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Titolo:
Bell numbers, log-concavity, and log-convexity
Autore:
Asai, N; Kubo, I; Kuo, HH;
Indirizzi:
Nagoya Univ, Grad Sch Math, Nagoya, Aichi 4648602, Japan Nagoya Univ Nagoya Aichi Japan 4648602 Math, Nagoya, Aichi 4648602, Japan Hiroshima Univ, Grad Sch Sci, Dept Math, Higashihiroshima 7398526, Japan Hiroshima Univ Higashihiroshima Japan 7398526 hihiroshima 7398526, Japan Louisiana State Univ, Dept Math, Baton Rouge, LA 70803 USA Louisiana StateUniv Baton Rouge LA USA 70803 , Baton Rouge, LA 70803 USA
Titolo Testata:
ACTA APPLICANDAE MATHEMATICAE
fascicolo: 1-3, volume: 63, anno: 2000,
pagine: 79 - 87
SICI:
0167-8019(200009)63:1-3<79:BNLAL>2.0.ZU;2-G
Fonte:
ISI
Lingua:
ENG
Soggetto:
NOISE;
Keywords:
Bell numbers; log-concavity; log-convexity; CKS-space; characterization theorem; white noise distribution theory;
Tipo documento:
Article
Natura:
Periodico
Settore Disciplinare:
Physical, Chemical & Earth Sciences
Citazioni:
8
Recensione:
Indirizzi per estratti:
Indirizzo: Asai, N Int Inst Adv Studies, 9-3 Kizugawadai, Kyoto 6190225, Japan Int Inst Adv Studies 9-3 Kizugawadai Kyoto Japan 6190225 5, Japan
Citazione:
N. Asai et al., "Bell numbers, log-concavity, and log-convexity", ACT APPL MA, 63(1-3), 2000, pp. 79-87

Abstract

Let {b(k)(n)}(n=0)(infinity) be the Bell numbers of order k. It is proved that the sequence {b(k)(n)/n!}(n=0)(infinity) is log-concave and the sequence {b(k)(n)}(n=0)(infinity) is log-convex, or equivalently, the following inequalities hold for all n greater than or equal to0,1 less than or equal to b(k)(n+2)b(k)(n)/b(k)(n+1)(2) less than or equal ton+2/n+1. Let {alpha (n)}(n=0)(infinity) be a sequence of positive numbers with alpha (0)=1. We show that if {alpha (n)}(n=0)(infinity) is log-convex, thenalpha (n)alpha (m)less than or equal to alpha (n+m), For Alln,m greater than or equal to0. On the other hand, if {alpha (n)/n!}(n=0)(infinity) is log-concave, thenalpha (n+m) less than or equal to [n+m/n] alpha (n)alpha (m),For Alln,m greater than or equal to0. In particular, we have the following inequalities for the Bell numbersb(k)(n)b(k)(m) less than or equal to b(k)(n+m) less than or equal to [n+m/n] b(k)(n)b(k)(m), For Alln,m greater than or equal to0. Then we apply these results to characterization theorems for CKS-space in white noise distribution theory.

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Documento generato il 22/10/20 alle ore 05:39:55