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.

1-(4-amino-3-(benzo[d]thiazol-2-yldiazenyl)phenyl)ethanone has been synthezied by reaction the diazonium salt of 2-aminobenzothiazole with 4-aminoacetophenone. Specroscopic studies ( FTIR,UV-Vis, 1H and 13CNMR) and microelemental analysis (C.H.N.S.O) are use to identified of the azo ligand. Metal chelates of some transition metals were performed as well depicted. Complexes were identified using atomic absorption of flame, elemental analysis, infrared and UV-Vis spectral process as well conductivity and magnetic quantifications. Nature of compounds produced have been studied followed the mole ratio and continuous contrast methods, Beer's law followed during a concentration scope (1×10-4 - 3×10-4 mol/L). height molar absorbtivity of compoun

Since the introduction of the HTTP/3, research has focused on evaluating its influences on the existing adaptive streaming over HTTP (HAS). Among these research, due to irrelevant transport protocols, the cross-protocol unfairness between the HAS over HTTP/3 (HAS/3) and HAS over HTTP/2 (HAS/2) has caught considerable attention. It has been found that the HAS/3 clients tend to request higher bitrates than the HAS/2 clients because the transport QUIC obtains higher bandwidth for its HAS/3 clients than the TCP for its HAS/2 clients. As the problem originates from the transport layer, it is likely that the server-based unfairness solutions can help the clients overcome such a problem. Therefore, in this paper, an experimental study of the se

    The Atoms in Molecules (AIM) analysis for triosmium cluster, which contains trihydridede, carbon, carbonyl and 2-methylbenzothiazolide ligands, [Os₃(µ-H)₃(µ³-ɳ²-CC₇H₃(2-CH₃)NS)(CO)₈] is reported. Bonding features in this cluster has been analyzed based on QTAIM ("Quantum Theory of Atoms in Molecules") in this work. The topological indices derived from electron density of relevant interactions in triosmium compound have been studied. The major interesting point of the AIM analyses is that the core of part (Os₃H₃) reveals the absence of any critical points and bond paths connecting any pairs of O

A novel Schiff base (SB) ligand, abbreviated as HDMPM, resulted from the condensation of 2-amino-4-phenyl-5-methyl thiazole and 4-(diethylamino)salicyaldehyde, and its metal complexes with [Co(II), Cu(II), Ni(II), and Zn(II)] ions in high yield were formed. The physico-chemical techniques such as elemental analysis, molar conductance, IR, 1H and 13C NMR, mass spectroscopy, and electronic absorption studies were utilized to characterize the synthesized compounds. The studied compounds were examined for their possible anticancer activity against a number of human cancerous cell lines, including A549 lung carcinoma, HepG2 liver cancer, HCT116 colorectal cancer, and MCF-7 breast cancer cell lines, with doxorubicin serving as the standard. The s

The optical properties for the components CuIn(SexTe1-x)2 thin films with both values of selenium content (x) [0.4 and 0.6] are studied. The films have been prepared by the vacuum thermal evaporation method with thickness of (250±5nm) on glass substrates. From the transmittance and absorbance spectra within the range of wavelength (400-900)nm, we determined the forbidden optical energy gap (Egopt) and the constant (B). From the studyingthe relation between absorption coefficient (α) photon energy, we determined the tails width inside the energy gap.
The results showed that the optical transition is direct; we also found that the optical energy gap increases with annealing temperature and selenium content (x). However, the width of l

This book includes four main chapters: 1. Indefinite Integral. 2. Methods of Integration. 3. Definite Integral. 4. Multiple Integral. In addition to many examples and exercises for the purpose of acquiring the student's ability to think correctly in solving mathematical questions.

The operating characteristics of optoelectronic devices depend critically on the properties physical of the constituent materials, interesting compound has been focused on this research formed from group III and V of the periodic table. Thin film n-InSb heterjuntion were successfully fabricated on p-Si substrates by thermal evaporation technique at different annealing temperature (as prepared, 400,500,600) °C. The effect of annealing temperature on the structural, surface morphology, optical and optoelectronic properties of InSb films were investigated and studied. The crystal structure of the film was characterized by X-ray diffraction and techniques. AFM techniques inspect the surface morphology of InSb films, the study presented the val