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.

In this paper we prove the boundedness of the solutions and their derivatives of the second order ordinary differential equation x ?+f(x) x ?+g(x)=u(t), under certain conditions on f,g and u. Our results are generalization of those given in [1].

The aqueous extract of Citrullius colocynthis dried seeds (160 ?g/ml) was in vitro evaluated for its effect on phagocytic index (PI) and lymphocyte transformation index (LTI) of blood cells obtained from 30 apparently healthy blood donors (15 males and 15 females). The PI was further in vivo evaluated in cells of peritone, spleen and liver of mice treated with the extract at a dose of 0.64 mg/kg. The results revealed that in in vitro study, phagocytic cells treated with the extract showed a significant increased percentage as compared with untreated cells (60.0 vs. 44.1%). Phagocytes obtained from peritone (44.1 vs. 30.0%) and spleen (45.6 vs. 39.6 %) of treated and untreated mice behaved in a similar manner, while liver phagocytes showed n

This work was conducted to study the oxidation of phenol in aqueous solution using copper based catalyst with zinc as promoter and different carrier, i.e. γ-Alumina and silica. These catalysts were prepared by impregnation method.
The effect of catalyst composition, pH (5.6-9), phenol to catalyst concentration ratio (2-0.5), air feed rate (30-50) ml/s, stirring speed (400-800) rpm, and temperature (80-100) °C were examined in order to find the best conditions for phenol conversion.
The best operating conditions which lead to maximum phenol conversion (73.1%) are : 7.5 pH, 4/6 phenol to catalyst concentration, 40 ml/s air feed rate, 600 rpm stirring speed, and 100 °C reaction temperature. The reaction involved an induction period

This study was designed to investigate the hypoglycemic and hypolipidemic activity of aqueous green tea (GT) extract in normal and alloxan-induced diabetic rats. Forty adult male albino rats weighing 180-200 g were divided into four groups of 10 rats each: The first group was served as control; the second group was treated with GT (250 mg/kg b.w); the third group was affected by inducing experimental diabetes by intraperitonial injection of alloxan (150 mg/kg b.w); and the fourth group was affected by inducing diabetes and treated with GT (250 mg/kg b.w). Level of blood glucose and lipid profile [total cholesterol (TC), triglycerides (TG), high-density lipoprotein cholesterol (HDL-C), low density lipoprotein cholesterol (LDL-C) and ve

The present research was carried out to assess the toxic effect of oral administration of the aqueous extract of Nerium oleander leaves and flowers daily at doses of (25) mg/kg body weight for four weeks in mice. The toxicity of this plant parts was determined after two and four weeks by measuring the parameters of cytogenetic (mitotic index, micronucleus %), and serum levels of the hematological (RBC, Hb, WBC) and biochemical (GOT, GPT, ALT, AST) indexes in comparison with that of the control (normal saline), also clinical signs were determined. The results showed a significant decrease in mitotic index while an obvious raise was seen in micronucleus percentage in comparison with that of the control after the two periods of admini

Natural dye sensitized solar cell was prepared using strawberry and pomegranate dyes with anatase nanocrystalline titanium dioxide powder. A study of the optical properties of the two dyes, involving the absorption spectrum was determined in the visible region. I-V characteristics under illumination were performed. The results showed that the two prepared dye sensitized solar cells have acceptable values efficiency about (0.94 with Fill factor (45)) and (0.74 with Fill factor (44)) for strawberry and pomegranate dyes, respectively.

Recently emerging pandemic SARS CoV-2 conquered our world since December 2019. Continuous efforts have been done to find out effective immunization and precise treatment stetratigies A way from therapeutic options that were tried in SARS CoV-2, an increased attention is directed to predict natural products and mainly phytochemicals as collaborative measures for this crisis. In this review, most of the mentioned compounds specially flavonoids (biacalin, hesperidin, quercetin, luteolin,, and phenolic (resveratrol, curcumin, and theaflavin) exert their effect through interfering with the action of one or more of this proteins (spike protein, papain like protease, 3 chymotrypsin like cysteine protease, and RNA dependent RNA 

In this paper, we study the growth of solutions of the second order linear complex differential equations  insuring that any nontrivial solutions are of infinite order. It is assumed that the coefficients satisfy the extremal condition for Yang’s inequality and the extremal condition for Denjoy’s conjecture. The other condition is that one of the coefficients itself is a solution of the differential equation .

في البداية اود الاشارة الى ان فهم حقيقة الازمة هو ذو جانب فني يتعلق بالجينات الوراثية لنظام يملك في احيناته قدرة عالية على تفريخ المشتقات. هذا النظام الذي يزداد عقما وتدميرا يزداد قدرة على خلق النقود الائتمانية/المشتقات، وكلما اقتربنا اكثر من فهم هذا الجانب كلما اسقطت في ايدينا تلك التوصيفات الاكاديمية الجاهزة في نقص الرقابة والاشراف، تركيز المخاطر،....الخ التي تناولتها الكتابات الشائعة في معظم طروحات