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1.
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
2.
C. Andreoiu D. Rudolph I. Ragnarsson C. Fahlander R.A.E. Austin M.P. Carpenter R.M. Clark J. Ekman R.V.F. Janssens T.L. Khoo F.G. Kondev T. Lauritsen T. Rodinger D.G. Sarantites D. Seweryniak T. Steinhardt C.E. Svensson O. Thelen J.C. Waddington 《The European Physical Journal A - Hadrons and Nuclei》2002,14(3):317-348
High-spin states in 59Cu were populated using the fusion-evaporation reaction 28Si + 40Ca at a beam energy of 122 MeV. The Gammasphere Ge-detector array in conjunction with the 4π charged-particle detector array
Microball allowed for the detection of γ-rays in coincidence with evaporated light particles. The resulting extensive high-spin
decay scheme of 59Cu is presented, which comprises more than 320 γ-ray transitions connecting about 150 excited states. Their spins and parities
have been assigned via directional correlations of γ-rays emitted from oriented states. Average quadrupole moments of rotational
bands have been determined from the analysis of residual Doppler shifts. Shell model calculations in the fp shell are invoked to study some of the low-spin states, while the experimental characteristics of the rotational bands are
analyzed in the configuration-dependent cranked Nilsson-Strutinsky (CNS) approach.
Received: 15 February 2002 / Accepted: 23 April 2002 相似文献
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A series of laboratory and modelling experiments on the oxidation of propene in the gas phase has been undertaken to determine conditions which give high yields of propene oxide. The conditions under which the experiments were conducted were 505–549 K and up to 4 bar pressure. It is proposed that propene oxide is formed from propene by reaction with several peroxy radicals including HO2 and CH3CO3. However, one of the more important radicals is hydroxypropylperoxy. Its reaction with propene, under these conditions is more important than concerted decomposition to formaldehyde and acetaldehyde. © 1995 John Wiley & Sons, Inc. 相似文献
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7.
Frank D. Popp Miland Rajopadhye David S. Brown David Waddington Barrie C. Uff 《Journal of heterocyclic chemistry》1987,24(1):261-265
The title compounds have been prepared by the cyclocondensation of mercaptosuccinic acid with isatin-3-imines. The 1-benzyl derivatives have been synthesized by simultaneously reacting 1-benzylisatin, substituted anilines and mercaptosuccinic acid. The structure of the products has been confirmed by X-ray diffraction measurements. 相似文献
8.
Since the band for OH stretching of HOD molecules solvating perchlorate ions is clearly resolved, the remaining band can be analysed to give values for the OH absorption for the cation solvation shell: these are closely correlated with NMR shift data. 相似文献
9.
We describe our full report of the catalytic asymmetric addition of simple and functionalized dialkylzinc reagents to a broad range of saturated ketones and enones. The functionalized organozinc reagents contain esters, silyl ethers, alkyl chlorides, and alkyl bromides. In general, the resulting tertiary alcohol products are isolated with high ee's. With some substrates, yields are low as a result of the formation of aldol byproducts. Most substrates undergo additions with good yields reaching as high as 91%. 相似文献
10.
Keith P. Brierley Joseph Howard Clifford J. Ludman Keith Robson Thomas C. Waddington John Tomkinson 《Chemical physics letters》1978,59(3):467-471
Inelastic neutron scattering spectra of KHCO3 and CsH(NO3)2 have been obtained in the region 400 → 2400 and 400 → 2800 cm?1 respectively. The in- and out-of-phase bending vibrations of the hydrogen bonds have been observed and assigned. For CsH(NO3)2 the two bending modes are closer in frequency than in KHCO3 and they are not resolved from the antisymmetric stretch. 相似文献