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 .

Investigations made and soil samples brought from 14 sites in different areas, including Abu Ghraib and Al Anbar. Tests and measurements made in the Microbiology Laboratory at the College of Agriculture, University of Anbar. Department of Soil Sciences and water Resources, in order to isolate bio-fertilizers and test isolates fixing nitrogen in atmosphere and solvents for phosphorous compounds efficiency. The experiment included isolating and diagnosis of bacteria from rhizosphere soils of different plants that were brought from different agricultural areas, 74 isolates obtained by soils alleviation, and then the bio-chemical morphological and microscopic characteristics of these soils studied. The results showed that the most abundant and

The aim of this study is to identify the effect of particle size and to increase the concentration of Iraqi bentonite on rheological properties in order to evaluate its performance and to know if it can be used as drilling fluid without additives or not. In this study, Iraqi bentonite was carried out by mineral composition (XRD), chemical composition (XRF) and Particle size distribution (PSD), and its rheological properties were measured at different particle size and concentration. The results showed that when the particle size of Iraqi bentonite decreased, and the rheological properties were increased with increased concentration of Iraqi bentonite. Also, Iraqi bentonite was unable to use as drilling fluid without certain additives.

The Population growth and decay issues are one of the most pressing issues in many sectors of study. These issues can be found in physics, chemistry, social science, biology, and zoology, among other subjects.

We introduced the solution for these problems in this paper by using the SEJI (Sadiq- Emad- Jinan) integral transform, which has some mathematical properties that we use in our solutions. We also presented the SEJI transform for some functions, followed by the inverse of the SEJI integral transform for these functions. After that, we demonstrate how to use the SEJI transform to tackle population growth and decay problems by presenting two applications that demonstrate how to use this transform to obtain solutions.

Fin

The petroleum sector has a significant influence on the development of multiphase detection sensor techniques; to separate the crude oil from water, the crude oil tank is used. In this paper, a measuring system using a simple and low cost two parallel plate capacitance sensor is designed and implemented based on a Micro controlled embedded system plus PC to automatically identify the (gas/oil) and (oil/water) dynamic multi-interface in the crude oil tank. The Permittivity differences of two-phase liquids are used to determine the interface of them by measuring the relative changes of the sensor’s capacitance when passes through the liquid’s interface. The experiment results to determine the liquid’s interface is sa

Survival analysis is widely applied to data that described by the length of time until the occurrence of an event under interest such as death or other important events. The purpose of this paper is to use the dynamic methodology which provides a flexible method, especially in the analysis of discrete survival time, to estimate the effect of covariate variables through time in the survival analysis on dialysis patients with kidney failure until death occurs. Where the estimations process is completely based on the Bayes approach by using two estimation methods: the maximum A Posterior (MAP) involved with Iteratively Weighted Kalman Filter Smoothing (IWKFS) and in combination with the Expectation Maximization (EM) algorithm. While the other

Several directional wells have been drilled in Majnoon oilfield at wide variation in drilling time due to different drilling parameters applied for each well. This technical paper shows the importance of proper selection of the bit, Mud type, applied weight on Bit (WOB), Revolution per minute (RPM), and flow rate based on the previous wells drilled. Utilizing the data during drilling each section for directional wells that's significantly could improve drilling efficiency presented at a high rate of penetration (ROP). Based on the extensive study of three directional wells of 35 degree inclination (MJ-51, MJ-52, and MJ-54) found that the applied drilling parameters for MJ-54 and the bit type within associated drilling parameters to drill

Two different oxidative desulfurization strategies based on oxidation/adsorption or oxidation/extraction were evaluated for the desulfurization of AL-Ahdab (AHD) sour crude oil (3.9wt% sulfur content). In the oxidation process, a homogenous oxidizing agent comprising of hydrogen peroxide and formic acid was used. Activated carbons were used as sorbent/catalyst in the oxidation/adsorption process while acetonitrile was used as an extraction solvent in the oxidation/extraction process. For the oxidation/adsorption scheme, the experimental results indicated that the oxidation desulfurization efficiency was enhanced on using activated carbon as catalyst/sorbent. The effects of the operating conditions (contact time, temperat

The present work is devoted to investigate the performance of a homemade Y-shape catalytic microreactor for degradation of dibenzothiophene (DBT), as a model of sulphur compounds including in gas oil, utilizing solar incident energy. The microchannel was coated with TiO2 nanoparticles which were used as a photocatalyst. Performance of the microreactor was investigated using different conditions (e.g., DBT concentration, LHSV, operating temperature, and (H₂O₂/DBT) ratio). Our experiments show that, in the absence of UV light, no reaction takes place. The results revealed that outlet concentration of DBT decreases as the mean residence time in the microreactor increases. Also, it was noted that operating temperature s

There are several oil reservoirs that had severe from a sudden or gradual decline in their production due to asphaltene precipitation inside these reservoirs. Asphaltene deposition inside oil reservoirs causes damage for permeability and skin factor, wettability alteration of a reservoir, greater drawdown pressure. These adverse changing lead to flow rate reduction, so the economic profit will drop. The aim of this study is using local solvents: reformate, heavy-naphtha and binary of them for dissolving precipitated asphaltene inside the oil reservoir. Three samples of the sand pack had been prepared and mixed with a certain amount of asphaltene. Permeability of these samples calculated before and after mixed with asphaltenes. Then, the