Unusual course of a type II photoreaction

The type II photoreaction of 1-acetyl-2-ethylidene-1-methoxycyclohexane (1) affords 2-ethylidene-1-methoxy-6-methylbicyclo[3.1.1]heptan-6-ol (2) as a result from ring closure of the least stable 1,4-biradical.     

On-line γ-ray investigation of the14N+27Al reaction at 30 MeV/u

The cross-sections of target-like residues following the¹⁴N+²⁷Al reaction at 30 MeV/u have been measured from in-beam and radioactiveγ-ray spectra. The recoil velocities of some fragments have been estimated from theγ-ray Doppler broadening.     

Conformal symplectic geometry,deformations, rigidity and geometrical (KMS) conditions

Deformations admitting a unit element of a local associative algebra defined on the space of functions on a manifold. Definition and properties of the * ^f -products and conformal symplectic geometry. Deformations of a * ^f -products. A theorem of rigidity. Application to statistical mechanics (KMS conditions).     

Note on double points of immersions

We show that not any smooth manifold can be double point manifold of a smooth self-transverse immersion of a closed n-manifold into the euclidean spaceR ^n+k. We investigate also the double covers which can (or can not) occur in this situation. Supported by the A.v. Humboldt Foundation     

Homoclinic period blow-up in reversible and conservative systems

We show that in conservative systems each non-degenerate homoclinic orbit asymptotic to a hyperbolic equilibrium possesses an associated family of periodic orbits. The family is parametrized by the period, and the periodic orbits accumulate on the homoclinic orbit as the period tends to infinity. A similar result holds for symmetric homoclinic orbits in reversible systems. Our results extend earlier work by Devaney and Henrard, and provide a positive answer to a conjecture of Strömgren. We present a unified approach to both the conservative and the reversible case, based on a technique introduced recently by X.-B. Lin.Dedicated to Prof. Klaus Kirchgässner on the occasion of his sixtieth birthday     

Yrast and side bands in the odd-odd160, 162Tm nuclei

High-spin states in²⁰⁵Bi, populated in the²⁰⁵Tl(α, 4n) reaction with bombarding energies around 50 MeV have been studied usingγ-ray spectroscopic techniques. Spins and parities have been assigned on the basis of angular distribution andγ-ray linear polarization measurements. States with spins up to 39/2⁺ and excitation energies around 6 MeV have been identified. Calculations using the empirical shell model have been performed in order to assign configurations.     

Rectilinear group Steiner trees and applications in VLSI design

 Given a set of disjoint groups of points in the plane, the rectilinear group Steiner tree problem is the problem of finding a shortest interconnection (under the rectilinear metric) which includes at least one point from each group. This is an important generalization of the well-known rectilinear Steiner tree problem which has direct applications in VLSI design: in the detailed routing phase the logical units typically allow the nets to connect to several electrically equivalent ports. We present a first (tailored) exact algorithm for solving the rectilinear group Steiner tree problem (and related variants of the problem). The algorithm essentially constructs a subgraph of the corresponding Hanan grid on which existing algorithms for solving the Steiner tree problem in graphs are applied. The reductions of the Hanan grid are performed by applying point deletions and by generating full Steiner trees on the remaining points. Experimental results for real-world VLSI instances with up to 100 groups are presented. Received: November 7, 2000 / Accepted: December 19, 2001 Published online: September 5, 2002     

The Einstein Relation for Random Walks on Graphs

This paper investigates the Einstein relation; the connection between the volume growth, the resistance growth and the expected time a random walk needs to leave a ball on a weighted graph. The Einstein relation is proved under different set of conditions. In the simplest case it is shown under the volume doubling and time comparison principles. This and the other set of conditions provide the basic framework for the study of (sub-) diffusive behavior of the random walks on weighted graphs.