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

At a time when the general rules in the different legal systems require the presence of two parties to the contract, one of which is issued the first expression of the will and is called the offer, and the other is issued from the other and is called the acceptance. A special type of contracts emerged in the beginning of the last century called the “unilateral contracts”. The side sparked a major jurisprudential dispute, as well as the issuance of several contradictory judicial rulings on it. Hence, this research came to highlight this special type of contract. Key words: the definition of a unilateral contract, its distinction from other legal situations, and its effects.

The aim of the research is to identify the imaginative thinking skills included in the content of the chemistry textbook for fifth-grade students in biological sciences at the preparatory stage, which is approved by the Ministry of Education, General Directorate of Curricula in the academic year 2020-2021. To achieve the objective of the study, the researcher depends on the previous studies in the field and content of imaginative thinking skills for preparing a list of skills that includes (3) essential skills and (11) sub-skills and (28) items related to all skills. The researcher adopted the analytical descriptive approach because of its appropriation of the goals of the research. Then the researcher analyzed the content of the book de

      In this paper, the researcher suggested using the Genetic algorithm method to estimate the parameters of the Wiener degradation process,  where it is based on the Wiener process in order to estimate the reliability of high-efficiency products, due to the difficulty of estimating the reliability of them using traditional techniques that depend only on the failure times of products. Monte Carlo simulation has been applied for the purpose of proving the efficiency of the proposed method in estimating parameters; it was compared with the method of the maximum likelihood estimation. The results were that the Genetic algorithm method is the best based on the AMSE comparison criterion, then the reliab

Iraq within the ranks of the fledgling communities characterized by a broad base of the population pyramid, because they pose the age group (under 15 years) of a large proportion of the community, as it exceeded the proportion (40%) during the years of research extended (1986-2010) Despite the relative decline in the rates fertility during that period, but the proportion of young people remained high, especially for groups of at least five years, amounting to about 14% in 2012, a little more than the proportion of what constitutes age group (5-9 above) years, where it was (13%) and this naturally predicts continuing population increases in coming decades, due to the entry of those numbers of individuals in the reproductive stage,

A field study investigated the degree of need for managers working in the directories of education to develop their skills for the exercise of administrative empowerment, and it adopted the descriptive analytical approach. The research community, was determined which consisted of 126 principals, and the sample was selected with arte of randomly Statistics and by (100%) of the research community, as the number of respondents was (126) of managers working in the directories of education. A questionnaire was built which included 40 items distributed among the fields of study. Researchers verified its validity and reliability. The research data were analyzed using software (SPSS), the questionnaire was applied in the second semester of the a

               The bank deposits is fuel banking activity and raw material products for the commercial bank and the basis of its activity and its lifetime So the bank, which seeks to continue the successful development of the volume of cash deposits has translated the work of the bank to meet the needs of different sectors by providing the necessary funding, and from this point of view was the research problem a lack of interest departments of banking services to commercial banks as a means for the development of electronic cash deposits have, and which represents the basis for the supplier commercial bank fund.

The aim of the research is to identify the impact of the dimensions of the European Excellence Model in evaluating the performance of the bank of the research sample, as well as to interpret which dimensions are more important to the banks of the research sample. Based on the dimensions of this model, the United Bank for Investment and Finance has chosen a research community, and has met with officials of the United Bank for Investment and Finance at various administrative levels to measure the practices of excellence management in the European model, and the analytical approach has been the case study and the construction of the checklist as a tool to collect information. The research has reached the most important results There is a discr

In the mist of developments in the course of scientific research in general and humanities in particular and the accompanying changes in the visions and policies inspired by the need for these sciences to follow the qualitative methods in dealing with many of the topics or problems that require for their solution to obtain qualitative information which can be provided by resorting to quantitative research. Therefore, a new trend has emerged in many public relations› researchers who believe that qualitative research methods should be used by establishing scientific foundations and methodological classification based on the use of these methods and determining the nature of the subjects applied in them to reach results that are character

Photos of the backwardness of the Muslims and their backwardness in creating
sustainable development policies have driven them to a state of civilization , which witnesses
Avckaddoha time ago and not disrupt the adversary is a phenomenon thought the youth to
exercise its role and duty in the construction and development of the state witnesses Mdanah
civilized nation.
The vigilance thought the youth of its slumber correct form could provide opportunities for
growth and development in the Arab and Islamic worlds, and both material and moral support
through the creation model youth Islamic social role models, but that the image of the model
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