuring that any nontrivial solutions are of infinite order. It is assumed that the coefficients satisfy the extremal condition for Yang’s inequality and the extremal condition for Denjoy’s conjecture. The other condition is that one of the coefficients itself is a solution of the differential equation .