This paper studies vanishing of Ext modules over Cohen--Macaulay local rings. The main result of this paper implies that the Auslander--Reiten conjecture holds for maximal Cohen--Macaulay modules of rank one over Cohen--Macaulay normal local rings. It also recovers a theorem of Avramov--Buchweitz--Şega and Hanes--Huneke, which shows that the Tachikawa conjecture holds for Cohen--Macaulay generically Gorenstein local rings. [ABSTRACT FROM AUTHOR]
*KNOT theory, *ONE (The number), *LOGICAL prediction, *MATHEMATICAL formulas, *MATHEMATICS
Abstract
In the present paper, we show that the Morimoto Conjecture on the super additivity of the tunnel numbers of knots in S3 is true for knots K1,K2 in S3 in which each Ki is either a tunnel number one or m-small, i = 1, 2. This extends two known results by Morimoto. [ABSTRACT FROM AUTHOR]
A formula on the scattering length for 3-dimensional Brownian motion was conjectured by M. Kac and proved by others later. It was recently proved under the framework of symmetric Markov processes by Takeda. In this paper, we shall prove that this formula holds for Markov processes under weak duality by the machinery developed mainly by Fitzsimmons and Getoor. [ABSTRACT FROM AUTHOR]
Published
2010
Discovery Service for Jio Institute Digital Library
For full access to our library's resources, please sign in.