In this paper, we proved that if R is a prime ring, U be a nonzero Lie ideal of R , d be a nonzero (?,?)-derivation of R. Then if Ua?Z(R) (or aU?Z(R)) for a?R, then either or U is commutative Also, we assumed that Uis a ring to prove that: (i) If Ua?Z(R) (or aU?Z(R)) for a?R, then either a=0 or U is commutative. (ii) If ad(U)=0 (or d(U)a=0) for a?R, then either a=0 or U is commutative. (iii) If d is a homomorphism on U such that ad(U) ?Z(R)(or d(U)a?Z(R), then a=0 or U is commutative.

An efficient combination of Adomian Decomposition iterative technique coupled Elzaki transformation (ETADM) for solving Telegraph equation and Riccati non-linear differential equation (RNDE) is introduced in a novel way to get an accurate analytical solution. An elegant combination of the Elzaki transform, the series expansion method, and the Adomian polynomial. The suggested method will convert differential equations into iterative algebraic equations, thus reducing processing and analytical work. The technique solves the problem of calculating the Adomian polynomials. The method’s efficiency was investigated using some numerical instances, and the findings demonstrate that it is easier to use than many other numerical procedures. It has

The major aim of this work is to propose a novel method, the Variation Iteration Adomain Decomposition Method (VIADM), an iterative semi-analytical method to achieve an approximate analytical solution for nonlinear (Volterra / Fredholm) integral equations. This technique depends on applying the Adomain Decomposition Method (ADM) to a nonlinear term that can be solved using Adomain polynomials. The VIADM has been used to break down the Volterra integral equation solution into infinite components. Furthermore, some illustrative examples are given, and the results obtained indicate the proposed method’s accuracy, efficiency, and reliability.

A study of taxonomic quality of algae attaching Three concert bridges built on the Tigris River within city of Baghdad including Al-Jadriyah Bridge in Al-Jadriyah area and the Bab Al-Mu'adam Bridge in Al-Shalajiya area, while the third site included Al-Muthanna Bridge in north of Baghdad city, for the period from Autumn 2021 and Winter 2022. The study identified 114 species of 32 Genus in which the predominance of Bacillariophceae (74 species, 14 Genus) Followed by Cyanophyceae (30species, 12 Genus) and 10 species (6 Genus) of Chlorophyceae. The study showed an increase in species of Bacillariophceae, Cyanophyceae which has the ability to secretion gelatinous substances that enable it to stick to solid stand, the number of the larges

The research of three-based financial indicators to create value for shareholders, have been identified research problem in a number of the questions revolved around the extent to which it can express its based performance metrics to create value for the essence and the reality of the surveyed enterprises performance, Can the departments surveyed companies to choose the scale or the most harmonizing index and an expression of the actual performance of the company, has the goal of research is to diagnose the strengths and weaknesses in the performance of the surveyed enterprises through the use of a number of based on the concept of creating economic value and the search for the most suitable indicator to the reality of the perfor

The tetradentate N2O2 Schiff base ligand, which is produced via the condensation reaction of 2-hydroxynaphthaldehyde with phthalohydrazide, is prepared in this work with a fair yield. The prepared ligand was characterized using a microanalysis technique (C.H.N), UV-vis, FTIR, 1H-,13C-NMR, mass spectrometry, and thermal gravimetric analysis (TGA). New complexes were synthesized by a reaction between ligand (N'1E,N'2Z)-N'1,N'2-bis((1-hydroxynaphthalen-2yl)methylene)phthalohydrazide and metal chloride of Co+2, Ni+2, and Zn+2 ions in absolute ethanol. The present complexes are also characterized by techniques such as C.H.N, UV-vis, FTIR, TGA, molar conductivity, atomic absorption, and magnetic moment measurements. The in vitro antimicro

          يهدف البحث لمحاولة دراسة واقع ادارة الوقت لدى عينه من  رؤوساء الأقسام العلمية في كليات ومعاهد هيئة التعليم التقني اذ بلغ حجم العينة (47% )  فرداً  تم احتيارهم عشوائياً من (15) كلية ومعهد موزعة في (69 من محافظات القطر  وبلغ حجم عينة البحث (17%) من عدد رؤوساء الاقسام العلمية في الهيئة ،  ولغرض جمع البيانات تم  أعداد استمارة استبيان تمت صياغتها بشكل يؤمن توثيق الوقت الفعل

Problem: Find dimensions of the problem by answering the following question: what the effect of using the Six Thinking Hats strategy to acquire the historical concepts and retain the fourth-grade students in the subject of literary history. Importance of research: current research is gaining importance in many ways, including: 1. Keep pace with the new in the field of education and modern educational strategies. 2. Shed light on innovative education strategy in the teaching of history, which is one of the materials that need to renew the tragedy of instruction methods for students. 3. Out of the monotony and traditional way of teaching to a method and a new strategy to develop the teacher and the learners thinking skills through various