In this work, the modified Lyapunov-Schmidt reduction is used to find a nonlinear Ritz approximation of Fredholm functional defined by the nonhomogeneous Camassa-Holm equation and Benjamin-Bona-Mahony. We introduced the modified Lyapunov-Schmidt reduction for nonhomogeneous problems when the dimension of the null space is equal to two.  The nonlinear Ritz approximation for the nonhomogeneous Camassa-Holm equation has been found as a function of codimension twenty-four.

ملخص البحث:

    ان الله تعالى هو الذي خلق جميع المخلوقات ، والذي بيده الموت والحياة وان كل هذه المخلوقات تحتاج الى اوامر ، وهذه الاوامر الالهية وجهها الله لعبادة بوساطة انبياءه ( عليهم السلام) فكانوا هم اول المستسلمين والمنقادين لأوامره ، فجاءت الآيات الكريمة مخاطبة للأنبياء واقوامهم بشكل عام ولنبينا محمد (r) بشكل خاص.

اما عن المضمون البحثي فقد جاءت مادته مقسمة الى ثل

Different methods can be used to remove tissue during gingivectomy and produce a good gingival margin, the most common is the conventional gingivectomy which is done by the use of scalpel, now a day’s Laser is widely spread and can be used to perform surgeries. Materials and methods: 50 patients divided into two equal groups, Group 1 gingivectomy was done by Diode Laser, Group 2 gingivectomy was done by scalpel, plaque and gingival index were measured at 1st, 2nd and 3rd visit, swab were taken and sent foe detecting bacterial growth and biopsy were taken for histopathological examination. Group 1 show no significant differences in plaque and gingival means between the visits, the bacteriological examination showed no growth of bact

Abstract The current research aims to identify the most prominent beliefs about coronavirus of Baghdad University students, as well as to identify the prominent beliefs toward coronavirus of male and female students. To achieve the research objectives, a questionnaire of (15) items was administered to a sample of (600) male and female students collected from ten different colleges at the university of Baghdad. The findings of the research illustrated that item (8) took priority as students believe there is a misleading about coronavirus spreading by governments, item (2) which indicated that coronavirus is man-made took level two, followed by item (10), it proposes that coronavirus emerged from the American military base in china. Additiona

abstract:

Objectives: The study aims to reveal the approach of Imam Al-Salmi in the weighting between the apparently conflicting texts, and to show the extent of his agreement and disagreement with the rest of the fundamentalists, and does he have vocabulary that can be used to elicit legal rulings in modern contemporary issues?

Method: The method of induction and analysis is one of the main tools to reach the research results. The study resorted to following the sayings of Imam Al-Salmi in various sources and fatwas and standing on them, then analyzing and applying them to the various branches of jurisprudence in the various jurisprudential chapters.

The main function of the auditing process is to get a financial report provide information about the activities of the economic entities. The financial report's information is intended to be useful in making decisions and planning for entities future. Such information became more effective and efficient if the auditors process analytical auditing procedures, by using those financial analysis tools, which mean more detailed indicators.

The objectives of this research are to investigate auditor's use of analytical procedures in Oman and identify the main objectives for using these procedures. A questionnaire was used to gather the data for the study. A sample of 65 auditors and the response rate was 80% (52).

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 This research aims to investigate the impact of a training program for teachers of chemistry according to the strategies for both sides of the brain together in academic achievement for their students, the sample consisted of a 12 teachers of both genders who are teaching chemistry for the students of the fifth scientific secondary schools of the General Directorate for the Education in Garmiyan/Sulaymaniyah governorate, Iraqi Kurdistan region, where five teachers of them randomly selected to involve the training program, and seven teachers did not participate in the proposed training program, where a sample of students was selected for each group of teachers about 147 male and female students for teachers of the experiment

الملاخص

This study discussed modern variable in the organizational thought that is the high performance organizations in the two of Iraqi public organizations. The aim of study determines to know the level of the performance in this organizations (high or not). The data was Collected by questionnaire which contain (8) characteristics, the organizational design, strategy, process, technology, leadership, the roles, culture, and external environment). The sample contain from (76) employees;

Results points that the two organizations didn’t reach to the high level of performance, and there are significance's difference  among them.