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21.
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 相似文献
22.
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. 相似文献
23.
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 相似文献
24.
Patrick Lacoste 《Comptes Rendus Mathematique》2004,339(10):727-732
. 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). 相似文献
25.
Patrick Ingram 《Journal of Number Theory》2007,123(2):473-486
Let n?5 be an integer. We provide an effective method for finding all elliptic curves in short Weierstrass form E/Q with j(E)∈{0,1728} and all P∈E(Q) such that the nth term in the elliptic divisibility sequence defined by P over E fails to have a primitive divisor. In particular, we improve recent results of Everest, Mclaren, and Ward on the Zsigmondy bounds of elliptic divisibility sequences associated with congruent number curves. 相似文献
26.
We consider toy cosmological models in which a classical, homogeneous, spinor field provides a dominant or sub-dominant contribution to the energy-momentum tensor of a flat Friedmann-Robertson-Walker universe. We find that, if such a field were to exist, appropriate choices of the spinor self-interaction would generate a rich variety of behaviors, quite different from their widely studied scalar field counterparts. We first discuss solutions that incorporate a stage of cosmic inflation and estimate the primordial spectrum of density perturbations seeded during such a stage. Inflation driven by a spinor field turns out to be unappealing as it leads to a blue spectrum of perturbations and requires considerable fine-tuning of parameters. We next find that, for simple, quartic spinor self-interactions, non-singular cyclic cosmologies exist with reasonable parameter choices. These solutions might eventually be incorporated into a successful past- and future-eternal cosmological model free of singularities. In an Appendix, we discuss the classical treatment of spinors and argue that certain quantum systems might be approximated in terms of such fields. 相似文献
27.
The exciton-exciton interaction is investigated for spatially indirect excitons in coupled quantum wells. The Hartree-Fock and Heitler-London approaches are improved by a full two-exciton calculation including the van der Waals effect. Using these potentials for the singlet and triplet channel, the two-body scattering matrix is calculated and employed to derive a modified relation between exciton density and blue shift. Such a relation is of central importance for gauging exciton densities on the way toward Bose condensation. 相似文献
28.
We consider the 3D Navier–Stokes equation with generalized impermeability boundary conditions. As auxiliary results, we prove the local in time existence of a strong solution (‘strong’ in a limited sense) and a theorem on structure. Then, taking advantage of the boundary conditions, we formulate sufficient conditions for regularity up to the boundary of a weak solution by means of requirements on one of the eigenvalues of the rate of deformation tensor. Finally, we apply these general results to the case of an axially symmetric flow with zero angular velocity. 相似文献
29.
We construct division algebras with involution containing a Baer ordering with noninvariant order ring. This gives a negative
answer to a question of Holland, whether the order ring is always invariant under inner automorphisms. Furthermore, we give
examples of any index. Previously, the only known examples of division algebras containing Baer orderings were of index 2
n
or of indexp forp a prime of the form 4m + 3.
Supported in part by the National Science Foundation. 相似文献
30.
Justina Grabowska Karuna Kar Nanda R.T. Rajendra Kumar J.P. Mosnier M.O. Henry Simon B. Newcomb Patrick McNally Lisa OReilly Xu Lu Enda McGlynn 《Superlattices and Microstructures》2007,42(1-6):327
Self-organized ZnAl2O4 nanostructures with the appearance (in SEM) of high aspect ratio horizontal nanowires are grown on uncatalysed c-sapphire by vapour phase transport. The nanostructures grow as three equivalent crystallographic variants on c-sapphire. Raman and cathodoluminescence spectroscopy confirm that the nanostructures are not ZnO and TEM shows that they are the cubic spinel, zinc aluminate, ZnAl2O4, formed by the reaction of Zn and O with the sapphire substrate. 相似文献