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

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

The aim of this paper is to study the Zariski topology of a commutative KU-algebra. Firstly, we introduce new concepts of a KU-algebra, such as KU-lattice, involutory ideal and prime ideal and investigate some basic properties of these concepts. Secondly, the notion of the topology spectrum of a commutative KU-algebra is studied and several properties of this topology are provided. Also, we study the continuous map of this topological space.

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.

Logic is one of the sciences that have receded and regressed in the field of Islamic sciences. This regression is the result of several factors, the most important of which are:

1- The Aristotelian logic, concerned with the seemingly essential shape and the underlying truth in the text, which has been translated into Arabic, is no longer able to keep pace with scientific revelations and epistemological spaces of our time.
2- The existence of logic in the curricula of Islamic studies was not subject to a study linking logic and Islamic sciences. Therefore, we find that the student studies logic as if it were a strange subject that has nothing to do with the subjects of Islamic studies and even Islamic philosophy.
3- Logic is

Background: Oral health is important to the quality of life of all individuals. Oral lesions can cause discomfort or pain that interferes with mastication, swallowing, and speech. Oral disease is a health problem that is not only a matter of oral hygiene and local condition, but can also be a precursor to other dangerous and potentially life threatening illnesses. The present study was designed to analyze the main clinicopathological aspects of most common oral lesions in patients who visit the Oral Diagnosis Clinic of the College of Dentistry, University of Sulaimani, Kurdistan region, Iraq. Patients and methods: This prospective study was performed on 3144 patients from July 2009-July 2010. In this study a total of 3144 patients were e

Bekhme formation, Dernir Dagh well -1 has been divided into two facies units using core
sample slides and depending on sedimentary structures and diagenetic processes .The facies
reflect the environment of the foreslope.This work proves the absence of Bekhme formation
in Dernir Dagh
Well- 1 as a tongue as reported by the Oil Exploration Company. Some species and genera of
bentonic foraminifera were identified. The age of Bekhme formation was estimated
depending on the recognized index fossils to be lower Maastrichtian.