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.

New Schiff bases derivatives [IV]a-e is prepared via condensation of Derythroascorbic acid with p-substituted aldehydes in dry benzene. To obtain these derivatives, the 5,6-O-isopropylidene-L-ascorbic acid[I] was chosen as starting material, compound prepared from the reaction of L-ascorbic acid as starting material. Compound[I] was prepared from the reaction of L-ascorbic acid with dry acetone in the presence of hydrogen chloride. The esterification of hydroxyl groups at C-2 and C-3 positions with excess ofethyl α –chloroacetate in the presence of sodium acetate produce acorresebonding ester [II] , which was condensed with hydrazine hydrate to give new hydrazide [III] . The new Schiff bases [IV]a-e were synthesized by reaction of acid h

The main aim of this paper is to study the application of Weyl module resolution in the case of two rows, which will be specified in the skew- partition (6, 6)/(1,1) and (6,6)/(1,0), by using the homological Weyl (i.e. the contracting homotopy and place polarization).

   on this research is to study the effect of nickel oxide substitution on the pure phases superconductor Tl_0.5Pb_0.5Ba₂Ca_n-1Cu_n-xNi_xO_2n+3-δ (n=3) where x=(0,0.2,0.4,0.6,0.8.and 1.0). The specimens in this work were prepared with used  procedure of solid state reaction with sintering temperature 850⁰C for 24 h .we used technical (4-prob)to calculated and the critical temperature T_c . The results of the XRD diffraction analysis showed that the structure for pure and doped phases was tetragonal with phases high-T_c phase (1223),(1212) and low-T_c phase (1202)  and add

Oil flow lines are used to transport oil and its derivatives from a well over long distances, and because oil wells produce other potentially corrosive products, such as carbon dioxide and Hydrogen sulfide, it is necessary to take methods to protect the pipeline from corrosion. One of these methods is the use of corrosion inhibitors in this study. Prepare 5-acetyl-2-anilino-4-dimethylaminothiazole and test it as a corrosion inhibitor on a sample of the Rumaila flow line at a constant temperature 25°C in (3.5%) NaCl and (3.5%) KCl solution in the absence and presence of different concentrations of inhibitor (0 mM, 0.01 mM, 0.03 M, 0.05 mM). by using liner polarization (Tafel slope). The inhibiter exhibited the best performance at hi

This research includes the synthesis of some new nucleoside analogues via 1,3-
dipolar cycloadditon reaction starting with 1,3,4,6- Tetra- O-benzoyl –2 – azido-2-
deoxy- β – D- fructofuranose (F3) which was prepared in three steps ,protection
(benzoylation ) , bromination and azotation ((F1-F3) from D- fructose as sugar
moiety while the base moiety , 2-substituted benzimidaole derivatives (A1-A5)
were synthesized by condensation of O-phenylenediamine with different aromatic
aldehyde .
Nucleophilic substitution of propargyl bromide with benzimidaole derivatives (gave
the N- substituted compounds (B1-B5) which were reacted with azido sugar through
1,3- dipolar cycloadditon reaction to give nucleoside analo

    Human urinary Adenosine-3',5'-cyclic monophosphate (cAMP) was studied in 90 normal healthy volunteers (49 males and 41 females) aged between (11 months -55 years), and 86 leukemia patients (48 males and 38 females) of four types (25 ALL, 28 AML, 14 CLL, 19 CML) aged between (11 months - 65 years). The study includes the following:- Extraction and purification of urinary cAMP from the interfering nucleotides, proteins, phosphates and pyrophosphates, by using Zinc sulphate –Barium hydroxide precipitation. The extracted cAMP was purified by using Dowax 50W-H+ hydrogen form column chromatography (1x5 cm). Identification of the purified cAMP, this was achieved by applying the following techniques: a- U.V analysis: -

Two series of Schiff Bases [VI]n and thiazolidin-4-one derivatives[VII]n were synthesized by many steps starting from cyclization of 4- hydroxyacetophenon with thiourea in iodine to yield 1,3-thiazole compound which was reacted with pentoxy bromide in anhydrous potassium carbonate to converted compound[II] and this reacted with Phenol to yield azo compound[III]. The azo compound reacted with ethyl chloro acetate in basic medium to get a new easter compound[IV] which is converted to their acid hydrazid[V]. The later compound condensation with n-alkoxy benzaldehyde to give new Schiff bases[VI]n . Imine group undergoes addition cyclization with thioglycolic acid to get thiazolidinone compounds[VII]n .Also, two new series of Schiff Bases [XII]n

 Two series of Schiff Bases [VI]n and thiazolidin-4-one derivatives[VII]n were synthesized by many steps starting from cyclization of 4- hydroxyacetophenon with thiourea in iodine to yield 1,3-thiazole compound which was reacted with pentoxy bromide in anhydrous potassium carbonate to converted compound[II] and this reacted with Phenol to yield azo compound[III]. The azo compound reacted with ethyl chloro acetate in basic medium to get a new easter compound[IV]  which is converted to their acid hydrazid[V]. The later compound condensation with n-alkoxy benzaldehyde to give new Schiff bases[VI]n . Imine group undergoes addition cyclization with thioglycolic acid to get thiazolidinone compounds[VII]n .Also, two new series of Schi

Small molecules drug conjugate mutual prodrug design  (SMDC) composed of folate and lethal agent conjugate, rigidly bonded via hydrophilic bridge and self immolative disulfide  bond   ;  represent new interesting approaches for cancer treatment , the component of SMDC intended  for targeting    folate receptor , along with greater conservation  of component until reaching  the target tumor tissue . The  designing and synthesis of compound VI and VIII derived from 6-Mercaptopurine (6-MP) and Methotrexate ( MTX) conjugate altogether as mutual prodrugs were  processed forward  successfully by multistep reaction  procedures , and by Thin Layer Chromatography (TLC) for