Convergence analysis of implicit iterative algorithms for asymptotically nonexpansive mappings

In this paper, we consider the weak and strong convergence of an implicit iterative process with errors for two finite families of asymptotically nonexpansive mappings in the framework of Banach spaces. Our results presented in this paper improve and extend the recent ones announced by many others.     

Preparation of durable hydrophobic cellulose fabric from water glass and mixed organosilanes

Durable superhydrophobic cellulose fabric was prepared from water glass and n-octadecyltriethoxysilane (ODTES) with 3-glycidyloxypropyltrimethoxysilane (GPTMS) as crosslinker by sol-gel method. The result showed that the addition of GPTMS could result in a better fixation of silica coating from water glass on cellulose fabric. The silanization of hydrolyzed ODTES at different temperatures and times was studied and optimized. The results showed that silanization time was more important than temperature in forming durable hydrophobic surface. The durability of superhydrophobicity treatment was analyzed by XPS. As a result, the superhydrophobic cotton treated under the optimal condition still remained hydrophobic properties after 50 washing cycles.     

《数学实验》课程建设的认识与实践

我们认为 :数学实验 ,就是对数学进行折腾 .我们提出一些饶有趣味而又有深刻背景的问题 ,让学生尝试自己去解决 ,借助于计算机 ,自己动手去折腾 ,在折腾过程中学习 ,观察现象和结果 ,猜测和验证规律 ,尝试和体验数学的探索、发现和应用     

Comment on the paper: “Forced oscillation of certain neutral hyperbolic equations with continuous distributed deviating arguments” [Math. Comput. Modeling 49 (2009) 1211–1220]

In recent years, many results on oscillation criteria of second-order nonlinear neutral delay differential equations with distributed deviating argument have been obtained, but some of these criteria are incorrect due to a mistake in a crucial auxiliary result. We give two counterexamples.     

Characteristics of a vacuum switching contact based on bipolaraxial magnetic field

Axial magnetic field (AMF) contacts can increase the interruption capability of vacuum interrupters. Depending on the design, the principles of the local axial field arrangement are different. For unipolar arrangements the direction of the axial magnetic field is the same within the whole contact area. For bipolar arrangements, the polarity of the field changes once. In this paper investigations have been carried out to characterize a bipolar AMF contact system and to test its interruption performance. The influence of the bipolar AMF on the arc development and the thermal stress is described by high speed camera and contact surface pictures. In addition, three-dimensional AMF simulations have been performed by means of a finite-element program to estimate the influence of slots within the contact plates on the AMF performance. The high interruption capability of the bipolar AMF contact system has been verified in different test laboratories up to 12 kV/80 kA_RMS (symmetrical) and 36 kV/40 kA_RMS (including 40% DC) by three and single phase tests. The investigations are completed by measuring the post-arc current and the shield-potential during recovery period, both describing the switching behavior of the contact system     

Optimal Control of Variational Inequalities with Delays in the Highest Order Spatial Derivatives

In this paper, an optimal control problem for parabolic variational inequalities with delays in the highest order spatial derivatives is investigated. The well-posedness of such kinds of variational inequalities is established. The existence of optimal controls under a Cesari-type condition is proved, and the necessary conditions of Pontryagin type for optimal controls is derived.     

Silver-catalyzed decarboxylative cross-coupling of α-keto acids with alkenes giving approach to chalcones

A silver-catalyzed decarboxylative cross-coupling of α-keto acids with alkenes is reported. The method, with a wide range of substrate tolerance and mild operational conditions, can produce various chalcone derivatives in moderate to high yields from easily available starting materials.