Our aim of this research is to find the results of numerical solution of Volterra linear integral equation of the second kind using numerical methods such that Trapezoidal and Simpson's rule. That is to derive some statistical properties expected value, the variance and the correlation coefficient between the numerical and exact solutionâ–¡ 

The main objective of this research is to use the methods of calculus ???????? solving integral equations Altbataah When McCann slowdown is a function of time as the integral equation used in this research is a kind of Volterra

     Let R be a commutative ring with unity and an R-submodule N is called semimaximal if and only if

 the sufficient conditions of F-submodules to be semimaximal .Also the concepts of (simple , semisimple) F- submodules and quotient F- modules are  introduced and given some  properties .

     The aim of the study is to investigate the effects of space weather on the troposphere, where our climate exists. This work is useful to give us an idea of ​​the interaction between solar activity and some meteorological parameters. The sunspot number (SSN) data were extracted from the World Data Center for the production, preservation, and dissemination of the international sunspot number (SILSO), top net solar radiation (TSR) and temperature 2 meters from the ERA5 model of the Copernicus Climate Change Service (C3S) from the Climate Data Store with 0.25 grid Resolution, providing a rich source of climate data for researchers. This study was conducted from 2008 to 2021 (solar cycle 24 and the beginning of 25) over Iraq loca

In this paper the modified trapezoidal rule is presented for solving Volterra linear Integral Equations (V.I.E) of the second kind and we noticed that this procedure is effective in solving the equations. Two examples are given with their comparison tables to answer the validity of the procedure.

In this paper Volterra Runge-Kutta methods which include: method of order two and four will be applied to general nonlinear Volterra integral equations of the second kind. Moreover we study the convergent of the algorithms of Volterra Runge-Kutta methods. Finally, programs for each method are written in MATLAB language and a comparison between the two types has been made depending on the least square errors.

In some cases, researchers need to know the causal effect of the treatment in order to know the extent of the effect of the treatment on the sample in order to continue to give the treatment or stop the treatment because it is of no use. The local weighted least squares method was used to estimate the parameters of the fuzzy regression discontinuous model, and the local polynomial method was used to estimate the bandwidth. Data were generated with sample sizes (75,100,125,150 ) in repetition 1000. An experiment was conducted at the Innovation Institute for remedial lessons in 2021 for 72 students participating in the institute and data collection. Those who used the treatment had an increase in their score after

The study of properties of space of entire functions of several complex variables was initiated by Kamthan [4] using the topological properties of the space. We have introduced in this paper the sub-space of space of entire functions of several complex variables which is studied by Kamthan.

Background: Periodontitis is an inflammatory disease that affects the supporting tissues of the teeth; Smoking is an important risk factor for periodontitis induces alveolar bone loss and cause an imbalance between bone resorption and bone deposition. The purpose of this study is to detect and compare the presence of incipient periodontitis among young smokers and non-smokers by measuring the distance between cement-enamel junction and alveolar crest (CEJ-Ac) using Cone Beam Computed Tomography (CBCT). Material and methods: The total sample composed of fifty two participants, thirty one smokers and twenty one non-smokers (age range 14-22 years). Periodontal parameters: plaque index (PLI), gingival index (GI) were recorded for all teeth exc

In this paper we use non-polynomial spline functions to develop numerical methods to approximate the solution of 2nd kind Volterra integral equations. Numerical examples are presented to illustrate the applications of these method, and to compare the computed results with other known methods.