Serendipity Virtual Elements for General Elliptic Equations in Three Dimensions

The authors study the use of the virtual element method (VEM for short) of order k for general second order elliptic problems with variable coefficients in three space dimensions. Moreover, they investigate numerically also the serendipity version of the VEM and the associated computational gain in terms of degrees of freedom.     

CuCo2S4系统的掺杂与超导电性

尖晶石型CuM2S4(M=Co，Rh，Ir)族硫化物中，CuRh2S4为4．7K的超导体，CuIr2S4在230K经历金属-绝缘体相变，用Zn替代Cu后可成为超导体，CuCo2S4是否具有超导电性目前仍有争议．本研究了CuCo2S4及其掺杂体系的成相及其电、磁性质，表明单相CuCo2S4在1．8K以上不超导，而在Cu1 xCo2-xS4和CoS2的复相样品中观察到～3．5K的超导转变．另外少量Zn替代Cu引入杂相，在样品中未能观察到超导电性．     

Backstepping synchronization of uncertain chaotic systems by a single driving variable

In this paper a parameter observer and a synchronization controller are designed to synchronize unknown chaotic systems with diverse structures. Based on stability theory the structures of the observer and the controller are presented. The unknown Coullet system and Rossler system are taken for examples to demonstrate that the method is effective and feasible. The artificial simulation results show that global synchronization between the unknown Coullet system and the Rossler system can be achieved by a single driving variable with co-operation of the observer and the controller, and all parameters of the Coullet system can be identified at the same time.     

Uniqueness of Limit Cycles in a Predator-Prey Model with Sigmoid Functional Response

In this paper, we prove that a predator-prey model with sigmoid functional response and logistic growth for the prey has a unique stable limit cycle, if the equilibrium point is locally unstable. This extends the results of the literature where it was proved that the equilibrium point is globally asymptotically stable, if it is locally stable. For the proof, we use a combination of three versions of Zhang Zhifen''s uniqueness theorem for limit cycles in Li$\acute{\rm e}$nard systems to cover all possible limit cycle configurations. This technique can be applied to a wide range of differential equations where at most one limit cycle occurs.     

单位球上不同 Bergman空间之间的广义 Ces\`{a}ro 算子

In this paper,we obtain the characterizations on μ for（p,q）-φCarleson measure,and discuss the boundedness（and compactness） of the extended Cesaro operators T g between different weighted Bergman spaces as some application.