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

Systems on Chips (SoCs) architecture complexity is result of integrating a large numbers of cores in a single chip. The approaches should address the systems particular challenges such as reliability, performance, and power constraints. Monitoring became a necessary part for testing, debugging and performance evaluations of SoCs at run time, as On-chip monitoring is employed to provide environmental information, such as temperature, voltage, and error data. Real-time system validation is done by exploiting the monitoring to determine the proper operation of a system within the designed parameters. The paper explains the common monitoring operations in SoCs, showing the functionality of thermal, voltage and soft error monitors. The different

The concept of the order sum graph associated with a finite group based on the order of the group and order of group elements is introduced. Some of the properties and characteristics such as size, chromatic number, domination number, diameter, circumference, independence number, clique number, vertex connectivity, spectra, and Laplacian spectra of the order sum graph are determined. Characterizations of the order sum graph to be complete, perfect, etc. are also obtained.

An energy and exergy thermodynamic analysis using EES program was done for a domestic refrigerator working with R-134a using vapor compression refrigeration cycle. The analysis deals with the system component, i.e. compressor, condenser, evaporator and the expansion device. The analysis depends on the entropy generation minimization approach to improve the refrigerator performance by exploring the optimum design points. These design points were derived from three different theories governing the entropy generation minimization using exergy analyzing method. These theories were first applied to find the optimum balance between the hot inner condenser area and the cold inner evaporator area of the refrigerator and between

 A problem of solid waste became in the present day common global problem among all countries, whether developing or developed countries, and can say that no country in the world today is immuning from this dilemma which must find appropriate solutions. The problem has reached a stage that can not ignore or delay, but has became a daily problem occupies the minds of ecologists, economists and politicians took occupies center front in the lists of  priorities for the countries in terms of finding solutions to the rapid scientific and radical them. and that transport costs constitute an important component of total costs borne by the municipal districts in the process of disposal of solid waste, so any improvement in the

This paper aims at the analytical level to know the security topics that were used with data journalism, and the expression methods used in the statements of the Security Media Cell, as well as to identify the means of clarification used in data journalism. About the Security Media Cell, and the methods preferred by the public in presenting press releases, especially determining the strength of the respondents' attitude towards the data issued by the Security Media Cell. On the Security Media Cell, while the field study included the distribution of a questionnaire to the public of Baghdad Governorate. The study reached several results, the most important of which is the interest of the security media cell in presenting its data in differ

Preparing teacher occupies the attention of many thinkers and philosophers since the age of
kaldinics ( people of mesoptam / 2342 pH ) to the Islamic age where moslems philosophers
focus their attention on thought and philosophy where the philosophy of that teaching
depends on : teacher , student and family begin .
So , the issue of preparing and training teacher occupies the attention of education scientists
depending on his vital and important role in implementing of teaching policies in philosophies
and Islamic educational thought , therefore , the preparing and development of the teacher
regards as one of the basics of teaching development because of its importance in
development of teaching performance and th

Aim: To learn more about Oral Lichen Planus Iraqi patients, including their background information, symptoms, and prognosis. Materials and Methods: From the Oral and Maxillofacial Pathology Department, College of Dentistry, Baghdad University, we retrospectively reviewed the medical records of 68 patients with a histologically confirmed clinical diagnosis of oral lichen planus and subsequently contacted the patients by phone to evaluate their prognosis. Results: Females were more likely than males to experience severe pain; the reticular form of Oral Lichen Planus was the most prevalent at 38.2%, but the erosive type was more prevalent among females. Only 53 of 68 patients responded to phone calls. More than 37% of those respondents reporte