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.

El Quijote no es sólo una novela para leer. Es también un acontecimiento
celebrado en todos los medios de expresión artísticos y literarios: la poesía, el
ensayo, la ilustración, la pintura, la escultura, las artes decorativas, la iconografía
popular, el humor.
Las figuras de Don Quijote y Sancho Panza, como arquetipos que entran a
formar parte de la vida cotidiana de las gentes, aparecen representados en miles de
cuadros, grabados, esculturas y tapices. El cine, el ballet y la ópera han sido y
siguen siendo espectáculos de acogida para nuestros personales. No faltan las obras
musicales que se inspiran en ellos y sus figuras aparecen representadas en objetos
tan variados como utensilios de cocina, vest

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.

Este breve estudio expone algunas erratas gramaticales y semánticas en dos versiones árabes de la novela El amor en los tiempos de cólera del gran novelista colombiano Gabriel García Márquez, las dos versiones árabes son: la versión 1 (por el traductor Saleh Almani) y la versión 2 (por el traductor Ahmed Magdi). Identifica estas erratas explicando cada caso de ambas versiones. Además determinar la versión más aceptable y satisfactoria

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

Le professeur Taranne et La non-Communication

     Suppose that F is a reciprocal ring which has a unity and suppose that H is an F-module. We topologize La-Prim(H), the set of all primary La-submodules of H , similar to that for FPrim(F), the spectrum of fuzzy primary ideals of F, and examine the characteristics of this topological space. Particularly, we will research the relation between La-Prim(H) and La-Prim(F/ Ann(H)) and get some results.

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.

       This paper aims at providing the teaching staff members with the necessary skills so as to become capable of tackling various situations, and treating daily problems that face students learning Spanish as a Second Language.  This is made as an attempt to make teachers of foreign languages in general acquainted with modern trends of teaching with less complicated methods, specifically in teaching e earlier stages of foreign languages.

Abstracto:

      En el presente trabajo pretendemos dotar al docente no nativo de Lenguas extranjeras, con algunos de los métodos necesari

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