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 .

A series of new compounds including p-bromo methyl pheno acetate [2]. N-( aminocarbonyl)–p-bromo pheno acetamide [3] , N-( aminothioyl) -p-bromo phenoacetyl amide [4], N-[4-(p-di phenyl)-1,3-oxazol-2-yl]-p-bromopheno acetamide [5],N-[4-p-di phenyl]-1,3-thiazol-2-yl-p-bromo phenoacet amide [6], p-bromopheno acetic acid hydrazide [7] , 1-N-(p-bromo pheno acetyl)-1,2-dihydro-pyridazin-3,6- dione [8], 1-N-(p-bromo pheno acetyl)-1,2-dihydro-phthalazin-3,8- dione[ 9], 1-(p-bromo pheno acetyl)-3-methylpyrazol-5-one [10] and 1-(p-bromo phenol acetyl)- 3,5-dimethyl pyrazole [11] have been synthesized. The prepared compounds were characterized by m.p.,FT-IR and 1H-NMR spectroscopy. Also ,the biological activity was evaluated .

Recently, several concepts and expressions have emerged that have often preoccupied the world . around the concept of environment and sustainability. This is due to the negative and irresponsible impact of man and his innovations in various industrial and technological fieldsthat have damaged the natural environment. Architecture and cities at the broader level are some of the man made components that caused these negative impacts and in the same time affected by them. What distinguishes architectural and urban projects is the consumption of large . quantities of natural resources and production larger amounts of waste and pollution, along the life of these projects. At the end of the twentieth century and the beginning of the twenty-fir

Tirzepatide is a revolutionary and promising medication with a high impact in the treatment of Obesity and T2DM with their complications. Its efficacy was proven through different trials in achieving favorable weight loss and a significant reduction in glycemic index. It also treated a large diversity of related co-morbidities, including fatty liver, cardiovascular disease, dyslipidemia, and more. Tirzepatide is well tolerated, has a good safety profile, and is highly reliable and suitable for use in a population.

The operative system of theatrical performance depends on the construction of the scenographic space, as it constitutes the most aesthetic effect of the recipient, and the body of the theatrical discourse that contains the signs of the show, and it comes as an embodiment of the directing vision of the show director, so most of the world directors resorted to attention to the output treatment to establish the scenographic space, and thus it possesses a contrast in The embodiment of the directing vision according to the stylistic and hermeneutical dimension of the director, so the two researchers found the importance of studying the topic, and the study came under the title (Directing Treatments of the Scenographic Space in the Iraqi Theat

Attention has recently been given to finding alternative and sustainable raw material sources for wood and metal adhesives, such as polyvinyl alcohol (PVA), corn starch (CS), arabic gum (AG), and dextrins (D). Modifying polymer dispersion using unique substances, such as modifying reactive elastomer liquid (EL) using PVA, CS, AG, or D results in sufficiently moisture-resistant adhesive joins. In the present study, the physical characteristics of EL/blended with the natural polymers PVA, CS, AG, and D, based on high-density fiberboard (HDF) wood and aluminum (Al) adhesives and coatings, were investigated and compared to those of pure EL. The EL was blended with PVA, CS, AG, or D at a ratio of 60/40 (w/w) to form EL/blends. The che

Evaluation of trace elements in Iraqi chewing gums are unavailable, particularly pollution of toxic elements, materials which change the values of PH in the Oral. Atomic Absorption Spectroscopy (AAS) were successfully employed to determine the concentration of 7 trace elements (essentially toxic and nonessential) and the PH, in thirteen different brands of chewing gum generally consumed in Iraq. Combined wet and dry digestion procedures were applied. Two types of heated graphite tubes were used, coated and uncoated tubes treated with tungsten solution. Result showed that Cu, Al and Zn were at very high levels in almost all brands whereas Mn was found to be high in brands A and O only.

A simple and novel membraneless paper-based microfluidic fuel cell was presented in this study. The occurrence of laminar flow was employed to ensure no mixing of the fuel and oxidant fluids along the bath of reaction. The acidic wastewater was used as a fuel. It was an air-breathing cell, so air and tab water were used as oxidants. Both the fuel and tab water flowed continuously under gravity. Whatman filter paper was used for preparation of the fuel cell channel and two carbon fibre electrodes were used and firmed on the edges of the cell. The performance of the cell was examined over three consecutive days. The results indicated that the present cell has the potential to generate electric power, but an extensive study is required to harv

The current research deals with spatial relations as a tool to link urban landmarks in a homogeneous composition with monumental sculptures, by identifying these landmarks and the extent of their impact on them, which constitutes an urgent need to evaluate the appropriate place and its effects on them, so that this analytical study is a critical approach adopted in artistic studies of monumental models in Arabcapitals .The current research came in four chapters, the first chapter of which dealt with the research problem, its importance and the need for it, then its objectives that were determined in revealing the spatial relations and their impact on

Background: Osteoporosis is a skeletal defect manifested by a reduction of bone strength as a result of reduced bone mass to the extent that there is a higher risk of fracture even on minor trauma. Hysterectomy in a premenopausal woman is a well known cause of ovarian failure resulting in an increased risk of osteoporosis.

Objective : To clarify bisphosphonate's preventive effect on osteopenia and osteoporosis in premenopausal women after hysterectomy.

Type of the study: Cross –sectional study.

Method:  84 premenopausal females post hysterectomy aged between 40 – 50 years, were enrolled in this randomized controlled double blinded trail a