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.

Arabs knew the art of diction and elocution as part of their life in peace and war and in lamentation, satire, narration and description, as they were distinguished by influential and meaningful speeches in war and battle times, and the most prominent topics of the pre-Islamic rhetoric were pride, enthusiasm, bravery and other meanings related to heroism and call for war. It was not a long time when Arabs paid more attention to this great phonetic phenomenon, as they see that it elevates the status of the word and shows its meanings and significances. The current research aims to reveal the function of diction in conveying the meaning in radio drama.
The research methodology: the researcher adopted the analytic descriptive method gui

In this research, we find the Bayesian formulas and the estimation of Bayesian expectation for product system of Atlas Company.  The units of the system have been examined by helping the technical staff at the company and by providing a real data the company which manufacturer the system.  This real data include the failed units for each drawn sample, which represents the total number of the manufacturer units by the company system.  We calculate the range for each estimator by using the Maximum Likelihood estimator.  We obtain that the expectation-Bayesian estimation is better than the Bayesian estimator of the different partially samples which were drawn from the product system after  it checked by the

Students’ feedback is crucial for educational institutions to assess the performance of their teachers, most opinions are expressed in their native language, especially for people in south Asian regions. In Pakistan, people use Roman Urdu to express their reviews, and this applied in the education domain where students used Roman Urdu to express their feedback. It is very time-consuming and labor-intensive process to handle qualitative opinions manually. Additionally, it can be difficult to determine sentence semantics in a text that is written in a colloquial style like Roman Urdu. This study proposes an enhanced word embedding technique and investigates the neural word Embedding (Word2Vec and Glove) to determine which perfo

Spatial data observed on a group of areal units is common in scientific applications. The usual hierarchical approach for modeling this kind of dataset is to introduce a spatial random effect with an autoregressive prior. However, the usual Markov chain Monte Carlo scheme for this hierarchical framework requires the spatial effects to be sampled from their full conditional posteriors one-by-one resulting in poor mixing. More importantly, it makes the model computationally inefficient for datasets with large number of units. In this article, we propose a Bayesian approach that uses the spectral structure of the adjacency to construct a low-rank expansion for modeling spatial dependence. We propose a pair of computationally efficient estimati

Methods of estimating statistical distribution have attracted many researchers when it comes to fitting a specific distribution to data. However, when the data belong to more than one component, a popular distribution cannot be fitted to such data. To tackle this issue, mixture models are fitted by choosing the correct number of components that represent the data. This can be obvious in lifetime processes that are involved in a wide range of engineering applications as well as biological systems. In this paper, we introduce an application of estimating a finite mixture of Inverse Rayleigh distribution by the use of the Bayesian framework when considering the model as Markov chain Monte Carlo (MCMC). We employed the Gibbs sampler and

The use of data envelopment analysis method helps to improve the performance of organizations in order to exploit their resources efficiently in order to improve the service quality. represented study a problem in need of the Iraqi Middle East Investment Bank to assess the performance of bank branches, according to the service quality provided, Thus, the importance of the study is to contribute using a scientific and systematic method by applying  the data envelopment analysis method in assessing the service quality provided by the bank branches, The study focused on achieving the goal of determining the efficiency of the  services quality provided by the bank branches manner which reflect the extent of utilization of a

The research explain the analysis of finance investments through  analyze the finance tables for commercial banks, by using the pointers to indicate the limits of economical benefit for these investments, and fix the negative deviations and as well positive, for the purpose of  diagnostic the negative (disadvantage) and develop the advantage deviation, For the importance of finance investments in the development operation and economical growth, further to that the finance investments is represent one of the most activities in the commercial banks in which aim the adequate incomes as a result of the commercial banks act to receipt the banks deposits and then make it growth and develop through  commercial advantage o

The aim of this research is to identify the availability of visual thinking skills in the chemistry textbook scheduled for the third intermediate grade for the academic year (2020-2021) in the Republic of Iraq. The study sample consisted of all (85) images contained in the chemistry course for the third intermediate grade, which are (85) form using the curriculum.  Analytical descriptive A list of visual thinking skills was prepared, and the unit of form was adopted as a unit of analysis and repetition as a unit of counting, and frequencies and percentages were used for statistical treatment, and validity and reliability were calculated.  And using the Holste equation.  The following results were reached: The skill

This paper study two stratified quantile regression models of the marginal and the conditional varieties. We estimate the quantile functions of these models by using two nonparametric methods of smoothing spline (B-spline) and kernel regression (Nadaraya-Watson). The estimates can be obtained by solve nonparametric quantile regression problem which means minimizing the quantile regression objective functions and using the approach of varying coefficient models. The main goal is discussing the comparison between the estimators of the two nonparametric methods and adopting the best one between them