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

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,

The current study aims to find out:

1. The ingratiating behavior of university students.
2. The differences of statistical significance in The ingratiating behavior among university students according to the variables of sex and specialization

The current study is determined by University of Baghdad students of both genders (males and females) and for both majors (scientific and humanities) for the academic year (2019-2020).

In order to achieve the researcher's objectives:Ingratiating behavior scale has been constructed. It consists in its final form of (32) items divided into four behaviors. The researcher has extracted scale validity and reliability.

The researcher based the two scales

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

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, several conclusions

This study presents a comprehensive list of the freshwater and marine bivalves distributed in Iraq. A total of 51 species were recorded, and distributed as: 14 freshwater species, and 37 marine species, these species belonging to 25 families, all available remarks on the distribution, taxonomy, and nomenclature of these species were given. This study included the recently collected specimens along with those previously studied and recorded in Iraq.

Encouraging children towards the cognitive motivation through the discovery and knowledge of the environment around them is essential. Thus, during the two researchers’ supervision of the practical lessons that involved the female students’ application of their experience in the Applied Kindergarten Laboratory, it has been noticed that there was a difference in the cognitive motivation of kindergarten children. In order to reinforce the research problem, the two researchers sent an open questionnaire to a sample of randomly selected kindergarten teachers from Al-Karkh and Al-Rasafa sides. The responses collected accentuated the researchers’ sense of the existing problem. To achieve the aim of the study represented by examining the