Common hypercyclic vectors for the conjugate class of a hypercyclic operator

Given a separable, infinite dimensional Hilbert space, it was recently shown by the authors that there is a path of chaotic operators, which is dense in the operator algebra with the strong operator topology, and along which every operator has the exact same dense Gδ set of hypercyclic vectors. In the present work, we show that the conjugate set of any hypercyclic operator on a separable, infinite dimensional Banach space always contains a path of operators which is dense with the strong operator topology, and yet the set of common hypercyclic vectors for the entire path is a dense Gδ set. As a corollary, the hypercyclic operators on such a Banach space form a connected subset of the operator algebra with the strong operator topology.     

Note on the iterative methods for computing the generalized inverse over Banach spaces

In this paper, we construct iterative methods for computing the generalized inverse A over Banach spaces, and also for computing the generalized Drazin inverses a^d of Banach algebra element a. Moreover, we estimate the error bounds of the iterative methods for approximating A or a^d. Copyright © 2011 John Wiley & Sons, Ltd.     

Matrix elements of doubly degenerate vibrations and the Herzberg-Teller series

The non-zero terms in doubly degenerate vibrations in the Herzberg-Teller series are discussed and simplified formulae for the matrix elements for transitions between the degenerate l-components of such vibrational levels in upper and lower electronic states are given, with the emphasis on the change of vibrational frequency accompanying the transition. The results are applied to the analysis of degenerate components in the ν₆ and ν₁₆ vibrational transitions in the benzene system, and it is shown that in cases where the second order Herzberg-Teller terms are important, cancelation effects in the matrix elements can lead to the disappearance of certain transitions which are otherwise allowed.     

Generalization of matching extensions in graphs (III)

Proposing them as a general framework, Liu and Yu (2001) [6] introduced (n,k,d)-graphs to unify the concepts of deficiency of matchings, n-factor-criticality and k-extendability. Let G be a graph and let n,k and d be non-negative integers such that n+2k+d+2?|V(G)| and |V(G)|−n−d is even. If on deleting any n vertices from G the remaining subgraph H of G contains a k-matching and each k-matching can be extended to a defect-d matching in H, then G is called an (n,k,d)-graph. In this paper, we obtain more properties of (n,k,d)-graphs, in particular the recursive relations of (n,k,d)-graphs for distinct parameters n,k and d. Moreover, we provide a characterization for maximal non-(n,k,d)-graphs.     

Multivariate causality tests with simulation and application

This paper extends the test established by Hiemstra and Jones (1994) to develop a nonlinear causality test in a multivariate setting. A Monte Carlo simulation is conducted to demonstrate the superiority of our proposed multivariate test over its bivariate counterpart. In addition, we illustrate the applicability of our proposed test for analyzing the relationships among different Chinese stock market indices.     

车载自组网下分布式身份认证机制

针对车载自组网中存在的安全隐患,提出一种身份认证机制.将门限RSA签名技术应用到车载自组网中,从而保证了车载自组网中节点通信信息的保密性、真实性、完整性及不可否认性.实验结果表明,在成员数量和门限值不断变换下,分发时间和合成时间变换比较稳定,说明此模型是稳定性较好的模型,所以将门限RSA签名技术应用于保证车载自组网节点通信的信息安全性是正确可行的.     

Investigating the inner structure of irregular $ \beta$ -lactoglobulin spherulites

When -lactoglobulin in low p H aqueous solutions is exposed to high temperature for extended time, spherulites composed of amyloid fibrils of the -lactoglobulin protein form. Many of these spherulites have fibrils that radiate out from a centre and, under crossed polarisers, exhibit a symmetric Maltese Cross structure. However, a significant fraction (50 of the 101 observed spherulites) of -lactoglobulin spherulites formed under these conditions demonstrate various forms of irregularity in apparent structure. The irregularities of spherulites structures were qualitatively investigated by comparing optical microscopy images observed under crossed polarisers to computationally produced images of various internal structures. In this way, inner spherulite structures are inferred from microscopy images. Modelled structures that were found to produce computed images similar to some of the experimentally viewed images include fibrils curving as they radiate from a single nucleation point; multiple spherulites nucleating in close proximity to one another; and fibrils curving in opposite directions above and below a single nucleation point.     

Sequence characterization of Riordan arrays

In the realm of the Riordan group, we consider the characterization of Riordan arrays by means of the A- and Z-sequences. It corresponds to a horizontal construction of a Riordan array, whereas the traditional approach is through column generating functions. We show how the A- and Z-sequences of the product of two Riordan arrays are derived from those of the two factors; similar results are obtained for the inverse. We also show how the sequence characterization is applied to construct easily a Riordan array. Finally, we give the characterizations relative to some subgroups of the Riordan group, in particular, of the hitting-time subgroup.     

Improved algorithm for broadcast scheduling of minimal latency in wireless ad hoc networks

A wide range of applications for wireless ad hoc networks are time-critical and impose stringent requirement on the communication latency. One of the key communication operations is to broadcast a message from a source node. This paper studies the minimum latency broadcast scheduling problem in wireless ad hoc networks under collision-free transmission model. The previously best known algorithm for this NP-hard problem produces a broadcast schedule whose latency is at least 648（rmax/rmin）^2 times that of the optimal schedule, where rmax and rmin are the maximum and minimum transmission ranges of nodes in a network, respectively. We significantly improve this result by proposing a new scheduling algorithm whose approximation performance ratio is at most （1 ＋ 2rmax/rmin）^2＋32, Moreover, under the proposed scheduling each node just needs to forward a message at most once.     

Water de/adsorption associated with single‐crystal‐to‐single‐crystal structural transformation of a series of two‐dimensional metal–organic frameworks, [M(bipy)(C4O4)(H2O)2]·3H2O (M = Mn (1), Fe (2), and Zn (3), and bipy=4,4′‐bipyridine)

An assembly of three metal coordination polymers (CPs), [M(bipy)(C₄O₄)(H₂O)₂]·3H₂O (M = Mn ( 1 ), Fe ( 2 ), Zn ( 3 ), and bipy = 4,4′‐bipyridine, C₄O₄^2? (squarate) = dianion of H₂C₄O₄ (squaric acid)), was synthesized and structurally characterized. Single‐crystal X‐ray structural determination reveals that compounds 1 – 3 are iso‐structural, in which the M(II) ions are six‐coordinate in a distorted octahedral geometry. C₄O₄^2? and bipy both act as bridging ligands with bis‐monodentate coordination mode connecting the M(II) ions to form a two‐dimensional (2D) layered metal–organic framework (MOF). Adjacent 2D layers are then arranged in parallel and interpenetrated manners to construct their three‐dimensional (3D) supramolecular architecture. Compounds 1 , 2 , and 3 undergo two‐step dehydration processes with the first and second weight losses of 14.1 and 8.6% for 1 , of 12.1 and 7.5% for 2, and of 11.2 and 8.1% for 3 , respectively, corresponding to the weight losses of the three guest water molecules and the two coordinated water molecules, and all exhibit reversible sponge‐like water de/adsorption properties during de/rehydration processes for guest water molecules as per cyclic thermogravimetric analysis (TGA). The single‐crystal‐to‐single‐crystal (SCSC) structural transformation during the reversible de/rehydration processes of three guest water molecules was identified and monitored using exhaustive single‐crystal and powder X‐ray diffraction measurements.