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.

A series of heterogeneous basic catalysts of CaO, MgO and CaMgO₂ at different calcination temperature were synthesized via solution combustion method. Different characterization techniques have been carried out to investigate the structure of the produced catalysts i.e. X-ray diffraction (XRD), particle size analyzer, morphology by atomic force microscope (AFM) and reflection using UV-VIS diffuse reflectance spectra. The particles size analyzer revealed that the mixed oxide catalysts calcined at different calcination temperature possess smaller nano size particles compared to pure CaO. Moreover, the energy band gap was calculated based on the results of diffuse reflectance spectra. The energy band gap was redu

The novel heterocyclic organozinc compounds were prepared from the reaction of diazonum salt cytosine zinc chloride with thymol and vanilin as coupler components. The prepared compounds were characterized by elemental analysis and UV-Vis, FTIR and 1HMNR spectroscopic techniques. The biological activity was also studied for all prepared compounds. 

الوصف New complexes of Cu (ll), Ni (II)„Co (II), and Zn (ll) with 2-amino-5-p-Flouro Phenyl 1, 3, 4-Thiadiazole have been synthesized. The products were isolated, studied and characterized by physical measurements, ie,(FT-IR)„UV-Vis and the melting points were determined. The new Schiff base (L) has been used to prepare some complexes. The prepared complexes were identified and their structural geometry were suggested

Objective: Matrix tablet approach is one of the delivery systems intended for poorly water-soluble drugs, like candesartan cilexetil (CC). CC is a class II drug used for the treatment of hypertension. Methods: Matrix tablets from (F1x to F18z) were prepared in the presence of β‑cyclodextrin. Matrix tablet formulation ensures control release of the drug and higher dissolution by β‑cyclodextrin. Fourier transform infrared spectroscopy (FTIR), and differential scanning calorimetry (DSC) were used to study compatibility. Results: The angle of repose determination showed good flow for most of the formulas, besides having good compressibility. Weight variation test for all formulas showed accepted value. Drug content measurement sho

Therapeutically and prophylactically using Microspheres containing doxycycline isolated from shell of shrimp. Low molecule weight poly lactic acid was prepared. In this study, Poly lactic acid (PLA)/ poly vinyl alcohol (PVA)/poly ethyleneglycol(PEG) loading doxycycline blend solutions was prepared. Also Poly lactic acid (PLA)-Tannin blend via solvent evaporation method was prepared. Microspheres of chitosan/gelatin microsphere loading doxycycline was prepared by emulsion crosslinking technique. Both microsphere and blends were characterized by Fourier transform infrared (FTIR) spectrophotometer. The FTIR spectra were shown distinguish bands. The in vitro release of doxcycline from its matrix at pH 7 was studied. The prophylactic

Bismuth oxide nanoparticle Bi2O3NPs has a wide range of applications and less adverse effects than conventional radio sensitizers. In this work, Bi2O3NPs (D1, D2) were successfully synthesized by using the biosynthesis method with varying bismuth salts, bismuth sulfate Bi2(SO4)3 (D1) or bismuth nitrate. Penta hydrate Bi(NO3)3.5H2O (D2) with NaOH with beta-vulgaris extract. The Bi2O3NPs properties were characterized by different spectroscopic methods to determine Bi2O3NPs structure, nature of bonds, size of nanoparticle, element phase, presence, crystallinity and morphology. The existence of the Bi2O3 band was verified by the FT-IR. The Bi2O3 NPs revealed an absorption peak in the UV-visible spectrum, with energy gap Eg = 3.80eV. The X-ray p

  The work is concerned with the characterization of as cast films of neat and UV-stabilized nylon 6,6 by employing FTIR measurements. Band assignment is made for neat and UVstabilized nylon 6,6 using FTIR spectra confirm their molecular structure. UV-stabilizer added to nylon 6,6 has caused reduction in the absorbance of the vibrational bands and thus stabilizes the behavior of the polymer in the end and uses specially in harsh environment.

Objective: Matrix tablet approach is one of the delivery systems intended for poorly water-soluble drugs, like candesartan cilexetil (CC). CC is a class II drug used for the treatment of hypertension. Methods: Matrix tablets from (F1x to F18z) were prepared in the presence of β‑cyclodextrin. Matrix tablet formulation ensures control release of the drug and higher dissolution by β‑cyclodextrin. Fourier transform infrared spectroscopy (FTIR), and differential scanning calorimetry (DSC) were used to study compatibility. Results: The angle of repose determination showed good flow for most of the formulas, besides having good compressibility. Weight variation test for all formulas showed accepted value. Drug content measurement sho