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.

Nowadays, university education stands in front of both students who feel they are weak and teachers who are addicted to using traditional and dependent teaching. This has led to have negative repercussions on the learner from different aspects, including the mental aspect and the academic achievement process. Therefore, the present research is concerned with finding a new teaching method that adopts the motivation by the fear of failure technique. Thus, the study aims to examine the effect of adopting this method on students’ academic achievement. To achieve this aim, an experimental method was used, and an achievement test was built for the curriculum material of level two students. The pretest test was applied on 17 male and female s

In this paper, some chalcone derivatives (C1, C2) were synthesized based on the reaction of equal amount of substituted acetophenone and substituted banzaldehyde in basic medium. Oxazine and thiazine derivatives were prepared from the reaction of chalcones (C1-C2) with urea and thiourea respectively in a basic medium. Pyrazole derivatives were prepared based on the reaction of chalcones with hydrazine mono hydrate or phenyl hydrazine in the presence of glacial acetic acid as a catalyst. The new synthesized compounds were identified using various physical techniques like1 H-NMR and FT-IR spectra.