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 Asphalt cement is produced as a by-product from the oil industry; the asphalt must practice further processing to control the percentage of its different ingredients so that it will be suitable for paving process. The objective of this work is to prepare different types of modified Asphalt cement using locally available additives, and subjecting the prepared modified Asphalt cement to testing procedures usually adopted for Asphalt cement, and compare the test results with the specification requirements for the modified Asphalt cement to fulfill the paving process requirements. An attempt was made to prepare the modified Asphalt cement for pavement construction in the laboratory by digesting each of the two penetration grade Asphalt c

the chormanal some complement of barbus grypius is found to be 98 consisting of 22 melaccntricsomes it is probably a tetraploid species and more advanced than other speice haveing the same ehromosome under and belonging yo the genus barbus

Through this study, the following has been proven, if  is an algebraically paranormal operator acting on separable Hilbert space, then  satisfies the ( ) property and  is also satisfies the ( ) property for all . These results are also achieved for  ( ) property.    In addition, we prove that for a polaroid operator with finite ascent then after the property ( ) holds for  for all.

This is a survey study that presents recent researches concerning factional controllers. It presents several types of fractional order controllers, which are extensions to their integer order counterparts. The fractional order PID controller has a dominant importance, so thirty-one paper are presented for this controller. The remaining types of controllers are presented according to the number of papers that handle them; they are fractional order sliding mode controller (nine papers), fuzzy fractional order sliding mode controller (five papers), fractional order lag-lead compensator (three papers), fractional order state feedback controller (three papers), fractional order fuzzy logic controller (three papers). Finally,

Cooperation spectrum sensing in cognitive radio networks has an analogy to a distributed decision in wireless sensor networks, where each sensor make local decision and those decision result are reported to a fusion center to give the final decision according to some fusion rules. In this paper the performance of cooperative spectrum sensing examines using new optimization strategy to find optimal weight and threshold curves that enables each secondary user senses the spectrum environment independently according to a floating threshold with respect to his local environment. Our proposed approach depends on proving the convexity of the famous optimization problem in cooperative spectrum sensing that stated maximizing the probability of detec

In this study, the kinetics for the reaction of tert-butanol esterification with acetic acid in the presence of Dowex 50Wx8 catalyst was investigated. The reaction kinetic experiments were conducted in 1000 milliliter vessel at temperatures ranged from 50 - 80 oC, catalyst loading 25-50 g/L, and the molar ratios of acetic acid to tert-butanol from 1/3 – 3/1. The reaction rate was found to increase with increasing temperature and catalyst loading. It was also found the conversion of the tert-butanol increases as the molar ratio of acid to alcohol increases from 1/3 – 3/1. The Non-ideality of the liquid phase was taken into account by using activities instead of molar fractions. The activity coefficients were calculated according to th

The world has seen in recent years as a result of rapid changes in the information and communication revolution until his limbs became distant as if a small screen can be controlled at the touch of which resulted in a stunning advance in all areas of life button, these changes were not accompanied by all the positive development, but it has many drawbacks on humans resulted in many of the psychological, social, intellectual and cultural problems.

As it is the cultural alienation of the most important challenges faced by the community in light of the tremendous technological progress and rapid jumps that exceeded all expectations in addition to the economic, social and political changes experienced by the country led to the desire