Assume that G ≅ HN the Harada–Norton group. In this paper, effective investment for the graph ΓRI HN standard features to acquire meaningful algebraic results for the graph ΓRI HN and its corresponding group HN. For instance, marketing a modern methods to understand the way of create a precise small subgroups in G. Furthermore, performing a full investigation for getting particular ΓRI HN parameters.

Throughout this paper R represents commutative ring with identity and M is a unitary left R-module. The purpose of this paper is to investigate some new results (up to our knowledge) on the concept of weak essential submodules which introduced by Muna A. Ahmed, where a submodule N of an R-module M is called weak essential, if N ? P ? (0) for each nonzero semiprime submodule P of M. In this paper we rewrite this definition in another formula. Some new definitions are introduced and various properties of weak essential submodules are considered.

In this paper we define and study new concepts of fibrewise topological spaces over B namely, fibrewise closure topological spaces, fibrewise wake topological spaces, fibrewise strong topological spaces over B. Also, we introduce the concepts of fibrewise w-closed (resp., w-coclosed, w-biclosed) and w-open (resp., w-coopen, w-biopen) topological spaces over B; Furthermore we state and prove several Propositions concerning with these concepts.

Throughout this paper R represents commutative ring with identity and M is a unitary left R-module. The purpose of this paper is to investigate some new results (up to our knowledge) on the concept of weak essential submodules which introduced by Muna A. Ahmed, where a submodule N of an R-module M is called weak essential, if N ? P ? (0) for each nonzero semiprime submodule P of M. In this paper we rewrite this definition in another formula. Some new definitions are introduced and various properties of weak essential submodules are considered.

Czerwi’nski et al. introduced Lucky labeling in 2009 and Akbari et al and A.Nellai Murugan et al studied it further. Czerwi’nski defined Lucky Number of graph as follows: A labeling of vertices of a graph G is called a Lucky labeling if  for every pair of adjacent vertices u and v in G where . A graph G may admit any number of lucky labelings. The least integer k for which a graph G has a lucky labeling from the set 1, 2, k is the lucky number of G denoted by η(G). This paper aims to determine the lucky number of Complete graph K_n, Complete bipartite graph K_m,n and Complete tripartite graph K_l,m,n. It has also been studied how the lucky number changes whi

Background: Arterial stiffness is related with atherosclerosis and cardiovascular disease events. Patients with atherosclerotic disease show to have larger diameters, reduced arterial compliance and lower flow velocities. Aim of study : To compare between patients of two age groups with concomitant diseases diabetes and hypertension in regard to intima media thickness and blood flow characteristics in order to estimate the blood perfusion to the brain via the common and internal carotid arteries. Subject and Methods : 40 patients with (diabetic and hypertension) diseases were enrolled , they were classified according to age. Color Doppler and B mode ultrasound was used to determine lumen Diameter (D), Intima – media thickness (IMT)

Several new derivatives of 1, 2, 4-triazoles linked to phthalimide moiety were synthesized through following multisteps. The first step involved preparation of 2, 2-diphthalimidyl ethanoic acid [2] via reaction of two moles of phthalimide with dichloroacetic acid. Treatment of the resulted imide with ethanol in the second step afforded 2, 2-diphthalimidyl ester [3] which inturn was introduced in reaction with hydrazine hydrate in the third step, producing the corresponding hydrazide derivative [4]. The synthesized hydazide was introduced in different synthetic paths including treatment with carbon disulfide in alkaline solution then with hydrazine hydrate to afford the new 1, 2, 4-triazole [10]. Reaction of compound [10] with different alde

هدفت هذه الدراسة إلى تحليل نتائج الاختبار الوطني الموحد الذي تطبقه وزارة التربية والتعليم الفلسطينية في مادة الرياضيات لطلبة الصف الثامن الأساسي في المدارس الحكومية في محافظة طولكرم، وذلك لمعرفة مستوى الطلبة على هذا الاختبار في ضوء متغيرات الجنس والمنطقة التعليمية ونوع المدرسة، ومعرفة علاقة التحصيل على هذا الاختبار بتحصيل الطلبة المدرسي والمعدل العام. ولتحقيق ذلك تم تحليل درجات (3218) طالباً وطالبة؛ وهم ي