Embedding 5-cycle systems into pentagon triple systems

We show that the spectrum for pentagon triple systems is the set of all n≡1,15,21 or . We then construct a 5-cycle system of order 10n+1 which can be embedded in a pentagon triple system of order 30n+1 and also construct a 5-cycle system of order 10n+5 which can be embedded in a pentagon triple system of order 30n+15, with the possible exception of embedding a 5-cycle system of order 21 in a pentagon triple system of order 61.     

Dynamic feedback control for cycle slipping in a phase-controlled system

This paper concerns the problem of cycle slipping for continuous phase-controlled systems with periodic nonlinearity. The number of slipped cycles is an important property in the transient mode of such nonlinear systems. On the basis of the Yakubovich–Kalman lemma, linear matrix inequality (LMI) characterizations are derived for the number of slipped cycles of such systems and an efficient way of estimating the number is proposed by solving a generalized eigenvalue minimization problem. Furthermore, by virtue of these results, a dynamic output feedback controller is designed to guarantee the nonexistence of cycle slipping. As a result, the transient performance of phase-controlled system is improved. A concrete application to the phase-locked loop shows the applicability and validity of the proposed approach.     

Cm□Cn的支撑树的一些性质

积图G1□G2是一个以笛卡儿积V(G1)×V(Gt)作为其点集．其中点(u,v)点(x,y)相邻当且仅当u=v且v与y在G2中相邻,或者v=y且u与z在G2相邻．证明了对图Cm□Cn的任意支撑树T,其中m和n不全为偶数,总存在一条Cm□CnT之外的边,添加到T上形成一个长度至少为m n-1的圈．这解决了陈(Dis-creteMathemstics 287(2004)11-15)给出的一个公开问题．     

Weakly distance-regular digraphs

We introduce the concept of weakly distance-regular digraph and study some of its basic properties. In particular, the (standard) distance-regular digraphs, introduced by Damerell, turn out to be those weakly distance-regular digraphs which have a normal adjacency matrix. As happens in the case of distance-regular graphs, the study is greatly facilitated by a family of orthogonal polynomials called the distance polynomials. For instance, these polynomials are used to derive the spectrum of a weakly distance-regular digraph. Some examples of these digraphs, such as the butterfly and the cycle prefix digraph which are interesting for their applications, are analyzed in the light of the developed theory. Also, some new constructions involving the line digraph and other techniques are presented.     

A counterexample to the bipartizing matching conjecture

The bipartizing matching conjecture (BMC) is a rather new approach to the nowhere zero 5-flow conjecture (NZ5FC) and the cycle double cover conjecture (CDCC). We show that the BMC is wrong in its actual version by constructing a counterexample. The construction arises from the investigation of the problem to cover the vertices of a graph by two induced Eulerian subgraphs. Finally, we state a modified version of the BMC which has the same impact on the NZ5FC and CDCC.     

花瓣状微球MoS_2/石墨烯复合材料的制备及其电化学性能

采用有利于二维层状结构形成的L-半胱氨酸作为硫源,钼酸钠作为钼源,制备聚乙烯基吡咯烷酮(PVP)辅助水热合成花瓣状微球形貌的MoS2/还原氧化石墨烯复合电极材料(PVP-MoS2/RGO).X射线衍射(XRD)及透射电子显微镜(TEM)证实,经过PVP的适量添加,MoS2有序堆垛结构的片层数目明显减少.扫描电子显微镜(SEM)显示,添加适量PVP的MoS2/石墨烯材料具有分散性更好的花瓣状微球形貌.上述的少层有序堆垛结构及复合材料的良好分散性缩短了MoS2中锂离子的嵌入/脱出路径,使其具有更高的容量、循环稳定性和倍率性能.     

Moments of Additive Functions on Random Permutations

We obtain upper and lower bounds for the power moments of additive functions on random permutations. The main ideas of proofs have been originated in probabilistic number theory.      

圈布尔矩阵类的幂敛指数集

在布尔运算下, 布尔矩阵A的幂敛指数和周期分别是使A^k=A^k+p成立的最小非负整数k和最小正整数p. 人们对周期的认识已经相当完善.给定满足一个不等式的正整数n和s, 利用组合分析确定了有向图含至少一个s -圈的n×n布尔矩阵的幂敛指数可以取得的数值.