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.

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

Complexes of Au(III) ,Pd (II) , Pt (IV ) and Rh(III) with S – propynyle -2- thiobenzimidazole (BENZA) have been prepared and characterized by IR and UV- Visible spectral methods in addition to magnetic and conductivity measurements and micro – elemental analysis (CHN).The probable structures of the new complexes have been suggested.

Acid dissociation constants of some Schiff bases derived from 4, 6-dimethyl 2-amino pyrimidine of the type (1) in 50% V/V dioxane-water mixture in 0.003M KCl, at three different temperatures were determined potentiometrically. The thermodynamic energies were calculated and a good linear correlation was obtained between pKa and IR OH. Stretching frequencies.

A series of new 2-quinolone derivatives linked to benzene sulphonyl moieties were performed by many steps: the first step involved preparation of different coumarins (A1,A2) by condensation of different substituted phenols with ethyl acetoacetate. The compound A1 was treated with nitric acid to afford two isomers of nitrocoumarin derivatives (A3) and (A4). The prepared compounds (A2, A3) were treated with hydrazine hydrate to synthesize different 2-quinolone compounds (A5,A6) while the coumarin treated with different amines gave compounds (A7,A8). Then the synthesized 2-quinolone compounds (A5-A8) treated with benzene sulphonyl chloride to afford new sulfonamide derivatives (A9-A12). The synthesized compounds were characterized by FT-IR, 1H

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.

Nitrogen-comprising heterocyclic compounds and their derivatives have empirically been invaluable as therapeutic agents. Fundamentally, 4-chloro-6-nitro-2-amino-1,3-benzothiazole 1 was synthesized via bromination of 2-chloro-4-nitro aniline with ammonium thiocyanate. This new heterocyclic haloorganoamino-1,3-benzothiazole derivative, was a starting material, which condensed and tethered with three different aromatic aldehyde pendant arm in presence of ethanol and glacial acetic acid isolating an interesting sequence of tridentate Schiff bases 2-4. These compounds were used for complexation reactions in 1:1 (metal: ligand) stoichiometry to obtain heteroleptic Al(III), Ni (II) and K(I) benzothiazole chelat

A simple chemistry method approach was used to synthesise new ligand derivate from L-ascorbic acid and its complexes. All of them were water-soluble and are used quite extensively in the medical and pharmaceutical fields. This study synthesised the new ligand derivative from L-ascorbic acid-base using the following steps: A 5,6-O-isopropylidene-L-ascorbic acid was prepared by reacting dry acetone with L-ascorbic acid followed by reacting it with trichloroacetic acid to yield [chloro(carboxylic)methylidene]-5,6-O-isopropylidene-L-ascorbic acid in the second stage. In the third stage, the derivative was reacted with (methyl(6-methyl-2-pyridylmethyl)amine to create a new ligand (ONMILA). This novel ligand was identified using a number

الوصف A simple chemistry method approach was used to synthesise new ligand derivate from L-ascorbic acid and its complexes. All of them were water-soluble and are used quite extensively in the medical and pharmaceutical fields. This study synthesised the new ligand derivative from L-ascorbic acid-base using the following steps: A 5, 6-O-isopropylidene-L-ascorbic acid was prepared by reacting dry acetone with L-ascorbic acid followed by reacting it with trichloroacetic acid to yield [chloro (carboxylic) methylidene]-5, 6-O-isopropylidene-L-ascorbic acid in the second stage. In the third stage, the derivative was reacted with (methyl (6-methyl-2-pyridylmethyl) amine to create a new ligand (ONMILA). This novel ligand was identified using