Nonlinear differential equation stability is a very important feature of applied mathematics, as it has a wide variety of applications in both practical and physical life problems. The major object of the manuscript is to discuss and apply several techniques using modify the Krasovskii's method and the modify variable gradient method which are used to check the stability for some kinds of linear or nonlinear differential equations. Lyapunov function is constructed using the variable gradient method and Krasovskii’s method to estimate the stability of nonlinear systems. If the function of Lyapunov is positive, it implies that the nonlinear system is asymptotically stable. For the nonlinear systems, stability is still difficult even though

أن إحدى اكبر مشاكل الصحة العالمية هي ظهور مقاومة الميكروبية للأدوية الشائعة لذلك هناك حاجة ملحة لمضادات جرثومية جديدة ذات نشاط أحيائي معزز .في هذا الدراسة, تم تحضير خمسة مشتقات جديدة من الكينولين  A,B,C,D  وEكمضادات جرثومية. تم فحص بنية المركبات المحضرة باستخدام  UV light , FTIR NMR  . تم استخدام طريقة الانتشار بالحفر في الطبق لاختبار الخصائص المضادة للبكتريا للمركبات المحضرة في المختبر ضد نوعين من البكتريا الموجبة

      Strong and ∆-convergence for a two-step iteration process utilizing asymptotically nonexpansive and total asymptotically nonexpansive noneslf mappings in the CAT(0) spaces have been studied. As well, several strong convergence theorems under semi-compact and condition (M) have been proved. Our results improve and extend numerous familiar results from the existing literature.

It is well known that drilling fluid is a key parameter for optimizing drilling operations, cleaning the hole, and managing the rig hydraulics and margins of surge and swab pressures. Although the experimental works represent valid and reliable results, they are expensive and time consuming. In contrast, continuous and regular determination of the rheological fluid properties can perform its essential functions during good construction. The aim of this study is to develop empirical models to estimate the drilling mud rheological properties of water-based fluids with less need for lab measurements. This study provides two predictive techniques, multiple regression analysis and artificial neural networks, to determine the rheological

Abstract Background: The emptied sheep’s ovarian follicles recently used as a container for spermatozoa during cryopreservation, it was found a proper carrier to cryopreserving spermatozoa in vapor-dependent cryopreservation. The aim of this study was to evaluate the effect of two periods of exposure to liquid nitrogen (LN2)vapor on the parameter of spermatozoa during cryopreservation in this technique. Method: The study was conducted on 30 semen samples from patients with oligozoospermia diagnosed by semen analysis according to the standard criteria of World Health Orgnization (WHO) 2010. Sheep’s ovarian follicles obtained from local slaughterhouse and prepared by slicing the ovaries and evacuating the follicular fluid and oocyt