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.

          Using sodium4-((4,5-diphenyl-imidazol-2-yl)diazenyl)-3-hydroxynaphthalene-1-sulfonate (SDPIHN) as a chromogenic reagent in presence of non-ionic surfactant (Triton x-100) to estimate the chromium(III)  ion if the wavelength of this reagent 463 nm to form a dark greenish-brown complex in wavelength 586 nm at pH=10,the complex was stable for longer than 24 hours. Beer's low, molar absorptivity 0.244×10⁴L.mol^-1.cm^-1, and Sandal's sensitivity 0.021 µg/cm² are all observed in the concentration range 1-11 µg/mL. The limits of detection (LOD) and limit of quantification (LOQ), respectively, were 0.117 µg/mL and 0.385µg/mL. (mole ratio technique, job's method) were employed to

This study develops a systematic density functional theory alongside on-site Coulomb interaction correction (DFT + U) and ab initio atomistic thermodynamics approachs for ternary (or mixed transitional metal oxides), expressed in three reservoirs. As a case study, among notable multiple metal oxides, synthesized CoCu2O3 exhibits favourable properties towards applications in solar, thermal and catalytic processes. This progressive contribution applies DFT + U and atomistic thermodynamic approaches to examine the structure and relative stability of CoCu2O3 surfaces. Twenty-five surfaces along the [001], [010], [100], [011], [101], [110] and [111] low-Miller-indices, with varying surface-termination configurations were selected in this study.

Leucine aminopepotidase (LAP)[EC:3.4.11.1] activity has been assayed in (50) serum samples of patients with diabeties naphrophathy D.N (non-insulin dependent diabetic (NIDD) , and (50)serum sample of healthy individuals without any clinically detectable diseases have been as control group. The aim of this study is to measure leucine aminopeptidase activity and partially purifying the enzyme from sera of patients with diabetes nephropathy The results of this study revealed that Leucine aminopeptidase (LAP) activity of nephropathy patient’s serum shows a high signifiacant increase (p < 0.001) compared to that of the healthy subjects.LAP was purified from the serum of patients with diabetes nephropathy by dialysis and gel filtration (Se

A new set of metal complexes by the general formula [M(C)2(H2O)2]Cl2 has been prepared through the interaction of the new Ligand [N1, N4-bis(4-chlorophenyl)succinamide] (C) derived from succinyl chloride with 4-Chloroaniline with the transition metal ions Mn(II), Co(II), Ni(II), Hg(II), Cu(II) and Cd(II). Compounds diagnosed by TGA, 1 H, 13CNMR and Mass spectra (for (C)), Fourier-transform infrared and Electronic spectrum, Magnetic measurement, molar conduct, (%M, %C, %H, %N). These measurements indicate that (C) is associated with the metal ion in a bi-dentate fashion by nitrogen atoms (the amide group) and the octahedral composition of these complexes is suggested. The anti-bacterial action of the compounds towards three types of bacteria

A group of derivatives for compounds 2-Amino-3-carboxy-4,5,6,7-tetra hydrobenz -othiophene bearing different heterocyclic moieties such as Schiff bases. B-Lactum, 4-thiazolidinone.1,3-oxazepan. The newly synthesized derivatives have been supported by spectral data FT-IR, H¹-NMR. All the synthesized compounds were screened for their antimicrobial activities against gram-positive and gram-negative bacteria as reference.

New simple and sensitive spectrophotometric methods for the determination of paracetamol in aqueous medium were developed. The first method is based on coupling of paracetamol with p-amino-2-hydroxy sodium benzoate (AHB) in the presence of sodium periodate, as oxidizing agent, to form a brownish-orange compound which shows a λmax at 470 nm. The molar absorptivity (εmax) of the colored product was found to be (3371) l. mole1. cm-1 and Sandel’s index 0.0449 μg. cm-2. The method follows Beer’s law in the concentration range of 12.5-500.0 μg of paracetamol in a final volume of 25 ml (0.5-20.0) μg. ml-1 with relative standard deviation percent (RSD%) ranged between 0.26-4.71% and accuracy, expressed by recovery percent, 95-106% for five

Salicylaldehyde was react with 4-amino-2,3-dimethyl-1-phenyl-3-pyrazoline-5-on to produce the Schiff base ligand 2,3-dimethyl-1-phenyl-4-salicylidene-3-pyrazoline-5-on (L). The prepared ligand was identified by Microelemental Analysis, and FT.IR, UV-Vis spectroscopic techniques. A new complexes of Fe(III),Co(II),Ni(II),Cu(II),Ce(III) and Pb(II) with mixed ligands of dithizone (DTZ) and Schiff base were prepared in aqueous ethanol with a 2:2:1 M:L:DTZ. The prepared complexes were characterized using flame atomic absorption, (C.H.N) Analysis, FT.IR and UV-Vis spectroscopic methods as well as magnetic susceptibility and conductivity measurements. In addition biological activity of the ligands and complexes against two selected type of bacteria

2- amino -5- thiol-1,3,4- thiadiazole (S1) was prepared by cyclic locking of thiosemicarbazide in the presence of anhydrous sodium carbonate and CS2. diazotization of (S1) compound gave diazonium salt (S2) that reacts with different activated aromatic compounds to get the following azo compounds ,2 [(4- aminophenyl) diazenyl ] 1,3,4- thiazdiazole-5- thiol (S3) ,2-[4-amino- 1-naphthyl diazenyl] -1,3,4 – thiazdiazole-5-thiol (S4) , 3-amino-4-[(5- mercapto -1,3,4- thiadiazole -2-yl) diazenyl ] phenol(S5) ,1-[(5-mercapto-1,3,4-thiadiazole-2-yl) diazenyl] -2-naphthol (S6) , 5-{[4-(dimethylamino) phenyl] diazenyl}-1,3,4-thiadiazole-2- thiol(S7) ,5-{[4-(diethylamino) phenyl] diazenyl}-1,3,4- thiadiazole-2- thiol(S8) ,2- amino-5-[(5-mercapto-1,3

One of the most difficult tasks in modern medical societies is the process of identifying a cure for many infectious diseases caused by drug-resistant microbes. Therefore, it has become necessary to discover new compounds that work in this regard. The currently prepared Schiff base, derived from thiazole, has a biological activity against bacteria and biofilms and its activity increases when it is associated with copper, zinc and platinum ions and forms metal complexes. This study highlights the synthesis and evaluation of novel biological compounds as inhibitors of bacterial growth and biofilms. A three newly complexes are resulting from the reaction of a new Schiff base ligand (LC) with metal ions (Zn, Cu, Pt). The new ligand (LC)