In this paper we study the concepts of δ-small M-projective module and δ-small M-pseudo projective Modules as a generalization of M-projective module and M-Pseudo Projective respectively and give some results.

In this paper, we will give another class of normal operator which is (K-N)*
quasi-n-normal operator in Hilbert space, and give some properties of this concept
as well as discussion the relation between this class with another class of normal
operators.

The title compound was synthesized by 2:1 condensation between adamantan-1-ylamine and benzene-1,4- dicarbaldehyde in n-BuOH and produced a good yield 87% of new bis Schiff base. The compound skeleton was affirmed by FTIR, ¹H NMR, LC-MS, and X-ray powder diffraction. The structure was solved by a parallel tempering process and refined by using Rietveld refinement. Two adamantan-1-ylimino groups are connected in the anti-positions to the planar central 1,4-dimethylbenzene group. All rings of the adamantyl group possess normal chair conformation.

The concepts of generalized higher derivations, Jordan generalized higher derivations, and Jordan generalized triple higher derivations on Γ-ring M into ΓM-modules X are presented. We prove that every Jordan generalized higher derivation of Γ-ring M into 2-torsion free ΓM-module X, such that aαbβc=aβbαc, for all a, b, c M and α,βΓ, is Jordan generalized triple higher derivation of M into X.

Background: Apicoectomy and retrograde filling is indicated when conventional endodontic treatment is impossible or failed to achieve apical seal. The aim of this study was to evaluate the effect of ER: YAG laser on apical microleakage. Materials and Methods: Sixty extracted single-rooted teeth were used in this study. The roots were divided into six groups. Group 1: apicoectomy by fissure bur, and apical cavities prepared by round bur, then cavities were filled with MTA. Group 2: the roots preparations and fillings were the same as group 1, then the apical areas were treated by Er:YAG Laser. Group 3: apicoectomy by fissure bur, and apical cavities prepared by ultrasound retrotip and cavities were filled with MTA. Group 4: the roots prepara

(disputed areas) before the establishment of the national government in Iraq in 1921, had to search for Arab tribes and clans in which the recipe group is available as a social organization coherent based on the foundations of several of them tribalism and her Land relates know Deira in those areas during the period that preceded the establishment of the national government in Iraq in 1921, and based on the inter girls primary sources and published mostly before the establishment of the national government in Iraq, the source of their information search and direct inquiry.
Research has proved that the tribes and clans of Arab exist in all districts described by (disputed), except (judicial Akre and Tilkaif) and varying degrees of time

The present work includes the preparation and characterization of{Co(II) , Ni(II), Pd(II), Fe(III) , Ru(III),Rh(III), Os(III) , Ir(III) , Pt(IV) and VO(IV)}complexes of a new ligand 4-[(1-phenyl-2,3-dimethyl-3-pyrozoline-5-one)azo]-N,N-dimethylanline (PAD). The product (PAD) was isolated,studies and characterized by phsical measurements,i.e., (FT-IR), (UV) Spectroscopy and elemental analysis(C.H.N). The prepared complexes were identified and their structural geometric were suggested in solid state by using flame atomic absorption, elemental analysis(C.H.N), (FT-IR) and (UV-Vis) Spectroscopy, as well as magnetic susceptibility and conductivity measurements . The study of the nature of the complexes formed in( ethanolic solution) following t

Suppose that  is a finite group and  is a non-empty subset of  such that  and . Suppose that  is the Cayley graph whose vertices are all elements of  and two vertices  and  are adjacent if and only if . In this paper, we introduce the generalized Cayley graph denoted by  that  is a graph with vertex set consists of all column matrices  which all components are in  and two vertices  and  are adjacent if and only if , where  is a column matrix that each entry is the inverse of similar entry of  and  is  matrix with all entries in  ,  is the transpose of  and . In this paper, we clarify some basic properties of the new graph and assign the structure of  when  is complete graph , complete bipartite graph  and complete

A new Mannich base ligand was prepared by reacting the 2-chloro.-N-(5-mercapto-1, 3, 4-thiadazol -2-yl) acetamide and Piperidine in the presence (formaldehyde) (L) ligand. A series of ligand complexes were prepared from (L) with the metal ion Co (II), Ni (II), Cu (II), Pd (II), Pt (IV), and Au (III). Various spectroscopic techniques such as C.H.N.S, FTIR, UV-VIS, , ¹HNMR, ¹³CNMR, Magnetic moment, and molar conductivity successfully characterize the obtained compounds. The M: L ratio was determined using the molar ratio method in solution. All prepared compounds' antibacterial and antifungal activity was studied against two types of bacteria and one type of fungi at a rate of 0.02M. The standard ΔH°