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.

n this study new derivatives of Schiff bases (5-10) were synthesized from the new starting material 1 . Which has been synthesized by the reaction of (1 mol.) of dichloroacetic acid with two moles of morpholine, in the presence of potassium hydroxide, Ester derivatives 2 and 3 were synthesized by the reaction of 1 with methanol or ethanol respectively in the presence of sulphuric acid as catalyst . Compound 2 was also prepared from dimethylsulphate with high yield , 2 and 3 was used to synthesized 2,2-dimorpholinylacetohydrazide 4 via reaction with NH2NH2.H2O 80% .Imines (5-10) were synthesized via the reaction of 4 with appropriate aromatic aldehydes in the presence of G.A.A as a catalyst . Derivatives compounds (1-10) were identifie

The 3-parameter Weibull distribution is used as a model for failure since this distribution is proper when the failure rate somewhat high in starting operation and these rates will be decreased with increasing time .

In practical side a comparison was made between (Shrinkage and Maximum likelihood) Estimators for parameter and reliability function using simulation , we conclude that the Shrinkage estimators for parameters are better than maximum likelihood estimators but the maximum likelihood estimator for reliability function is the better using statistical measures (MAPE)and (MSE) and for different sample sizes.

Note:- n_s : small sample ; n_m=median sample

 

This work targeted studying organogel as a potential floating system. Organgel has an excellent viscoelastic properties, floating system posses a depot property.  Different formulations of 12-hydroxyoctadecanoic acid (HOA) in sesame oil were gelled and selecting F1, F3 and F5 HOA organogels for various examinations: tabletop rheology, optical microscopy, and oscillatory rheology studies. Also, the floating properties studies were conducted at in vitro and in-vivo levels. Lastly, the in-vitro release study using cinnarizine (CN) was to investigate the organogel depot property. Based on the results, the selected concentrations of HOA in sesame oil organogels showed temperature transitions fr

In this paper, the general framework for calculating the stability of equilibria, Hopf bifurcation of a delayed prey-predator system with an SI type of disease in the prey population, is investigated. The impact of the incubation period delay on disease transmission utilizing a nonlinear incidence rate was taken into account. For the purpose of explaining the predation process, a modified Holling type II functional response was used. First, the existence, uniform boundedness, and positivity of the solutions of the considered model system, along with the behavior of equilibria and the existence of Hopf bifurcation, are studied. The critical values of the delay parameter for which stability switches and the nature of the Hopf bifurcat

Five N-substituted poly diimides were prepared by two steps. First step was included the preparation of five N-substituted diamides by reaction of adipoyl chloride with different amines .The second step was involved reaction of diamides with poly acryloyl chloride to obtain five new poly diimides having different physical properties which may used in different applications.

Aspirin and clopidogrel are considered the most important oral platelets aggregation inhibitors. So it is widely used for treatment and prophylaxis of cardiovascular and peripheral vascular diseases related to platelets aggregation .In this study aspirin and clopidogrel were formulated together as floating bilayer tablet system. Three different formulas of 75 mg aspirin were prepared by wet granulation method as immediate release layer; different disintegrants used to achieve rapid disintegration. Formula with crosscarmellose as disintegrant achieve rapid disintegration was selected for preparation of bilayer tablet.

Different formulas of 75 mg clopidogrel were prepared as sustained release floating layer by wet granulation (effe

Background: The present study involved the following parts, the first part is evaluation of the levels of glycated hemoglobin(HbA1c), creatinine, uric acid(UA) and albumin in patients with diabetic nephropathy comparison with the group of healthy as a control group. The second part is the measurement and evaluation of oxidative stress represented in the malondihydehyde(MDA) as a biomarker of oxidative stress as well as the identification of vitamins C and E as an antioxidant in patients with diabetic nephropathy(DN) compared with the healthy group. Objective: The objective of this study is to estimate oxidative stress by calculate malondialdehyd as biomarker and evaluate some vitamins such as vit C and vit E as antioxidants in diabetic neph