In this paper, the homotopy perturbation method (HPM) is presented for treating a linear system of second-kind mixed Volterra-Fredholm integral equations. The method is based on constructing the series whose summation is the solution of the considered system. Convergence of constructed series is discussed and its proof is given; also, the error estimation is obtained. Algorithm is suggested and applied on several examples and the results are computed by using MATLAB (R2015a). To show the accuracy of the results and the effectiveness of the method, the approximate solutions of some examples are compared with the exact solution by computing the absolute errors.

A prey-predator interaction model has been suggested in which the population of a predator consists of a two-stage structure. Modified Holling's disk equation is used to describe the consumption of the prey so that it involves the additional source of food for the predator. The fear function is imposed on prey. It is supposed that the prey exhibits anti-predator behavior and may kill the adult predator due to their struggle against predation. The proposed model is investigated for existence, uniqueness, and boundedness. After determining all feasible equilibrium points, the local stability analyses are performed. In addition, global stability analyses for this model using the Lyapunov method are investigated. The chance of occurrence of loc

The research seeks to examine the ability of fifth preparatory students in solving a mathematical problem in relation to system thinking. To this end, the researcher chose (140) fifth preparatory students from four-different secondary schools in Kirkuk city for the academic year (2016-2017). Two tests were adopted to collect study data: a test of (5) items about skills in solving math problem designed by (Al-raihan, 2006); and a test of system thinking skills designed by the researcher himself consisted of (14) items. It was divided into four skills (analyzing the main system to subsystems, eliminating all inner gaps of system, identifying the inner connection of system, and reorganizing the system). The findings indicated a good ability

Background: Pain and the usage of local anesthetic agents are still real problem in pediatric dentistry, for these reasons, the use of minimal invasive dentistry (MID) in regard to the patient comfort is important especially for children, anxious and uncooperative patients. Chemomechanical caries removal (CMCR) methods involve the selective removal of the carious dentine hence it avoided the painful removal of the sound dentine and the anxiety resulted due to the vibration of the hand piece which is also decreased thus it appears to be more acceptable and comfortable to the patient. Aims of this study: This study was conducted among group of children to assess and compare the anxiety rating scale (during and after treatment) between the

This research deals with the most famous existing definitions of public relations, in an attempt to achieve a definition that will be added to the other existing and widespread definitions, especially that big developments have taken place in the concept of public relations and their idiomatic use.

In addition, many definitions of public relations have been restricted to some limited descriptions, therefore many of the descriptions given to the public relations are basically definitions as well as characteristics of the public relations.

This research aims at setting and formulating the definitions of public relations, it also deals with its credibility in achieving its significance in order to reach a new definition that

 A new technique in cultivation by installing membrane sheet below the crop’s root zone was helped to save irrigation water in the root zone, less farm losses, increasing the field water use efficiency and water productivity. In this paper, the membrane sheet was installed below the root zone of zucchini during the summer growing season 2017 in open field.  This research was carried out in a private field in Babil governorate at Sadat Al Hindiya Township reached 72 km from Baghdad. Surface trickle irrigation system was used for irrigation process. Two treatment plots were used, treatment plot T1 using membrane sheet and treatment plot T2 without using the membrane sheet. The applied irrigation water, time of

This research aims to find how three different types of mouthwashes affect the depth of artificial white spot lesions. Teeth with various depths of white spot lesions were immersed in either splat mouthwash, Biorepair mouthwash, Sensodyne mouthwash, or artificial saliva (control)twice daily for one minute for 4 weeks and 8 weeks at 37°C. After this immersion procedure, lesion depth was measured using a diagnosed pen score. A one-way analysis of variance, Dunnett T3 and Tukey's post hoc α = .05 were used to analyze the testing data. Splat mouthwash enhanced the WSL remineralization and made the lowest ΔF compared with other mouthwashes in shallow and deep enamel after 4 and 8 weeks of treatment. In the repair groups, after 4 weeks

Background: Diabetic mellitus type ? is a metabolic disorder of diverse etiological factors, characterized by hyperglycemia resulting from an absolute deficiency of insulin affected childhood and adolescent. Some of these patients seek an orthodontic care .The orthodontist who is treating these medically compromised patients should have a working knowledge of the multitude of medically complex problems. This information will support and enable for delivery of high standards of dental care in general and orthodontic care in particular. The aim of this study was to analyze serum IgG levels and salivary secretory IgA (sIgA) levels in human dentine extract (HDE) before (T0) and 6 months after (T6) orthodontic treatment and to correlate anti-HDE

KE Sharquie, HR Al-Hamamy, AA Noaimi, AF Tahir, Journal of Cosmetics, Dermatological Sciences and Applications, 2012 - Cited by 2