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 develop the work of Ghawi on close dual Rickart modules and discuss y-closed dual Rickart modules with some properties. Then, we prove that, if are y-closed simple -modues and if -y-closed is a dual Rickart module, then either Hom ( ) =0 or . Also, we study the direct sum of y-closed dual Rickart modules.

Background:

Uno de los rasgos más interesantes sobre España es la diversidad de sus lenguas, y aunque la mayoría de los españoles hablan español, pero una gran parte de la población es bilingüe y en algunas ocasiones, trilingüe. Hoy en día estas lenguas se usan y conviven juntas sin grandes problemas, aunque durante mucho tiempo esta convivencia ha sido muy complicada. Asi que el propósito de nuestro trabajo es enfocar la luz sobre la situación linguística actual de España.
Al estudiar la situación linguística de España encontramos que las lenguas son instrumentos vivos y dinámicos, inseparables de su propia historia, dos realidades, su pasado y su presente, que van conformando su propia estructura y su propio dominio lingüísti

Comparative literature is one of the important research topics in finding new relations and results that other types of studies do not allow.

The present research is a comparative study between two contemporary poets : Al-Sayyab and Prévert. The reason for accomplishing this research is Al-Sayyab’s reading for the western literature. Moreover, the study sheds a light on translational criticism.

It tackles the lives of the two writers and their points of similarities and differences. Prévert and Al-Sayyab’s are two modern poets. The first employed his daily routines to express reality, specially the events of the two world wars. The second’s pain, on the other hand, was the starting point to express others’ suffe

Worldwide attention is being focused on  nanocrystalline  zeolites  and they are replacing conventional ones due to their pronounced potential in many fields. In this study, NaY zeolite has been prepared hydrothermally using sol –gel method and modified to the proton type by ion –exchange process. Characterization is made using X-ray diffraction (XRD), thermogravimetric analysis (TGA),  Fourier transform infrared spectroscopy (FTIR),  Atomic force microscopy (AFM), Brunauer –Emmet- Teller (BET) nitrogen adsorption method, Ammonia Temperature programmed desorption (NH₃-TPD) and Scanning electron microscopy( SEM).  The effect of aging time, silica to alumina ratio is studied and the results sh

L'œuvre de fiction la plus ancienne qui nous soit restée, est aussi bien la première jamais écrite. L'épopée de Gilgamesh a été composée à l'aube de la civilisation mésopotamienne. Gilgamesh était le cinquième souverain après le déluge.

                      Sous son règne, trois millénaires environ avant Jésus-Christ, les Urukiens s’emparèrent des cités voisines, et formèrent ainsi ce que nous appellerions une petite nation. Pendant plus de deux mille ans, les civilisations du Proche-Orient ont fait de Gilgamesh leur héros épique. Il existe des

Let R be a commutative ring with identity and let M be a unital left Rmodule.
Goodearl introduced the following concept :A submodule A of an R –
module M is an y – closed submodule of M if is nonsingular.In this paper we
introduced an y – closed injective modules andchain condition on y – closed
submodules.

L'écrivaine française Marguerite Duras, née en Indochine en 1914, est considérée comme l'un des écrivains dont les œuvres se distinguent par la nouveauté. Cela lui accorde une grande renommée depuis le début de ses écrits. Il est vrai que Duras n’était pas une théoricienne, mais certains l'a mise avec les romanciers du Nouveau Roman comme Alain Robbe-Grillet, Nathalie Sarraute et Michel Butor. D’autres critiques l’étudient  en fonction de la modernité qui caractérise ses œuvres littéraires.

Cette recherche étudie la réception des œuvres littéraires de Marguerite Duras en Irak. L'étude comprend une introduction au roman en Irak : ses ressources, son développement, et l'effet du roman étrang

         The understanding exchange rate policy is fundamental in order to identify the mechanism by which works out macroeconomic, And the vital for macroeconomic analysis and empirical work to differentiate between the de facto regimes and de jure regimes, Where the proved surveys and studies issued by the international monetary fund that there is divergence between the de facto regime (Regime of exchange applied by the country actually) and between the de jure regime (Regime de jure through the documents and formal writings of officials of the central bank), And launched studies on the de facto regime (Being a the basis of evaluating monetary policy) Stabilized (peg-like)arrangements or