The investigation of determining solutions for the Diophantine equation  over the Gaussian integer ring for the specific case of  is discussed. The discussion includes various preliminary results later used to build the resolvent theory of the Diophantine equation studied. Our findings show the existence of infinitely many solutions. Since the analytical method used here is based on simple algebraic properties, it can be easily generalized to study the behavior and the conditions for the existence of solutions to other Diophantine equations, allowing a deeper understanding, even when no general solution is known.

‎تم في هذه الدراسة ، تزيين ‏رقائق أكسيد الجرافين (‏GO‏) بجسيمات ‏كوبلتيت النيكل النانوية ‏NiCo2O4‎‏(‏NC‏) عن طريق الترسيب في ‏الموقع ، وتم استخدام المتراكب ‏المحضر (‏NC: GO‏) كسطح ماز لإزالة ‏صبغة الميثيل الخضراء ( ‏MG‏) من ‏المحاليل المائية. تم التحقق من ‏التغطية الناجحة لأوكسيد الجرافين ‏بجزيئات كوبلتيت النيكل النانوية ‏‏(‏NC‏) باستخدام دراسات ‏FT-IR‏ وحيود ‏الأشعة السينية (‏XRD‏). كانت أحجام  ‏الجسيم

Background: Interleukin-6 (IL-6) is a cytokine that has several functions, including stimulating growth and inhibiting cell death. It has the potential to operate as a biomarker for the accurate prediction of disease severity and activity, platelets-rich plasma was used in the treatment of oral lichen planus and can change the salivary IL-6 level.

Objectives: To study the clinical outcome of intralesional platelets-rich plasma in patients with oral lichen planus and to measure salivary IL-6 levels before and after the treatment with platelets-rich plasma were the aims of this study.

Subjects and Methods: In this clinical trial, for each patient a standardi

This paper proposes a compact, plasmonic-based 4 × 4 nonblocking switch for optical networks. This device uses six 2 × 2 plasmonic Mach-Zehnder switch (MZS), whose arm waveguide is supported by a JRD1 polymer layer as a high electro-optic coefficient material. The 4 × 4 switch is designed in COMSOL environment for 1550 nm wavelength operation. The performance of the proposed switch outperforms those of conventional (nonplasmonic) counterparts. The designed switch yields a compact structure ( 500 × 70   µ m 2 ) having V π L = 12   V · µ m , 1.5 THz optical bandwidth, 7.7 dB insertion loss, and −26.5 dB crosstalk. The capability of the switch to route 8 × 40 Gbps WDM signal is demonstrated successfully.

What is important about this study is whether there is a relationship between the ability to balance and beating overwhelming for the Iraqi national team volleyball? The study aims to identify the percentage of the equilibrium contribution and its variables with the accuracy of the skill of beating the high spike Diagonal center (4) in the players. In the national volleyball team season (2016-2017), the researchers used the descriptive approach in the style of associative relationships to suit the problem of research. The research community included all the players specialized in the high beating of the Iraqi national team applicants in the ball The researchers concluded that the equilibrium variables contributed accurately and quickly to t