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 .

Forward-swept wings were researched and introduced to improve maneuverability, control, and fuel efficiency while reducing drag and they are often used alongside canards, to further enhance their characteristics. In this research, the effects of canard dihedral angles on the wing loading of a forward-swept wing in transonic flow conditions were studied, as the wing loading provides a measure of wing’s efficiency (lift/drag). A generic aircraft model from literatures was selected, simulated, and compared to, using CFD software ANSYS/Fluent where the flow equations were solved to calculate the aerodynamic characteristics. The research was carried at two different Mach numbers, 0.6 and 0.9, for five different canard dihedral angles which tra

This research worked on identifying the effect of increasing the volume of indebtedness by companies listed on the Iraq Stock Exchange on the trading volume of those companies, and this research included some theoretical concepts related to both debt financing and trading volume, and it represents the research community of the joint-stock companies listed in The Iraq Stock Exchange (the banking sector). As for the research sample, it was deliberately chosen represented by companies with continuous trading without stopping, which reached 10 joint-stock companies, and the period of research was extended during the period 2011-2015, and a set of indicators and financial methods were used In measuring research v

This  research aimes to expose the levels of geometrical thinking among the students of mathematic department in Basic Education College at AL-Mustansiriyah University throughout their respondes on the test of  geometrical thinking which consists (50) multi- choice items  distributed on the first four levels of Van Hiele ( recognition – analysis – ordering – deduction ).

The validity and the reliability of the test have been investigated. Besides, the difficulty and its discrimination have been measured. The activity of the wrong variables has been measured.

The test has been applied on (180) male and female students of the first, second and third grades.

The thermal stability of previously prepared tetraphenanthroporphyrazine (TPPH2) and its complexes with VO(IV) , Co(II) , Cu(II) , Zn(II) , Mg(II) , Ca (II) ions were studied by thermogravimetric analysis (TG & DTG) at temperature range (20-1000oC). The results indicated that these compounds have a high thermal stability comparable to those of phthalocyanine compounds (PC) and higher than those of hemiporphyrazine compounds (HP) . In general metal complexes were more stable than parent ligand . Data of magnetic susceptibility and electrical conductivity were also obtained as further support for the studied compoundes .

Experimental results for the density of states of hydrogenated amorphous silicon due to Jackson et al near the valence and conduction band edges were analyzed using Levenberg-Marquardt nonlinear fitting method. It is found that the density of states of the valence band and the conduction band can be fitted to a simple power law, with a power index 0.60 near the valence band edge, and 0.55 near the conduction band edge. These results indicate a modest but noticeable deviation from the square root law (power index=0.5) which is found in crystalline semiconductors. Analysis of Jackson et al density of states integral J(E) data over about (1.4 eV) of photon energy range, showed a significant fit to a simple power law with a power index of 2.11

         Values ​​are penetrating or interfering in the lives of individuals and groups and are connected to them in the sense of life itself, because they are closely linked to the motives of behavior, hopes and goals, and can be said that values ​​are everything. The concept of values ​​is one of the concepts that have received the attention of researchers from different disciplines. This has resulted in a kind of confusion and variation in use from one specialization to the other, and uses multiple uses within one specialization. Therefore, there is no uniform definition of values ​​because they relate to individuals. Individuals differ in many things, such as perception,

Man was closely associated with nature in its various forms, as it represented the incubator for him in all areas of his life, so writers often made it a material for their literature and a fertile ground for their productions, so it appeared in its various forms and man’s need for it, its good and its bad in literature throughout history, and the Arabs are like Other nations, since the pre-Islamic era, nature was an important outlet and a refuge for poets in the production and creativity of literature and to this day, and when we talk about a poet from the Fatimid state, we find that nature - especially spring and its flowers - in that period took its take from literature and represented a phenomenon for many Among the

Praise be to God, Lord of the worlds, and prayers and peace be upon our master and beloved Muhammad, the wise guide and great teacher, the guide to a straight path, the one sent as a mercy to the worlds, and upon his good and chosen family, his chosen companions, the working scholars, and those who follow them in righteousness until the Day of Judgment.

And after:

One of the important controversial topics shared between the sciences of the Noble Hadith and the Fundamentals of God is the issue of the innovator in terms of accepting and rejecting his narration and testimony, and the difference in it leads to disagreement in many branches of jurisprudence that were based on texts narrated by innovated narrators or those accu

Abstract: This article is a comparative analysis of the concept and types of homonyms in Russian and Arabic. Homonyms are lexical units that have the same sound but different meanings. The study of homonymy in different languages can help reveal the features of the semantic structure and syntactic rules of each language. The article discusses the main aspects of homonymy in Russian and Arabic, as well as a comparative analysis of the types of homonyms that exist in both languages. The study includes an analysis of the semantic meanings of homonyms, their use in context, and possible differences in syntactic features that may affect their interpretation and perception by native speakers of these languages. The purpose of the article is to id