New Oscillatory Theorems for Third-Order Nonlinear Delay Dynamic Equations on Time Scales

This paper is concerned with the oscillatory properties of the third-order nonlinear delay dynamic equations of the form??on time scales , where ?is a quotient of odd positive integers. Applying the inequality technique we present two new sufficient conditions which ensure that every solution of equations is oscillatory or converges to zero. The results obtained improve and complement some known results in the literature.

New Oscillation Criteria for the Second Order Nonlinear Differential Equations with Damping

In this paper, we are concerned with a class of second-order nonlinear differential equations with damping term. By using the generalized Riccati technique and the integral averaging technique of Philos-type, two new oscillation criteria are obtained for every solution of the equations to be oscillatory, which extend and improve some known results in the literature recently.

The Legends of Celestial Master Zhang and Jataka Tales

道教的张天师传说与佛教的佛本生故事均以两种宗教信奉的神圣偶像为中心人物来编织故事,都与本国的民间口头叙事有密切关联。二者因植根于不同的文化土壤而风格迥异:首先,佛本生故事通过虚构前生世界,将佛陀化为各种角色以展现其不凡品格,寄寓佛教义理;张天师传说则以张天师降妖除魔、护佑百姓为主题。其次,佛本生故事由佛教徒按照固定的程式将现成的民间故事简单改造而来;张天师传说则渊源于中国古代的"神仙传",由中国近现代民众的口头鲜活叙事构成。