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:

Applying grammatical rules of foreign languages regarding Time and Aspect to the Arabic language caused several problems, one of which led Orientalists to annul temporality in the Arabic language and consider it a language of aspectuality. This criterion has many fallacies, since each language differs from the other according to the syntactic and morphological norms, even in the structuring of the verbal system of each of them.

Si Alfonso x el sabio y la Escuela de Traductores de Toledo habia hecho del castellana una lengua apta para la expresión cientifica, fue Pablo Neruda quien aplicó su sentido artistico para crear una poesia amorosa de caracter lileraria. Por lo tanto, pocos poetas han llegado ton populares come. Pablo Neruda, en el mismg tiempo: se comsidera esccitor de una abundante producción literaria ne sólo en su ciudad natal de (Chile), Sino ha sida uno de los padres de la poesia hispanoamericana contemporónea. Ademas la influencia que ejerció en el grupo de poetas de la Generación del 27, con los que empezó a relacionarse durante su estancia en Madrid, fue decisiva también para la poesia espańola. Esa era la razon principal que me hizo pe

News headlines are key elements in spreading news. They are unique texts written in a special language which enables readers understand the overall nature and importance of the topic. However, this special language causes difficulty for readers in understanding the headline. To illuminate this difficulty, it is argued that a pragmatic analysis from a speech act theory perspective is a plausible tool for a headline analysis. The main objective of the study is to pragmatically analyze the most frequently employed types of speech acts in the news headlines covering COVID-19 in Aljazeera English website. To this end, Bach and Harnish's (1979) Taxonomy of Speech Acts has been adopted to analyze the data. Thirty headlines have been collected f

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

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.

El español es una lengua hablada por una ingente comunidad que abarca varios cientos de millones de personas. Son muchas las palabras con distintos significados que se escriben de similar manera. Hablamos, por ejemplo, de dos de ellas: el adjetivo solo y el adverbio sólo.

En este trabajo se plantea un estudio del adverbio sólo, palabra invariable cuya función consiste en (complementar la significación del verbo) y solo es un adjetivo (califica a un sustantivo).¿Cómo diferenciarlas para evitar errores ortográficos? Así, en estos casos (solo/ sólo), la distinción la da la tilde en la primera vocal. Ésta es la

Simple, sensitive and accurate two methods were described for the determination of terazosin. The spectrophotometric method (A) is based on measuring the spectral absorption of the ion-pair complex formed between terazosin with eosin Y in the acetate buffer medium pH 3 at 545 nm. Method (B) is based on the quantitative quenching effect of terazosin on the native fluorescence of Eosin Y at the pH 3. The quenching of the fluorescence of Eosin Y was measured at 556 nm after excitation at 345 nm. The two methods obeyed Beer’s law over the concentration ranges of 0.1-8 and 0.05-7 µg/mL for method A and B respectively. Both methods succeeded in the determination of terazosin in its tablets