Cohomology of Subregular Tilting Modules for Small Quantum Groups

Let U be a quantumgroup with divid d powers at root ofunity constructed froma rootsystem R .Let u U b th small quantumgroup.Th cohomologyof u with trivial coefficients was computed by Ginzburg and Kumar.It turns out to be isomorphic to the functions algebra of the nilpotent cone of a semisimpl algebraic group with root system R .In this not we calculate cohomology of u with coefficients in simplest reducible tilting modul with nontrivial cohomology.It appears to b isomorphic to th functions algebra of th closure of the subregular nilpotent orbit.     

Invariant subsets of rank 1 manifolds

It is proved that for a Riemannian manifold M with nonpositive sectional curvature and finite volume the space of directions at each point in which geodesic rays avoid a sufficiently small neighborhood of a fixed rank 1 vector v∈UM looks very much like a generalized Sierpinski carpet. We also show for nonpositively curved manifolds M with dim M≥ 3 the existence of proper closed flow invariant subsets of the unit tangent bundle UM whose footpoint projection is the whole of M. Received: 6 July 2000 / Revised version: 11 October 2001     

Möbius characterization of hemispheres

In this paper we generalize the Möbius characterization of metric spheres as obtained in Foertsch and Schroeder [4] to a corresponding Möbius characterization of metric hemispheres.     

On linear-fractional relations and images of angular operators

For plus-operators in a Banach indefinite space, we consider a linear-fractional relation. The classes of operators with the empty domain of definition for such a relation are described. The sufficient (and necessary, in some meaning) conditions for the chain rule to be valid are given.     

Mass spectrometric study of μ4-oxohexa-μ-acetatotetrazinc,Zn4O(CH3CO2)6

The electron impact mass spectrum of Zn₄O(CH₃CO₂)₆ isostructural to Be₄O(CH₃CO₂)₆ studied earlier is reported. The principal fragmentation paths of both compounds involve the elimination of M(CH₃CO₂)₂ where M is Zn, Be, or (CH₃CO)₂O. Further fragmentations proceed by the losses of CH₂CO and H₂O. The spectrum of Zn₄O(CH₃CO₂)₆ contains intense doubly charged ions. The results obtained are interpreted in terms of stereochemical considerations.     

Metric Möbius geometry and a characterization of spheres

We obtain a Möbius characterization of the n-dimensional spheres S ⁿ endowed with the chordal metric d ₀. We show that every compact extended Ptolemy metric space with the property that every three points are contained in a circle is Möbius equivalent to (S ⁿ , d ₀) for some n ≥ 1.     

Embedding of Hyperbolic Spaces in the Product of Trees

We show that for each n ≥ 2 there is a quasi-isometric embedding of the hyperbolic space Hⁿ in the product Tⁿ=T × ··· × T of n copies of a (simplicial) metric tree T. On the other hand, we prove that there is no quasi-isometric embedding for any metric tree T and any m ≥ 0.Mathematics Subject classification (2000). 54Exx.Supported by RFFI Grant 02-01-00090, CRDF Grant RMI-2381-ST-02 and SNF Grant 20-668 33.01. Supported by Swiss National Science Foundation.     

Fast Laplace Transforms for the Exponential Radon Transform

The Fourier slice theorem for the standard Radon transform generalizes to a Laplace counterpart when considering the exponential Radon transform. We show how to use this fact in combination with algorithms for the unequally spaced fast Laplace transform to construct fast and accurate methods for computing both the forward exponential Radon transform and the corresponding back-projection operator.