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141.
IfA is a -algebra on setX, thenl
0
(X,A) is a barrelled space of class 0. IfA is an algebra, there are conditions which imply thatl
0
(X,A) is suprabarelled. Here, wheneverA is an algebra, we give conditions forl
0
(X,A) to be not barrelled which are related with the existence of non-trivial convergent sequences.Supported in part by DGICYT, project PB91-0407 and by the Institució Valenciana d'Estudis i Investigació, project 023. 相似文献
142.
This paper studies the growth function, with respect to the generating set of edge identifications, of a surface group with fundamental domainD in the hyperbolic plane ann-gon whose angles alternate between /p and /q. The possibilities ofn,p andq for which a torsion-free surface group can have such a fundamental polygon are classified, and the growth functions are computed. Conditions are given for which the denominator of the growth function is a product of cyclotomic polynomials and a Salem polynomial.This work was supported in part by NSF Research Grants. 相似文献
143.
The papers of R. Ramer and S. Kusuoka investigate conditions under which the probability measure induced by a nonlinear transformation on abstract Wiener space(,H,B) is absolutely continuous with respect to the abstract Wiener measure. These conditions reveal the importance of the underlying Hilbert spaceH but involve the spaceB in an essential way. The present paper gives conditions solely based onH and takes as its starting point, a nonlinear transformationT=I+F onH. New sufficient conditions for absolute continuity are given which do not seem easily comparable with those of Kusuoka or Ramer but are more general than those of Buckdahn and Enchev. The Ramer-Itô integral occurring in the expression for the Radon-Nikodym derivative is studied in some detail and, in the general context of white noise theory it is shown to be an anticipative stochastic integral which, under a stronger condition on the weak Gateaux derivative of F is directly related to the Ogawa integral.Research supported by the National Science Foundation and the Air Force Office of Scientific Research Grant No. F49620 92 J 0154 and the Army Research Office Grant No. DAAL 03 92 G 0008. 相似文献
144.
Two partial ordersP andQ on a setX arecomplementary (written asPQ) if they share no ordered pairs (except for loops) but the transitive closure of the union is all possible ordered pairs. For each positive integern we form a graph Pos
n
consisting of all nonempty partial orders on {1, ,n} with edges denoting complementation. We investigate here properties of the graphs Pos
n
. In particular, we show:
| The diameter of Pos n is 5 for alln>2 (and hence Pos n is connected for alln); | |
| With probability 1, the distance between two members of Pos n is 2; | |
| The graphs Pos n are universal (i.e. every graph occurs as an induced subgraph of some Pos n ); | |
|
The maximal size (n) of an independent set of Pos
n
satisfies the asymptotic formula
|
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