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
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
... Show MoreSeven species of semi venomous Opisthoglypha snakes (Reptilia, Ophidia) of Iraq are listed with important characteristics in morphology due to geographical and individual variation of species, as well, the confusion in the scales count of Telescopus tessellatus martini (Schmidt, 1939) of Iraq are discussed.
Titanium-dioxide (TiO2) nanoparticles suspended in water, and ethanol based fluids have been prepared using one step method and characterized by scanning electron microscopy (SEM), and UV–visible spectrophotometer. The TiO2 nanoparticles were added to base fluids with different volume concentrations from 0.1% to1.5% by dispersing the synthesized nanoparticles in deionized water and ethanol solutions. The effective thermal conductivity, viscosity and pH of prepared nanofluids at different temperatures from 15 to 30 oC were carried out and investigated. It was observed that the thermal conductivity, pH, and viscosity of nanofluids increases with the increase in TiO2 nanoparticle volume fraction
... Show MoreGypseous soil is a collapsible soil, which causes large deformations in buildings that are constructed on it. Various methods have been used to minimise this effect, such as replacing the gypseous soil or using soil stabilisation (grouting or soil improvement). This study was carried out on four types of gypseous soils that have different properties and various gypsum contents. The testing was carried out on remoulded samples to evaluate the compressibility of gypseous soil under different conditions. The samples were grouted with acrylate liquid. The relationships between the injection pressure and the radius of flow, between time of injection and radius of flow, and between time and quantity of acrylate liquid are investigated on
... Show MoreSeven species of semi venomous Opisthoglypha snakes (Reptilia, Ophidia) of Iraq are listed with important characteristics in morphology due to geographical and individual variation of species, as well, the confusion in the scales count of Telescopus tessellatus martini (Schmidt, 1939) of Iraq are discussed.
Background: The microorganisms can impend the life of health care professional and particularly the dental practitioners. They can be transmitted by different ways like airborne and droplet transmission. The current study was carried out to identify whether the arch wires that received from the manufactures are free from microbial contamination and to determine the bacterial species attached to the arch wires. Materials and Methods: This study involved eighty samples, consisted of two types of arch wires (nitinol and stainless-steel) from four companies (3M, G&H, Jiscop, OrthoTechnology). These wires inserted in a plane tube that contains 10 -ml of (Tris [tris(hydroxymethyl)aminomethane] and EDTA (ethylenediaminetetraacetic acid) tri
... Show MoreThis study was conducted on the effect of the sedimentary source (the sediments coming from both the Iraqi-Iranian borderline and the Tigris river) on the optical and textural features, especially sphericity and roundness of feldspar minerals (potassium and plagioclase types) in soils of the southern part of the alluvial plain. Eight pedons were selected to represent the study area, five of them represented sediments coming from the borderline, which included pedons of (Badra, Taj Al-Din, Al-Shihabi, Jassan, and Galati), while two of them represent the sediments of the Tigris River (Essaouira, Al-Dabouni), the pedon of Ali Al-Gharbi was represented the mixing area of sediments of all the floods coming from the borderline and the sediments o
... Show MoreThe present analysis targets to recognize the influence of the separate teaching approach on the accomplishment of grammar for scholars of the College of Islamic Sciences. The target of attaining this target led the investigations developing the subsequent null theories: 1. No statistically substantial variance is happened at the consequence level of 0.05 between the mean scores of the scholars in the investigational category who learnt consistent with the separate learning approach and the mean scores of the scholars in the control category who learnt in the conventional method in the accomplishment test. 2. No statistically substantial variance has been observed at the consequence level of 0.05 in the mean differences between the
... Show More
