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.

Interleukins (IL-2 and IL-4) are increased in asthmatics and were reported to induce resistance to steroid therapy in some patients who fail to get benefit from glucocorticoids when used in full dose and for long period of time. In this context, the present study was conducted on Iraqi patients to provide additional laboratory mean, beside the clinical diagnosis, for the decision whether the asthma is steroid sensitive or resistant by monitoring the level of immunoglobulins, complement proteins and interleukins among asthmatic patients (steroid sensitive or resistant) and the possible contribution of other factors like age, sex and environments in the development of steroid resistance. A total number of 55 asthmatics and 28 normal subjec

Aluminum oxide (ALO) was grafted by acrylic acid monomer (AlO-AM) and then, it was polymerized to produce alumina grafted poly(acrylic acid) (AlO-AP). The prepared AlO-AM and AlO-AP were characterized by Fourier-transform infrared, differential scanning calorimetry , thermogravemetric analyzer and particle size distribution. Adsorption equilibrium isotherms, adsorption kinetics and thermodynamic studies of the batch adsorption process were used to examine the fundamental adsorption properties of phenol (P) and p-chlorophenol (PCP). The experimental equilibrium adsorption data were analyzed by three widely used two-parameters Langmuir, Freundlich and DubininRadushkevich isotherms. The maximum P and PCP adsorption capacities based on t

Indole acetic acid (IAA) produced from F. oxysporum (F2) was purified by several steps included extraction by cold ethyl acetate ; Column chromatography using silica gel and TLC chromatography . The pure indole acetic acid (IAA) which produce by F. oxysporum (IAA) was tested by ultraviolet spectra at (200-300)nm ; and appear that the maximum absorbance at 229nm , the high performance liquid chromatography (HPLC) used to test the purity of the indole acetic acid and the results showed one peak at appearance time 3.822 min

Stable new derivative (L) Bis[O,O-2,3;O,O-5,6(carboxylic methyliden)]L-ascorbic acid was synthesized in good yield by the reaction of L-ascorbic acid with dichloroacetic acid with ratio (1:2) in presence of potassium hydroxide. The new (L) was characterized by 1H,13C-NMR, elemental analysis (C,H) and Fourier Transform Infrared (FTIR). The complexes of the ligand (L) with metal ion, M+2= (Cu, Co, Ni, Cd and Hg) were synthesized and characterized by FTIR, UV-Visible, Molar conductance, Atomic absorption and the Molar ratio. The analysis evidence showed the binding of the metal ions with (L) through bicarboxylato group manner resulting in six-coordinated metal ion.

The corrosion inhibiting properties of the new furan derivative 5-(furan-2-ylmethylsulfonyl-4-phenyl-2,4- dihydro [1,2,4] triazole-3-thione in acidic solution (1.0 M HCl) were explored utilizing electrochemical, surface morphology (AFM), and quantum chemical calculations approaches. The novel furan derivative 5-(furan-2-ylmethylsulfonyl-4-phenyl-2,4- dihydro [1,2,4] triazole-3-thione shows with an inhibitory efficiency value of 99.4 percent at 150 ppm, carbon steel corrosion in acidic medium is effectively inhibited, according to the results. The influence of temperature on corrosion prevention was studied using adsorption parameters and activation thermodynamics. The novel furan derivative creates a protective layer over the metallic surfa

The target of this study was to study the natural phytochemical components of the head (capsule) of Cynara scolymus cultivated in Iraq. The head (capsule) of plant was extracted by maceration in70% ethanol for 72 hours, and fractioned by hexane, chloroform and ethyl acetate. Preliminary qualitative phytochemical screening was performed on the ethyl acetate fraction for capsule was revealed the presence of flavonoid and aromatic acids. These were examined by (high -performance liquid chromatography) (HPLC diodarray), (high- performance thin-layer chromatography)(HPTLC).

Flavonoids were isolated by preparative layer chromatography and aromatic acid was isolated by preparative high-

I've been in this research preparation and diagnostic complexes mixed Kandat of Alcavaúan Alpiculan ion Althaaossianat with some metal ions has been reactive in ethanol solvent and distilled water by (1:1) and water complexes and lotions to the accounts of the metal in the complex

The Mannich base ligand was synthesized in an ethanol medium through a condensation reaction of 2-mercaptobenzimidazole and ciprofloxacin at room temperature. Subsequently, several metal complexes of this ligand were prepared. To characterize both the base ligand and the metal complexes, various techniques were employed, including elemental analysis, FT-IR spectroscopy, UV-Vis spectroscopy, molar conductivity measurements, magnetic moment determination, and melting point analysis. The results were shown that the metal complexes formed have the formula [Cr(L)2Cl2] Cl.H2O and [Rh(L)2(H2O)2] Cl3.H2O, where L= mannich base ligand. Based on spectroscopic analytical, coordination with metal ions involves the 'N' donor atom of mannich base