Buyer-seller exactness in the assignment game

In the assignment game framework, we try to identify those assignment matrices in which no entry can be increased without changing the core of the game. These games will be called buyer-seller exact games and satisfy the condition that each mixed-pair coalition attains the corresponding matrix entry in the core of the game. For a given assignment game, a unique buyer-seller exact assignment game with the same core is proved to exist. In order to identify this matrix and to provide a characterization of those assignment games which are buyer-seller exact in terms of the assignment matrix, attainable upper and lower core bounds for the mixed-pair coalitions are found. As a consequence, an open question posed in Quint (1991) regarding a canonical representation of a “45^o-lattice” by means of the core of an assignment game can now be answered. Received: March 2002/Revised version: January 2003 RID="*" ID="*"  Institutional support from research grants BEC 2002-00642 and SGR2001-0029 is gratefully acknowledged RID="**" ID="**"  The authors thank the referees for their comments     

Gaussian estimates and L p -boundedness of Riesz means

We show that suitable upper estimates of the heat kernel are sufficient to imply the L ^p boundedness of several families of operators associated with the Schr?dinger group in various situations. This generalizes results by Sj?strand and others in the Euclidean case, and by Alexopoulos in the case of Lie groups and Riemannian manifolds. RID="*" ID="*"Research partially supported by the European Commission (European TMR Network "Harmonic Analysis" 1998-2001, Contract ERBFMRX-CT97-0159).     

An obstruction to the positivity of relative Yamabe invariants

For a supergroup , we describe an obstruction to the existence of positive scalar curvature metrics with minimal boundary condition on a compact n-dimensional -manifold W with nonempty boundary M, , in terms of the bordism class [M] in the Stolz obstruction group associated to [St2]. In par ticular, when W is a 5-dimensional spin manifold and the -invariant of a connected component of M is nonzero, we prove that W does not admit a positive scalar curvature metric with minimal boundary condition. Received: 4 July 2001; in final form: 5 February 2002 / Published online: 8 November 2002 RID="*" ID="*" Partially supported by the Grants-in-Aid for Scientific Research (C), Japan Society for the Promotion of Science, No. 11640070.     

The Baum-Connes conjecture for hyperbolic groups

We prove the Baum-Connes conjecture for hyperbolic groups and their subgroups. Oblatum 20-VI-2001 & 24-VIII-2001?Published online: 15 April 2002 RID="*" ID="*"The second author is partially supported by NSF and MSRI.     

Uniform Group Divisible Designs with Block Sizes Three and <Emphasis Type="Italic">n</Emphasis>

 The existence of group divisible designs of type g ^t with block sizes three and n, 4≤ n≤10, is completely settled for all values of g and t. Received: July 21, 1999 Final version received: September 10, 2001 RID="*" ID="*" This work was done in 1995 while the authors were graduate students at the University of Waterloo, Waterloo, Ontario N2L 3G1, Canada Acknowledgments. The authors would like to thank the referee for his careful reading and for pointing out some errors in an earlier draft of the paper.     

A unimodularly invariant theory for immersions into the affine space

We develop a unimodularly invariant theory for immersions with higher codimension into the affine space. Received: 6 September 2001; in final form: 22 November 2001 / Published online: 29 April 2002 RID="*" ID="*" Supported by the Deutsche Forschungsgemeinschaft     

Diophantine Approximations and Integer Points of Cones

The purpose of this note is to present a relation between directed best approximations of a rational vector and the elements of the minimal Hilbert basis of certain rational pointed cones. Furthermore, we show that for a special class of these cones the integer Carathéodory property holds true. Received May 6, 1998 RID="*" ID="*" Supported by a "Leibniz Preis" of the German Science Foundation (DFG) awarded to M. Gr?tschel. RID="†" ID="†" Supported by a "Gerhard-Hess-Forschungsf?rderpreis" of the German Science Foundation (DFG).     

Simple and immune relations on countable structures

 Let 𝒜 be a computable structure and let R be a new relation on its domain. We establish a necessary and sufficient condition for the existence of a copy ℬ of 𝒜 in which the image of R (?R, resp.) is simple (immune, resp.) relative to ℬ. We also establish, under certain effectiveness conditions on 𝒜 and R, a necessary and sufficient condition for the existence of a computable copy ℬ of 𝒜 in which the image of R (?R, resp.) is simple (immune, resp.). Received: 4 February 2001 Published online: 5 November 2002 RID="*" ID="*" The first three authors gratefully acknowledge support of the NFS Binational Grant DMS-0075899. RID="*" ID="*" The first three authors gratefully acknowledge support of the NFS Binational Grant DMS-0075899. RID="*" ID="*" The first three authors gratefully acknowledge support of the NFS Binational Grant DMS-0075899.     

Analytic continuation for Beltrami systems, Siegel's Theorem for UQR maps, and the Hilbert-Smith Conjecture

A uniformly quasiregular mapping, is a mapping of the m-sphere with the property that it and all its iterates have uniformly bounded distortion. Such maps are rational with respect to some bounded measurable conformal structure and there is a Fatou-Julia type theory associated with the dynamical system obtained by iterating these mappings. We begin by investigating the analogue of Siegel's theorem on the local conjuga cy of rotational dynamics. We are led to consider the analytic continuation properties of solutions to the highly nonlinear first order Beltrami systems. We reduce these problems to a central and well known conjecture in the theory of transformation groups; namely the Hilbert-Smith conjecture, which roughly asserts that effective transformation groups of manifolds are Lie groups. Our affirmative solution to this problem then implies unique analytic continuation and Siegel's theorem. Received: 14 September 2000 / Revised version: 23 November 2001 / Published online: 5 September 2002 RID="*" ID="*" Research supported in part by grants from the Marsden Fund and Royal Society (NZ).     

A posteriori error estimates for optimal control problems governed by parabolic equations

Summary. In this paper, we derive a posteriori error estimates for the finite element approximation of quadratic optimal control problem governed by linear parabolic equation. We obtain a posteriori error estimates for both the state and the control approximation. Such estimates, which are apparently not available in the literature, are an important step towards developing reliable adaptive finite element approximation schemes for the control problem. Received July 7, 2000 / Revised version received January 22, 2001 / Published online January 30, 2002 RID="*" ID="*" Supported by EPSRC research grant GR/R31980