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.

2,2'-(1-(3,4-bis(carboxydichloromethoxy)-5-oxo-2,5-dihydrofuran-2-yl)ethane-1,2-diyl)bis(oxy)bis(2,2-dichloroacetic acid) a derivative of L-ascorbic acid was prepared by reaction of L-ascorbic acid with trichloroacetic acid (1:4) ratio, in the presence of potassium hydroxide. A series of new metal complexes of this ligand were prepared by a reaction with the chlorides of Cd(II), Co(II), Ni(II), Cu(II) and Zn(II). The new ligand and its complexes were identified by C.H.N., IR, UV-visible spectra, Thermogravimetric analysis (TGA), as well as 1H, 13C-NMR and Mass spectra for ligand L. The complexes were also identified by molar conductance, atomic absorption, magnetic susceptibility and X-ray diffraction for Cu (II) complex. FT-IR spectra

This paper deals with numerical study of the flow of stable and fluid Allamstqr Aniotina in an area surrounded by a right-angled triangle has touched particularly valuable secondary flow cross section resulting from the pressure gradient In the first case was analyzed stable flow where he found that the equations of motion that describe the movement of the fluid

The present study aimed to look for the differences in the oxidative stress status in sera and saliva samples of type 2 diabetic Iraqi patients with and without proliferative diabetic retinopathy. As well as to look for the possibility whether this status can be measured in saliva as an alternative sample to that of serum, hence to achieve that total oxidant status, total antioxidant status and oxidative stress index were measured in both sera and saliva samples of two groups of patients with type 2 diabetes mellitus and the healthy individuals. Upon the comparison between patients without proliferative diabetic retinopathy and the control sample the results showed presence of a significant increase (p < 0.05) of total oxidant st

The present work aims to study the efficiency of coagulation/ flocculation as 1st stage, natural gravity water filter or microfiltration (MF) as 2nd stage and nanofiltration (NF) technology as final stage for treatment of water of main outfall drain (MOD) for injection in Nasiriyah oil field. Effects of operating parameters such as coagulant dosage, speed and time of slow mixing step and settling time in the 1st stage were studied. Also feed turbidity and total suspended solids (TSS) in the 2

Batch reactive distillation was studied in packed bed column. Esterification of methanol with acetic acid to produce methyl acetate and water with homogenous sulfuric acid as a catalyst was considered. This system was chosen because the reaction is reversible and the boiling point of reactant and products are different.
The reaction was carried out with and without distillation column and shows that the reactive distillation is more efficient from the conventional process (reactor and then separation). The conversion of acetic acid and concentration of methyl acetate increase by (30.43% and 75.14%) respectively at the best condition (reflux ratio 2, feed mole ratio 2 and batch time 90 minute).
The influence of various parameters, s

MPEG-DASH is an adaptive bitrate streaming technology that divides video content into small HTTP-objects file segments with different bitrates. With live UHD video streaming latency is the most important problem. In this paper, creating a low-delay streaming system using HTTP 2.0. Based on the network condition the proposed system adaptively determine the bitrate of segments. The video is coded using a layered H.265/HEVC compression standard, then is tested to investigate the relationship between video quality and bitrate for various HEVC parameters and video motion at each layer/resolution. The system architecture includes encoder/decoder configurations and how to embedded the adaptive video streaming. The encoder includes compression besi

In this paper, series of new complexes of Manganese(II), Cobalt(II), Nickel (II) Cupper(II) Zinc(II), Cadmium(II) and Mercury (II) are prepared from the new ligand [2-(3-benzoylthioureido)-3-(-4- hydroxyphenyl) propanoic acid (BHP) derived from tyrosine and benzoylisothiocyanate .Chemical structures are obtained from their 1 H, 13CNMR spectra (for BHP), elemental microanalyses, molar conductance, FTIR, UV–Vis, magnetic susceptibility in addition to TGA/DTG and DSC analysis, the suggested geometry for all complexes was tetrahedral. The biological activity of BHP and its complexes has been extensively studied against two bacterial species Staphylococcus aurous (G+) and Escherichia coli (G-) by agar-well diffusion technique, where Mn(II), Co

Breast cancer (BC) is the most common malignant tumor in women and the leading cause of cancer deaths worldwide. This work was conducted to estimate the roles of oxidative stress, vitamin B12, homocysteine (HCY), and DNA methylation in BC disease progression. Sixty BC patients (age range 33–80 years) and 30 healthy controls were recruited for this study. Patients with BC were split to group 1 consisted of stage II BC women (low level), and group 2 consisted of patients in stages III and IV (high level). Malondialdehyde (MDA), glutathione peroxidase 3 (GPX3), HCY, and vitamin B12 levels in the study groups were measured. Also, the 5-methylcytosine (5mC) global DNA methylation levels were evaluated. The results showed a significant