Our aim in this work is to investigate prime submodules and prove some properties of them. We study the relations between prime submodules of a given module and the extension of prime submodules. The relations between prime submodules of two given modules and the prime submodules in the direct product of their quotient module are studied and investigated.

The widespread of internet allover the world, in addition to the increasing of the huge number of users that they exchanged important information over it highlights the need for a new methods to protect these important information from intruders' corruption or modification. This paper suggests a new method that ensures that the texts of a given document cannot be modified by the intruders. This method mainly consists of mixture of three steps. The first step which barrows some concepts of "Quran" security system to detect some type of change(s) occur in a given text. Where a key of each paragraph in the text is extracted from a group of letters in that paragraph which occur as multiply of a given prime number. This step cannot detect the ch

This paper deals with founding an estimation of best approximation of unbounded functions which satisfied weighted Lipschitz condition with respect to the convex polynomials by means of weighted moduli of smoothness of fractional order  , ( , ) p f t . In addition we prove some properties of weighted moduli of smoothness of fractional order.

     Applications of quantitative methods, which had been explicit attention during previous period (the last two centuries) is the method of application sales man or traveling salesman method. According to this interest by the actual need for a lot of the production sectors and companies that distribute their products, whether locally made or the imported for customers or other industry sectors where most of the productive sectors and companies distributed always aspired to (increase profits, imports, the production quantity, quantity of exports. etc. ...) this is the part of the other hand, want to behave during the process of distribution routes that achieve the best or the least or most appropriate.

In this paper, the system of the power plant has been investigated as a special type of industrial systems, which has a significant role in improving societies since the electrical energy has entered all kinds of industries, and it is considered as the artery of modern life.

   The aim of this research is to construct a programming system, which could be used to identify the most important failure modes that are occur in a steam type of power plants. Also the effects and reasons of each failure mode could be analyzed through the usage of this programming system reaching to the basic events (main reasons) that causing each failure mode. The construction of this system for FMEA is dependi

The free zone or the free economy cities are cities with classification and functional specificity, although the history of  the concept of these areas has been It dates back to distant eras, but the intellectual and philosophical construction with the support of intellectual approaches, the most important of which is globalization contributed to its rapid spread globally and taking a variety of forms and models. With the diversity of its formulas and objectives countries have competed in adopting the establishment of these areas, meanwhile The influence of related trends affected the contemporary formation of these sites. Therefore ,the research was directed focus on the importance of adopting a set of common indicators (collection

  There are many researches deals with constructing an efficient solutions for real problem having Multi - objective confronted with each others. In this paper we construct a decision for Multi – objectives based on building a mathematical model formulating a unique objective function by combining the confronted objectives functions. Also we are presented some theories concerning this problem. Areal application problem has been presented to show the efficiency of the performance of our model and the method. Finally we obtained some results by randomly generating some problems.

      Strong and ∆-convergence for a two-step iteration process utilizing asymptotically nonexpansive and total asymptotically nonexpansive noneslf mappings in the CAT(0) spaces have been studied. As well, several strong convergence theorems under semi-compact and condition (M) have been proved. Our results improve and extend numerous familiar results from the existing literature.

The fuzzy assignment models (FAMs) have been explored by various literature to access classical values, which are more precise in our real-life accomplishment. The novelty of this paper contributed positively to a unique application of pentagonal fuzzy numbers for the evaluation of FAMs. The new method namely Pascal's triangle graded mean (PT-GM) has presented a new algorithm in accessing the critical path to solve the assignment problems (AP) based on the fuzzy objective function of minimising total cost. The results obtained have been compared to the existing methods such as, the centroid formula (CF) and centroid formula integration (CFI). It has been demonstrated that operational efficiency of this conducted method is exquisitely develo

The fuzzy assignment models (FAMs) have been explored by various literature to access classical values, which are more precise in our real-life accomplishment. The novelty of this paper contributed positively to a unique application of pentagonal fuzzy numbers for the evaluation of FAMs. The new method namely Pascal’s triangle graded mean (PT-GM) has presented a new algorithm in accessing the critical path to solve the assignment problems (AP) based on the fuzzy objective function of minimising total cost. The results obtained have been compared to the existing methods such as, the centroid formula (CF) and centroid formula integration (CFI). It has been demonstrated that operational efficiency of this conducted method is exquisitely deve