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

چکیده

کشورعراق مرزهای زمینی ایران دارد که علاوه بر این ، مشترکات وروابط متعدد اقتصادی ،سیاسی، فرهنگی ودينى ميان هر دو ملت می باشند . عراق بعلت موقعیت جغرافیایی ونزدیکی به ایران سهم بیشتری برای ورود واژه های فارسی به لهجه ی خود داشت ، علاوه بر این رویدادهای سیاسی متقابل قدیم و جدید میان دو کشور سبب ورود بسیاری از لغات فارسی به لهجه ی عراقی شد که کاربرد این لغات هم اکنون در لهجه ی عراقی آشکار است ، ای

The plant licorice is considered important plants as nutritionally and medically and economically, as a rich in phytochemical, vitamins and minerals, and being widely available, Research indicated the presence of many nutrients such as (proteins, Carbohydrates, vitamins and minerals) as well as presence of Glycyrrhizin which responsible of sweet taste, that allowing the possibility to use it as natural intensity sweetener with few calories in Sweetening of many food. This research is aimed to study the Stability of Glycyrrhizin toward the various manufacturing conditions such as (thermal treatment, pH of foods and microwaves), so three factorial experiments was implemented to find out the Stability as following: 100C° - 121C° - Microwa

The aim of this paper is to derive a posteriori error estimates for semilinear parabolic interface problems. More specifically, optimal order a posteriori error analysis in the - norm for semidiscrete semilinear parabolic interface problems is derived by using elliptic reconstruction technique introduced by Makridakis and Nochetto in (2003). A key idea for this technique is the use of error estimators derived for elliptic interface problems to obtain parabolic estimators that are of optimal order in space and time.

The  purpose of  this study was to investigate the effect of six thinking hats on creative thinking among 10^th grade female students in Tulkarm district. The sample comprises two sections of 10^th grade female students (n=80) in Adawiya secondary School, The two sections were divided into two groups; one as an experimental group which works with six thinking hats, and the second as control group that learns traditionally. Creative thinking exam was used to measure the creative thinking with reliability (0.88).

The results of the study have shown the following:

There were statistically significant differences at (α ≤ 0.05) in the creative thinking among 10^th grade female student

Developed and underdevelopment countries, on equal terms, face the problem of budget deficiency. Budget deficiency means that the public expenditure surpasses the public revenues. This, on the international level, is one of the most serious economic problems with many direct effects on the national economy, and depends, basically, on its finance chosen method. Looking for a solution to this problem, for this reason and many other ones, has been highlighted in spite of the many attempts to reduce the role of the governmental expenditure. Budget deficiency can not be attributed to a single unique cause since it is complex phenomenons the causes of which are related to many factors contribute to its occurrence, some of which refer t

This research set to indicate the role of the opportunity cost in the overall economic development (human and social development) by selecting the most appropriate alternative for the growth of the country in exchange for sacrificing profit limits to achieve this growth and development of the country, especially in the present circumstances of the country and after studying the reality of the economic case for him, as the problem lies with don't selecting the best alternative that enhances the gross domestic product, which extends to promote overall economic development and revive the industrial and agricultural sectors, productivity is more like Impotent, versus sacrifice alternative consumption may bring more financially lucrative than

The study aimed to know the degree of availability of integrated preparation criteria in the Arabic Teacher training Program in Syrian universities from the viewpoint of university students of the Educational qualification diploma, and the degree of availability of these standards in the outputs of the preparation program. To achieve the Goals of the study, a list of integrated preparation criteria was prepare comprising (110) indicators, distributed to (11) criteria. The list was applied to a randomly chosen sample of (45) educational qualification diploma students. The results of the study showed that the Standards for integrated preparation are provided in a medium degree overall in the program for preparing teachers of Arabic languag

This study rigorously investigates three 3d transition metal carbide (TMC) structures via LDA and GGA approximations. It examines cohesive energy (Ecoh), Vickers hardness (Hv), mechanical stability, and electronic properties. Notably, most 3d TMCs exhibit higher cohesive energy than nitrides, and rs-TiC demonstrates a Vickers hardness of 25.66 GPa, outperforming its nitride counterpart. The study employs theoretical calculations to expedite research, revealing mechanical stability in CrC and MnC (GGA) and CrC (LDA in cc structure), while all 3d TMCs in rs and seven in zb structures show stability. Charge transfer and bonding analysis reveal enhanced covalency along the series, influenced by the interplay between p orbitals of carbon and d o