In this paper, the process for finding an approximate solution of nonlinear three-dimensional (3D) Volterra type integral operator equation (N3D-VIOE) in R³ is introduced. The modelling of the majorant function (MF) with the modified Newton method (MNM) is employed to convert N3D-VIOE to the linear 3D Volterra type integral operator equation (L3D-VIOE). The method of trapezoidal rule (TR) and collocation points are utilized to determine the approximate solution of L3D-VIOE by dealing with the linear form of the algebraic system. The existence of the approximate solution and its uniqueness are proved, and illustrative examples are provided to show the accuracy and efficiency of the model.

Mathematical Subject Classificat

In this paper, the general framework for calculating the stability of equilibria, Hopf bifurcation of a delayed prey-predator system with an SI type of disease in the prey population, is investigated. The impact of the incubation period delay on disease transmission utilizing a nonlinear incidence rate was taken into account. For the purpose of explaining the predation process, a modified Holling type II functional response was used. First, the existence, uniform boundedness, and positivity of the solutions of the considered model system, along with the behavior of equilibria and the existence of Hopf bifurcation, are studied. The critical values of the delay parameter for which stability switches and the nature of the Hopf bifurcat

 This research sheds light on the use of metal in the manufacture of jewelry, which is represented by ornamental tools in the period between the third and second millennium BC, in addition to the most important molds used in their manufacture. Man has been interested in metals since early ages, and was able to make tools that he uses in his daily life, especially jewelry. And the Syrian people got acquainted with the types of minerals, their characteristics, and how to deal with them. Minerals played an effective and prominent role in the economy of ancient Syria. Trade with those countries and secure their roads.

Early childhood Is the of the important stages in the life of man and initiated full on others
reliability has been rise in growth toward independence and self-reliance, as is the transition
from the home environment to the kindergarten environment (kindergarten) (4-6) years where
starts in the interaction with the external environment, it is an essential stage in the
construction of sound personal to the child, and choose proper clothes at this age is one of the
important aspects in building the child's personality, as it reflects the clothing behavior and
taste his parents, especially his mother, she is the first responsible for providing clothes for
her children. Children at this stage are dependent the mothers in

Praise be to Allah, the Lord of the Worlds.
          Because it has a prominent role in the life of the Muslim person in particular, and in the stability, security, and safety of society in general, I found it appropriate to participate even a little in solving some of the problems that arise in the nation, and that Adello Badawi in this important issue that concerns everyone without exception And that I show that there are constants in the Koran, from which the scholars of the Ummah derived their evidence on this subject, and that there have been variables have occurred in some Islamic societies, in the issue of blood money that deserves the victim and his family, has allocated talk

Background Direct-acting antivirals (DAAs) combination therapies from various mechanisms of action and families have been revolutionized the management landscape of chronic hepatitis C virus (HCV). Ombitasvir, paritaprevir with ritonavir (OBV/PTV/r) ± ribavirin (RBV) is approved to treat HCV genotype 4 (GT4) infection. Here, our objective was to delineate the efficacy and safety of OBV/PTV/r plus RBV in treating of Egyptian naïve patients infected with HCV GT4.

Methods a cohort of 100 Egyptian patients infected with HCV GT4 was allocated and administered orally OBV/PTV/r with RBV. The primary endpoint of our study was a sustained virological response (HCV RNA < 12 IU/mL) 12 weeks after the c

Efficacy of Varnishes with: Bioactive Glass, Recaldent Technology and Silver Diamine Fluoride in Comparison with Sodium Fluoride on Tooth Surface Micro-hardness (an In Vitro Study)

Background: Thermocycling simulates the temperature dynamics in the oral environment. This in vitro study done to measure and compare the effect of thermocycling on the shear bond strength of stainless steel and sapphire brackets bonded to human enamel teeth using light cured orthodontic adhesive and debonded at various time, and to measure adhesive remnant index after debonding. Materials and Methods: one-hundred-twenty extracted upper first premolars for orthodontic reason were used in this study; depending on weather thermocycled or not, the sample was divided into two main groups, then within each group 30 teeth were used for stainless-steel brackets (Bionic®) and for sapphire brackets (Pure®). Both groups were subdivided into three

The importance of the research in the preparation of special exercises to develop some types of basketball scoring as a contribution to help the physical education teacher to find successful educational alternatives. The purpose of the study was to prepare special exercises for the cognitive (cognitive) survey in the development of motor satisfaction and learning some types of Scoring for basketball for students. Learn about the effect of cognitive exercises in cognitive development in students. The survey included students from the first stage of the Faculty of Physical Education and Sports Science \ University of Diyala (159) divided into 6 people. The sample was randomized by (b) and (b) D) and after dispersion by the standard method In

Objective: Rheumatoid arthritis (RA) patients have increased morbidity and mortality from premature cardiovascular (CV) disease (CVD). Framingham risk score (FRS) is a simplified coronary prediction tool developed to enable clinicians to assess the risk of a cardiovascular event and to identify candidate patients for risk factors modifications worldwide. The predictive ability of the FRS varies between populations, ethnic groups, and socio-economic status. The aim of this study is to find if there is any correlation between the Framingham risk score and the inflammatory and biochemical parameters used to measure disease activity and functional ability in Iraqi patients with active RA.