Let  be a commutative ring with 1 and  be a left unitary . In this paper, the generalizations for the notions of compressible module and  retractable module are given.

An   is termed to be  semi-essentially compressible if   can be embedded in every of a non-zero semi-essential submodules. An  is termed a semi-essentially retractable module, if   for every non-zero semi-essentially submodule of an . Some of their advantages characterizations and examples are given.  We also study the relation between these classes and some other classes of modules.

The optimum separators operating pressure is determined by using flash calculations and equilibrium ratios. In this study, the optimum separator size for Jambur field is calculated by using equations introduced by Arnold and Stewart and API12J Specification [1]. Because Jambur field has a high production rate two conditions are taken in the study to determine separator size, first based on production rate 80,000 bbl/day and second based on split the production between two banks A and B (40,000 bbl/day for each bank). The calculation resulted in optimum separator pressure for the first stage of 700 psi, and the second stage of 300 psi, and the third stage of 120 psi. The results show that as the number of stages increased above three

     The research aims to monitor environmental changes and study the state of desertification in the northeastern part of the Al-Najaf province, Iraq. The study area suffers from desertification and drought phenomena. Remote sensing systems "RS" and geographic information systems "GIS" are essential for monitoring environmental changes because they provide Earth observation satellites that contribute to detecting environmental changes. Two Sentinel 2 images were acquired on December 26, 2015, and November 29, 2021. The images were combined and used for indices calculations. Normalized vegetation difference index "NDVI,” Normalized difference index "NDWI," soil exposure index "BSI," and Normalized difference index "NDBI." The resul

The present study was designed to synthesize a number of new Ceftriaxone derivatives by its involvement with a series of different amines, through the chemical derivatization of its 2-aminothiazolyl- group into an amide with chloroacetyl chloride, which on further conjugation with these selected amines will produce compounds with pharmacological effects that may extend the antimicrobial activity of the parent compound depending on the nature of these moieties.

Ceftriaxone was first equipped with a spacer arm (linker) by the action of chloroacetyl chloride in aqueous medium and then further reacted with seven different aliphatic and aromatic amines which resulted in the production of the aimed final target products. The syntheses

Introduction: The study was intended for Roseomonas gilardii NTCC 13290 strain pigment extraction and characterization. Methodology: The pigment-producing bacterial were cultured on Columbia blood agar and nutrient media agar. Then the pigments were extracted by ethanol. The candidate pigment was further characterized by different biotechnological techniques: UV-Vis spectroscopy, FT-IR to analyze the functional group of the targeted pigment, and TLC media. Results: The cultivation of Roseomonas gilardii on media showed pink color and nearly runny texture. The bacterial colonies were microscopically gram stained and examined, the R. gilardii was seen as coccobacillus colonies that mostly form pairs arranged as short chains. The R. gilardii b

In this paper, we investigate and characterize the effects of multi-channel and rendezvous protocols on the connectivity of dynamic spectrum access networks using percolation theory. In particular, we focus on the scenario where the secondary nodes have plenty of vacant channels to choose from a phenomenon which we define as channel abundance. To cope with the existence of multi-channel, we use two types of rendezvous protocols: naive ones which do not guarantee a common channel and advanced ones which do. We show that, with more channel abundance, even with the use of either type of rendezvous protocols, it becomes difficult for two nodes to agree on a common channel, thereby, potentially remaining invisible to each other. We model this in

     A complex number  is called an extended eigenvalue for an operator  on a Hilbert space H if there exists a nonzero operator  such that: such  is called an extended eigenoperator corresponding to. The goal of this paper is to calculate extended eigenvalues and extended eigenoperators for the weighted unilateral (Forward   and Backward) shift operators. We also find an extended eigenvalues for weighted bilateral shift operator. Moreover, the closedness of extended eigenvalues for the weighted unilateral (Forward and Backward) shift operators under multiplication is proven.

After the persistence of the British policy of oppression and control over the American colonies and the attempts to obliterate the identity of their inhabitants, the colonies worked on moving forward towards achieving independence, and Virginia was the first to initiate the development of the new government frameworks, through George Mason in drafting the Virginia Bill of Rights in 1776, which expressed the philosophy of the era Enlightenment and independent revolutionary thought, which called for equality and natural rights for individuals and the need for a free popular government that works for the common good.

   In this paper, we introduce new classes of sets called g *sD -sets , g *sD −α -sets , g *spreD − sets , g *sbD − -sets and g *sD −β -sets . Also, we study some of their properties and relations among them . Moreover, we use these sets to define and study some associative separation axioms .