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 life insurance companies need a sound system to use it in selecting Insurable risks so they can avoid or reduce possible losses that may be insured to a minimum levels , But the application within IRAQI INSURANCE  COMPANY reflects that it still depends on a traditional ways in the procedures used to select that risks .

                 This  research represents an attempt to put acceptable suggestions about developing a system for selecting insurable risks which used now by iraqi insurance company by recognizing the risks of life insurance , determining kinds of risks which can difined as normal and upnormal risks , rectification of the

The article describes the basic principles of modeling a dictionary article in the “Dictionary of the Language of Russian Folklore Lexicon epics” (M. A. Bobunova, A. T. Khrolenko). Among such principles are the principle of linguocentrism (representation of universal cognitions in strict observance of the traditions of lexicographic science), the principle of anthropocentrism (language learning as a means of human consciousness / subconsciousness), the principle of expansionism (attracting material from various knowledge bases), the principle of explanatory ("explanatory moment"), and fractal principle (synergistic potential of the presented material: nonlinearity and self-similarity; hierarchical organizati

The first molecular research on Iraqi centipede fauna is presented in this article. Between October 2022 and May 2023, during various climatic circumstances, centipedes were collected from several locations in four provinces of Iraq. Three families, represented by four genera, underwent molecular identification, and five species were found. From the order Scolopendromorpha family Scolopendridae, two species were recorded, Scolopendra morsitans Linnaeus, 1758, and S. cingulata Latreille, 1829, Cormocephalus sp.; while from the order Lithobiomorpha, family Lithobiidae, one species was recorded for first time in Iraq; Lithobius crassipes L. Koch, 1862 from the order Geophilomorpha family Himantariidae, one species Bothriogaster Signata

Background: Repeated teenage pregnancy is a major burden on the healthcare system worldwide. Objective: We aimed to compare teenagers with their first and third pregnancies and to evaluate the likelihood of neonatal complications. Materials and Methods: This cross-sectional study was performed on female teenagers (aged ≤ 19 yr) with singleton pregnancies. The subjects (n = 298) were screened over 12 months. Ninety-six women were excluded, based on the exclusion criteria. The remaining subjects (n = 202) were divided into two groups: teenagers with first pregnancy (n = 96) and teenagers with third pregnancy (n = 47). The subjects were observed throughout pregnancy and delivery. The final sample size of the first and thi

Background: Small cardamom or green cardamom is the dried fruit of the tall perennial herbaceous plant, Elettaria cardamomum Maton belonging to the family Zingiberaceae. The major use of small cardamom on world wide is for domestic culinary purpose and in medicine. This study was conducted to test the effect of small cardamom extracts on Mutans streptococci and Candida Albicans in comparison to 0.2% chlorhexidine gluconate and de-ionized water in vivo. Materials and Methods: Mutans streptococci and Candid Albicans were isolated, purified and diagnosed according to morphological characteristic and biochemical test. In this experiments, the effect of control agents and small cardamom extracts as a mouth rinses was tested on the saliva

The current research aims to know the extent of the impact of performance evaluation in its dimensions as an explanatory variable in the behavioural and attitudinal work outputs with its dimensions as a response variable in order to reach appropriate solutions through which the University of Fallujah seeks to achieve its goal in the process of diagnosing the axes of strength and to benefit from them in the process of strengthening the status and sobriety of the academic position of the professor and the researcher relied on The descriptive and analytical approach in carrying out this study, and data was collected from university professors, including leaders, heads of departments and divisions, who numbered (97) teachers. And fie