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 .

Low-Density-Parity-Check (LDPC) codes are a cornerstone for achieving robust error correction capabilities in 5G New Radio applications, significantly improving the reliability of data transmission across noisy and unpredictable wireless channels. Since an evaluation and discussion of the performance with channel coding is significantly absent in two-dimensional Index Modulation (IM)-Differential Chaos Shift Keying (DCSK) schemes. Therefore, in this study, the 5G new radio LDPC codes based generalized joint subcarrier-time index modulation DCSK system (5G NR-LDPC-GJSTIM-DCSK) is proposed, where 5G NR-LDPC codes are used as channel coding. The aim is to improve the system’s performance specifically across AWGN (additive white gauss

The stories of children in Iraq during the past two decades have received a number of important scientific studies. Despite tyranny of the historical study method on most of these studies, they have been and still are very important, because they have established a chronicle of this literary style that has been neglected and based not only on the academic level and serious in-depth university studies but also on the enclosed sight that doesn’t consider studied art as an innovation with its specificity and its typical technical components. While many of the public impressions and self-reflections contributed to the dominance of some of the provisions and concepts that were circulated as critical remarks and adopted by som

يصدر القضاء الدستوري احكامه على وفق اختصاصاته المتعددة ، وأخصها احكامه المعدمة للقوانين المخالفة للدستور ، لذا فإن ذاتية احكامه وصفاتها تمايزت عما سواها من الاحكام القضائية ، وامتازت عليها بخصائص العموم والالزام المطلق والبتات النهائي ؛ من هنا تقايست تلك الاحكام مع القواعد القانونية التي تسن بخصائص العموم والتجريد حتى باتت تنشر بالجريدة الرسمية ذاتها وأصبحت لا تقبل المطاعن التمييزية كونها مقترنة بقر

Abstract

Agricultural Bank is an important source of funding Specialist His role in lending to farmers, it imposes a great job in providing the necessary head for any developmental process in the agricultural sector money. The ACB of ancient Iraqi banks, and that because of its importance to the advancement of the national economy and contribute to the development and regulation of the economic sector through the support and the assignment of the Iraqi agricultural sector in various agricultural activities because it is responsible

for the process of granting agricultural loans to farmers bank.

The aim of the internal control in the agricultural banks to

Catalytic removal of the S-content from thiophene is a central step in efforts aiming to reduce the environmental burdens of transportation fuels. In this contribution, we investigate the hydrodesulfurization (HDS) mechanisms of thiophene (C4H4S) over γ-Mo2N catalyst by means of density functional theory (DFT) calculations. The thiophene molecule preferentially adsorbs in a flat mode over 3-fold fcc nitrogen hollow sites. The HDS mechanism may potentially proceed either unimolecularly (direct desulfurization) or via H-assisted reactions (hydrogenation). Due to a sizable activation barrier required for the first Csingle bondS bond scission of 54.6 kcal/mol, we predict that the direct desulfurization to contribute rather very insignificant

The notion of a Tˉ-pure sub-act and so Tˉ-pure sub-act relative to sub-act are introduced. Some properties of these concepts have been studied.