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1.
Melvin Hausner 《Combinatorica》1985,5(3):215-225
Ifμ is a positive measure, andA
2, ...,A
n
are measurable sets, the sequencesS
0, ...,S
n
andP
[0], ...,P
[n] are related by the inclusion-exclusion equalities. Inequalities among theS
i
are based on the obviousP
[k]≧0. Letting
=the average average measure of the intersection ofk of the setsA
i
, it is shown that (−1)
k
Δ
k
M
i
≧0 fori+k≦n. The casek=1 yields Fréchet’s inequalities, andk=2 yields Gumbel’s and K. L. Chung’s inequalities. Generalizations are given involvingk-th order divided differences. Using convexity arguments, it is shown that forS
0=1,
whenS
1≧N−1, and
for 1≦k<N≦n andv=0, 1, .... Asymptotic results asn → ∞ are obtained. In particular it is shown that for fixedN,
for all sequencesM
0, ...,M
n
of sufficiently large length if and only if
for 0<t<1. 相似文献
2.
Nikolaos Marmaridis 《manuscripta mathematica》1984,47(1-3):55-83
Let
be a triangular matrix algebra, uhere k is an algebraically closed field, B is the path algebra of an oriented Dynkin diagram of type E6 or E7 or E8 and M is a finite dimensional k-B-bimodule. The aim of this paper is to determine the representation type of A for any orientation of the Dynkin diagram and for any indecomposable B-module M. This classification is obtained by comparing the representation types of the algebras
and
using the theory of tilting modules. 相似文献
3.
Richard P. Stanley 《Graphs and Combinatorics》1987,3(1):55-66
I. Bárány and L. Lovász [Acta Math. Acad. Sci. Hung.40, 323–329 (1982)] showed that ad-dimensional centrally-symmetric simplicial polytopeP has at least 2
d
facets, and conjectured a lower bound for the numberf
i
ofi-dimensional faces ofP in terms ofd and the numberf
0 =2n of vertices. Define integers
A. Björner conjectured (unpublished) that
(which generalizes the result of Bárány-Lovász sincef
d–1
= h
i
), and more strongly that
, which is easily seen to imply the conjecture of Bárány-Lovász. In this paper the conjectures of Björner are proved.Partially supported by NSF grant MCS-8104855. The research was performed when the author was a Sherman Fairchild Distinguished Scholar at Caltech. 相似文献
4.
Mingchu Gao 《数学学报(英文版)》1999,15(4):535-548
In this paper, we first give a sufficient and necessary condition for
to generate an exponentially bounded
-semigroup and discuss its relations to the C-wellposedness of the complete second order abstract Cauchy problem ((ACP2) for short) in some sense. Then we use these results and those in [1] to discuss the C-(exponential) wellposedness of a kind of (ACP2) with application backgrounds, and develop the results in [2].
This project is supported by the NNSF of China, and the Youth Science and Technique Foundation of Shanxi Province, China 相似文献
5.
Michel WEBER 《数学学报(英文版)》2006,22(2):377-382
Let D be an increasing sequence of positive integers, and consider the divisor functions:
d(n, D) =∑d|n,d∈D,d≤√n1, d2(n,D)=∑[d,δ]|n,d,δ∈D,[d,δ]≤√n1,
where [d,δ]=1.c.m.(d,δ). A probabilistic argument is introduced to evaluate the series ∑n=1^∞and(n,D) and ∑n=1^∞and2(n,D). 相似文献
6.
Werner Burau 《Annali di Matematica Pura ed Applicata》1956,42(1):381-393
Sunto Conoscendo il modello minimo
per la totalità degli S
k
I
d'una schiera giacenti su di una quadrica Q2k di S2k+1 si definisce il ? complesso lineare di S
k
I
? come imagine d'una sezione iperpiana di
. Il problema della classificazione projettiva di tali complessi lineari è posto e risolto per k≤5.
相似文献
7.
An attempt is made to classify the boundary of the coupled operator
and to construct the corresponding minimal semigroup and minimal coupled diffusion process. The sample properties and the conservative conditions of the process are discussed also. 相似文献
8.
Letn>1. The number of all strictly increasing selfmappings of a 2n-element crown is
. The number of all order-preserving selfmappings of a 2n-element crown is
相似文献
9.
We give an asymptotic formula for
|