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 research aims to shed light on the role of artificial intelligence in achieving Ambidexterity performance, as banks work to take advantage of modern technologies, artificial intelligence is an innovation that is expected to have a long-term impact, as well as banks can improve the quality of their services and analyze data to ensure that customers' future needs are understood. . The Bank of Baghdad and the Middle East Bank were chosen as a community for the study because they had a role in the economic development of the country as well as their active role in the banking market. A sample of department managers was highlighted in collecting data and extracting results based on the checklist, which is the main tool for the stu

The current study aims to identify the needs in the stories of the Brothers Grimm. The research sample consisted of (3) stories, namely: 1- The story of the Thorn Rose (Sleeping Beauty) 2- The story of Snow White 3- The story of Little Red Riding Hood. The number of pages analyzed reached (15.5) pages, and to achieve the research objectives, Murray's classification of needs was adopted, which contains (36) basic needs that are further divided into (129) sub-needs. The idea was adopted as a unit of analysis and repetition as a unit of enumeration, Reliability was extracted in two ways: 1- Agreement between the researcher and himself over time, where the agreement coefficient reached 97%. The second was agreement between the researcher and tw

One of the main environmental problems which affect extensively the areas in the world is soil salinity. Traditional data collection methods are neither enough for considering this important environmental problem nor accurate for soil studies. Remote sensing data could overcome most of these problems. Although satellite images are commonly used for these studies, however there are still needs to find the best calibration between the data and real situations in each specified area. Landsat satellite (TM & ETM+) images have been analyzed to study soil pollution (Exacerbation of salinity in the soil without the use of abandoned agricultural for a long time) at west of Baghdad city of Iraqi country for the years 1990, 2001 & 2007. All of the th

The primary toxin class discovered in freshwater pufferfish is a category of neurotoxins called PSTs (Paralytic shellfish toxins) and pufferfish toxin has been observed to have biological, biochemical, and cytotoxic effects on cancer cell lines. Therefore, it is crucial to determine the cytotoxic activity, toxins present in the ovary of T. leiurus, and interaction between ligand (toxin compound) and receptors test. This study used the MTT method in the T47D cell lines, liquid chromatograph-tandem mass spectrometry (LC-MS/MS), and analysis of the molecular interaction using molecular docking. The ovary of T. leiurus had cytotoxicity on the T47D cell, having an IC50 value of 229.535 μg/ml, and generated a chroma

The objective of this study is to evaluate the bacterial count and heavy metal concentration of river water on fish micronuclei. Fish and water samples are carried out in 1 May to 1 June 2013 from Tigris River. A total of fifty three fish sample are studied. The bacteriological quality of water showed that the total viable count is ranged from 150×103 to 352×103 cfu/ml and fecal coliform counts was 1250 cell/100ml during the study period. All the metals (Cu, Hg, Pb, and Zn) are within the normal limit, but Cd was slightly elevated in river water samples. The appearance of micronuclei in red blood cells of all fish species is detect , by recording a larger number of it, in ( Abu Alsomere , Hishne , Bannini Kaber al fam & Karkoor

A pure posteriorly posterior communicating artery (PCoA) aneurysm represents a surgical challenge. This is mainly when there is a need for good exposure of the aneurysmal neck, sac, PCoA, and anterior choroidal arteries. Ruptured pure posteriorly directed PCoA aneurysm imposes significantly extra challenge as the surgeon undergoes dissection through a tight brain. Even with measures commonly used to attain brain relaxation like the lumbar drain and cisternal fenestration. Here, we describe a technique for posterior temporal pole mobilization (TPM) as an integrated part of microsurgical clipping of ruptured pure posteriorly directed PCoA aneurysms. This technique is implicated in twenty-three successive cases of ruptured PCoA aneurys

Evaluation of the Antibacterial Efficacy of Electrolyzed Oxidizing Water as an Irrigant against Enterococcus faecalis (An In vitro Study), Noor A Khait*, Muna Saleem Kalaf

Prior to the start of production, several factors must be considered, including the price, effectiveness, and environmental friendliness of batteries. Ionic liquids and deep eutectic solvents have shown significant success when employed as electrolytes with Titanium-graphite cells, especially when combined with additives that enhance their conductivity by reducing the high viscosity of these liquids. Evaluating the discharge voltage of the AlCl3-chloroacetamide IL with DCM as an additive revealed a voltage of 1.16V and an internal resistance of 11 Ohm. These electrochemical cells exhibited an intriguing response. Otherwise, when utilizing CaCl2.2H2O: