In this paper we generalize Jacobsons results by proving that any integer  in   is a square-free integer), belong to . All units of  are generated by the fundamental unit  having the forms

our generalization build on using the conditions

This leads us to classify the real quadratic fields  into the sets  Jacobsons results shows that  and Sliwa confirm that  and  are the only real quadratic fields in .

The main objective of the central bank is to achieve price stability and target in fractionates. Therefore, the bank sought to use modern tools and policies in order to reduce the negative effects of the accumulation of foreign reserves represented by monetary sterilization, similar to developed and developing countries alike, but with different available tools that are possible and imposed by the local financial and monetary environments, such as the window for buying and selling foreign currency, open market operations and deposit facilities. And lending existing. Because any in crease in the monetary base resulting from the accumulation of foreign reserves will affect price stability directly due to the consumer nature of the

Background: This study aimed to evaluate the effect of zirconia different surface treatments (primer, sandblast with 50μmAl2O3, Er,Cr:YSGG laser) on shear bond strength between zirconia surface and resin cement. Material and methods: Sixty presintered Y-TZP zirconia cylinder specimens (IPS e.max ZirCAD, Ivoclar vivadent) will be fabricated and sintered in high temperature furnace of (1500 C for 8 hours) according to manufacturer’s instructions to the selected size and shape of (5mm. in diameter and 6mm in height). All specimens were ground flat using 600.800.1000.1200, aluminum oxide abrasive paper to obtain a standardized surface roughness. Surface roughness values were then recorded in µm using surface roughness tester (profi

Mobile ad-hoc networks (MANETs) are composed of mobile nodes communicating through wireless medium, without any fixed centralized infrastructure. Providing quality of service (QoS) support to multimedia streaming applications over MANETs is vital. This paper focuses on QoS support, provided by the stream control transmission protocol (SCTP) and the TCP-friendly rate control (TFRC) protocol to multimedia streaming applications over MANETs. In this study, three QoS parameters were considered jointly: (1) packet delivery ratio (PDR), (2) end-to-end delay, (3) and throughput. Specifically, the authors analyzed and compared the simulated performance of the SCTP and TFRC transport protocols for delivering multimedia streaming over MANETs.

One of the most important processes to obtain gasoline with high octane numbers is isomerization. In this paper, Pt/TiO2 was prepared successfully by using the sol–gel method by hydrolysis of titanium tetraisopropoxide as a titania source with ethanol and then platinum was loaded on the synthesized catalyst; the result shows that the sample prepared has a good crystallinity with a surface area of about 85 m2 /g and a pore volume of 0.1938 cm3 /g, while XRD shows that the prepared sample was anatase phase. The efect of both temperature and liquid hourly space velocity of the prepared catalyst was achieved by hydroisomerization of n-hexane in a fxed bed reactor with a temperature of 200–275 °C and LHSV 0.5–2h−1. The results show

    The Ozone Monitoring Instrument (OMI) measures the reflected solar radiation in the ultraviolet and visible part in the spectral range that is between 270 and 500 nm, using two channels with a spectral resolution of about 0.5 nm. Ground-level tropospheric ozone is one of the air pollutants of most concern. In the troposphere, near the Earth's surface, human activities lead to ozone concentrations several times higher than the natural background level. To evaluate the ozone distribution over Iraq, the ozone data from OMI were analyzed using geostatistical techniques. Theoretical spherical models provided the best fit for all monthly experimental variograms. The parameters of these variograms (sill, range and nugget) wer

The follower of the needs of the users of accounting information notices the necessity of adopting faithful representation of information Hence, IASB adopted the economic substance approach as the basis for the Formulation and development of international accounting standards Therefore, this research discusses the reflection of the economic phenomenon in terms of its economic substance on the subject of measurement , And it should be consistent measurement method where the problem of research is concentrated in the fact that the economic units operating in the local environment to address events and economic phenomena according to the legal form , as appropriate With the requirements of the unified accounting sys

Baghdad city has been faced numerous issues related to freshwater environment deteriorations due to many reasons, mainly was the discharge of wastewater without adequate treatment. Al-Rustamiya Wastewater Treatment Plant (WWTP) have been constructed among many plants in Baghdad city to reduce the amount of wastewater discharged into natural environment and its subsequent adverse effects. This study was conducted to evaluate the performance of the plant which consist of a conventional activated sludge (CAS) and sequencing batch reactors (SBR) systems as secondary treatment units and its ability to meet Iraqi specifications. A reliability level determination and analysis also were conducted to find the plant's stability an

Baghdad city has been faced numerous issues related to freshwater environment deteriorations due to many reasons, mainly was the discharge of wastewater without adequate treatment. Al- Rustamiya Wastewater Treatment Plant (WWTP) have been constructed among many plants in Baghdad city to reduce the amount of wastewater discharged into natural environment and its subsequent adverse effects. This study was conducted to evaluate the performance of the plant which consist of a conventional activated sludge (CAS) and sequencing batch reactors (SBR) systems as secondary treatment units and its ability to meet Iraqi specifications. A reliability level determination and analysis also were conducted to find the plant's stability and its capabi