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 .

This paper demonstrates the spatial response uniformity (SRU) of two types of heterojunctions (CdS, PbS /Si) laser detectors. The spatial response nonuniformity of these heterojunctions is not significant and it is negligible in comparison with p+- n silicon photodiode. Experimental results show that the uniformity of CdS /Si is better than that of PbS /Si heterojunction

             The synthesis of nanoparticles (GNPs) from the reduction of HAuCl₄ ^.3H₂O by aluminum metal was obtained in aqueous solution with the use of Arabic gum as a stabilizing agent. The GNPs were characterized by TEM, AFM and Zeta potential spectroscopy. The reduction process was monitored over time by measuring ultraviolet spectra at a range of λ 520-525 nm. Also the color changes from yellow to ruby red, shape and size of GNP was studied by TEM. Shape was spherical and the size of particles was (12-17.5) nm. The best results were obtained at pH 6.

Everybody is connected with social media like (Facebook, Twitter, LinkedIn, Instagram…etc.) that generate a large quantity of data and which traditional applications are inadequate to process. Social media are regarded as an important platform for sharing information, opinion, and knowledge of many subscribers. These basic media attribute Big data also to many issues, such as data collection, storage, moving, updating, reviewing, posting, scanning, visualization, Data protection, etc. To deal with all these problems, this is a need for an adequate system that not just prepares the details, but also provides meaningful analysis to take advantage of the difficult situations, relevant to business, proper decision, Health, social media, sc

Abstract

 Nano-crystalline ZSM-5 zeolite was synthesized by hydrothermal method using chelating agent and two gel compositions:Compositionɪ:Al₂O₃:86SiO₂:5.5TPA:12.7Na₂O:3.4Trien:3320H₂O.Compositionɪɪ:Al₂O₃:68SiO₂:5.4TPA:10Na₂O:2.6Trien:2626H₂O.Study of hydrothermal reaction factors on characteristics of nano- sized zsm-5 has been carried on ,among them are crystallization temperature, crystallization time and concentration of template ( TPAOH ) solution. Synthesis was accomplished in PTFE lined autoclave ( reactor ) . The product were characterized by X-ray diffraction ( XRD ),Atomic force microsc

The budget represents a critical accounting tool used for planning and control. It is considered a measure of the results expected to occur.

This study aims to identify the impact of the Kaizen Budget in reducing costs and continuous improvement on the General Company's operations for Light Industries. The research idea is based on the fact that preparing the budget based on constant improvement supports the higher management of people, processes, materials, and production methods, thus enabling them to manage and reduce their costs.

Research results that the prepared budget suffers from many shortages that limit the materials' usefulness for management

study aimed to recognize the relationship shyness and depression and to recognize the differences between the genders, according to the variable of shyness and depression, the sample consisted (214) students, (141) female (73) male, and the sample responded scale of shyness and Inventory beck for depression, The Results of this study show that: the sample has a low degree shyness and a high degree depression, . There are no statistically significant differences according to gender variable in shyness, and there are statistically significant differences according to gender variable in depression favor for male, and there are statistically significant relationships between the variables of the study at lev

Almost human societies are not void of poverty, as the latter accompanied the emergence of humanity, and it, thus, represents an eternal problem. To advance an individual's reality and raise the level of the poor social classes, social security networks have been established. Such networks operate in society following social systems and laws to provide food, and material support. Besides, such networks help to rehabilitate the individual academically and vocationally. They empower vulnerable groups through the establishment of courses and workshop, provide (conditional) subsidies related to the health and educational aspects in order to achieve the sustainable development goals of (2030), and apply developmental roles of social safety ne

As the word can fluctuate between central and peripheral dlalten it represents the first lexical meaning and the second represents the meaning that gain by the context in which it appear so this research came to show signs that can be acquired the root ( GUM ) and its derivatives from the contexts in which it is mentioned in the Koran as well as siqnificant Lexical if this research is divided on two first is eating Lexical semantics , the second handled connotations in the Koran was based on what the commentators and concemed with the meanings of the Koran and the owners Almagamat in astatement that the semantic .

The new organic reagent 2-[Benzo thiazolyl azo]-4,5-diphenyl imidazole was prepared and used as complexing agent for separation and spectrophotometric determination of Cu2+ ion in some samples include plants, soil, water and human blood serum. Initially determined all factors effect on extraction method and the results show optimum pH was (pHex=9), optimum concentration was 40?g/5mLCu2+ and optimum shaking time was (15min.), as well stoichiometry study appears the complex structure was 1:1 Cu2+: BTADPI. Interferences effect of cations were studied. Synergism effect shows MIBK gave increasing in distribution ratio (D). Organic solvent effect appears there is no any linear relation between dielectric constant for organic solvent used and dis