A Note on Log-Convexity of q-Catalan Numbers

The q-Catalan numbers studied by Carlitz and Riordan are polynomials in q with nonnegative coefficients. They evaluate, at q = 1, to the Catalan numbers: 1, 1, 2, 5, 14,…, a log-convex sequence. We use a combinatorial interpretation of these polynomials to prove a q-log-convexity result. The sequence of q-Catalan numbers is not q-log-convex in the narrow sense used by other authors, so our work suggests a more flexible definition of q-log convex be adopted. Received January 2, 2007     

激光准直仪的设计性物理实验

介绍了激光准直仪的结构、工作原理及其在设计性物理实验中的应用     

Identifying Linking-Pin Organizations in Inter-Organizational Networks

Within the large literature on inter-organizational networks, there has been some discussion of linking-pin organizations and the role they play in integrating these networks. Based on this verbal specification of linking-pin organizations, we construct operational criteria and empirical methods for identifying these structurally important organizations in potentially large and complex inter-organizational networks. These methods are based on ideas drawn from blockmodeling, structural holes, centrality and centralization of networks, and identifying cut-points in networks. These methods are applied to a constructed example and then to real empirical inter-organizational networks. Implications and contrasts with other methods are discussed, together with some open problems.     

Groups in which every non-abelian subgroup is permutable

A subgroupH of a groupG is said to bepermutable ifHX=XH for every subgroupX ofG. In this paper the structure of groups in which every subgroup either is abelian or permutable is investigated. This work was done while the last author was visiting the University of Napoli Federico II. He thanks the “Dipartimento di Matematica e Applicazioni” for its financial support.     

5-Spirocyclopropane Isoxazolidines as Versatile Intermediates in Organic Synthesis

The review outlines the various different azaheterocycles available from 5-spirocyclopropane isoxazolidines. These compounds can be regarded as versatile direct precursors of tetrahydro-, dihydropyridone and azetidinone derivatives. The current scope and limitations, and the selectivity aspects of the different processes are discussed therein.     

Ti(IV)/BINOL-catalyzed asymmetric aldol reaction of a masked acetoacetic ester: pronounced influence of catalyst concentration on nonlinear effects

Initial concentration of enantioenriched or enantiopure catalysts proved to be an important factor for the achievement of a more pronounced amplification of ee's in the Ti(IV)/BINOL-catalyzed aldol reaction of an O-silyldienolate.     

Evaluation of Polycation-Stabilized Lactate Oxidase in a Silica Sol–Gel as a Biosensor Platform

 Whereas glucose oxidase and related proteins are encapsulated readily in silica sol–gels, α-hydroxy enzymes such as lactate oxidase (LOx), are reported to be damaged by electrostatic interaction with these matrices. Based on a previous report, poly(ethyleneimine), PEI, was evaluated as a protecting compound under conditions suited to analytical measurements. With LOx and PEI co-encapsulated in a silica sol–gel, the enzyme retained 62% of its initial activity after 20 days. In the absence of PEI, activity was lost during the processing. Batch analytical measurements with enzyme-doped sol–gel yielded a linear response over the range 0.5–2.0 mM lactate and a detection limit of 0.03 mM lactate. Both simple incorporation of LOx in a silica sol–gel and an alternative protection method, blocking the ion-exchange sites on silica with La(III), failed. These negative results supported the hypothesis that the efficacy of PEI was related to its formation of a protective sheath around the enzyme. Author for correspondence. E-mail: coxja@muohio.edu Received July 29, 2002; accepted December 15, 2002 Published online May 19, 2003     

La condensation de la matrice masse,ou mass-lumping,pour les éléments finis mixtes de Raviart–Thomas–Nédélec d'ordre 1

. We present practical means to obtain a positive diagonal matrix for the first order Raviart–Thomas–Nédélec finite elements. Applying it to the second order Maxwell equations allows us to use explicit time schemes to solve the resulting differential system. To cite this article: P. Lacoste, C. R. Acad. Sci. Paris, Ser. I 339 (2004).     

Charge manipulation and imaging of the Mn acceptor state in GaAs by cross-sectional scanning tunneling microscopy

An individual Mn acceptor in GaAs is mapped by cross-sectional scanning tunneling microscopy (X-STM) at room temperature and a strongly anisotropic shape of the acceptor state is observed. An acceptor state manifests itself as a cross-like feature which we attribute to a valence hole weakly bound to the Mn ion forming the (Mn²⁺3d⁵+hole) complex. We propose that the observed anisotropy of the Mn acceptor wavefunction is due to the d-wave present in the acceptor ground state.