This paper generalizes and improves the results of Margenstren, by proving that the number of -practical numbers  which is defined by   has a lower bound in terms of . This bound is more sharper than Mangenstern bound when  Further general results are given for the existence of -practical numbers, by proving that the interval contains a -practical for all

The flexibility of interaction between the movement of macroeconomic variables that affect and are affected by the balance of payments, especially the movement of the current account, implies a perception of the maturity of economic development and what the theory assumes from the launch of a wide range of economic movement that varies in the degree of its influence according to the level of economic development and the vitality of the internal/external overlap relations through the assumed response to the movement of the macroeconomic variables. On this basis, it is possible to estimate the soundness and rationality of the economic decision taken that takes into account the required reciprocal repercussions between the current a

study aimed to recognize the relationship shyness and depression and to recognize the differences between the genders, according to the variable of shyness and depression, the sample consisted (214) students, (141) female (73) male, and the sample responded scale of shyness and Inventory beck for depression, The Results of this study show that: the sample has a low degree shyness and a high degree depression, . There are no statistically significant differences according to gender variable in shyness, and there are statistically significant differences according to gender variable in depression favor for male, and there are statistically significant relationships between the variables of the study at lev

عند إطلالتنا على هذا البلد العربي لابد من التقصي ولو بعجاله عن اقتصاده وهو الاهم باعتبار ان الاقتصاد هو شريان الحياة لأي أمة فلا غنى ولا تهاون في نفس الوقت عن هذا الجانب المهم الذي يرتبط مدى تطوره بتطور البلد وهذا الاخير مرتبط بما متوفر لديه من موارد بشريه ومادية وان تفاوتت النسبة بينها فلا ضير في ذلك فالاهم هو وجود الموجه والمخطط بالاتجاه الصحيح نحو الاستغلال الامثل لهذه الموارد
(وان قلّتْ) وبالتالي

Lexicography, the art and craft of dictionary-making, is as old as writing. Since its very early stages several thousands of years ago, it has helped to serve basically the every-day needs of written communication among individuals in communities speaking different languages or different varieties of the same language. Two general approaches are distinguished in the craft of dictionary-making: the semasiological and the onomasiological. The former is represented by usually-alphabetical dictionaries as such, i.e. their being inventories of the lexicon, while the latter is manifested in thesauruses. English and Arabic have made use of both approaches in the preparation of their dictionaries, each having a distinct aim ahead. Wit

The purpose of this paper is to identifying the level of skill self-esteem of the young tennis players in the Governorate of Baghdad, identifying some aspects of attention (acuteness, concentration, and diversion of attention) among the young tennis players of the Baghdad governorate, and identify the skills of serve and serve spiking in tennis by young tennis players in Baghdad governorate. The researchers used the descriptive approach in the correlative relations style for its suitability and the research problem. the research sample was chosen in a deliberate way from the youth team players in tennis for the Governorate of Baghdad and the participants in the 2021-2022 sports season, whose number is (20) male players and (4) young playe

       In light of the developments and intense competition that the world has witnessed, the need to search for a sustainable and continuous competitive advantage for economic units has emerged, as the economic units must not lose sight of their interest in the activities they perform to achieve that advantage, and it can be said that the goal of the research is to identify the theoretical dimensions of the green value chain represented by: (Green research and development, green design, green manufacturing, green marketing, green services) and the dimensions of the sustainable competitive advantage represented by (quality, creativity, innovation, cost, response to the customer), as well as identifyi

The research aimed mainly to discover the effectiveness of the (PEOE) model in teaching science to develop the skills of generating and evaluating information and the emotional side of the scientific sense of the intermediate first grade students. An experimental approach with a quasi-experimental design called pre-test and post-test control design was used. The research sample consisted of (60) students, who were selected in a random cluster method, (30) students in the experimental group studied the unit "The Nature of Material" using the (PEOE) model, and (30) students in the control group studied according to the prevailing method of teaching. The research materials and tools were represented in: a teacher's guide for teaching the un