Solution concepts ofk-convexn-person games

For any positive integersk andn, the subclass ofk-convexn-person games is considered. In casek=n, we are dealing with convexn-person games. Three characterizations ofk-convexn-person games, formulated in terms of the core and certain adapted marginal worth vectors, are given. Further it is shown that fork-convexn-person games the intersection of the (pre)kernel with the core consists of a unique point (namely the nucleolus), but that the (pre)kernel may contain points outside the core. For certain 1-convex and 2-convexn-person games the part of the bargaining set outside the core is even disconnected with the core. The Shapley value of ank-convexn-person game can be expressed in terms of the extreme points of the core and a correction-vector whenever the game satisfies a certain symmetric condition. Finally, theτ-value of ank-convexn-person game is given.     

Introduction to the physics of Brownian motors

A detailed introduction to directed transport in Brownian motors occurring in spatially periodic systems far from equilibrium is presented. We elucidate the prominent physical concepts and novel phenomena with a representative dissipative Brownian motor dynamics. Its main ingredient is a thermal noise with time-dependent temperature modulations that drive the system out of thermal equilibrium in a spatially asymmetric (ratchet-) potential. Yet, this asymmetric setup does not exhibit a concomitant obvious bias into one or the other direction of motion. Symmetry conditions for the appearance (or not) of directed current, its reversal upon variation of certain parameters, and various other generic features and applications are discussed. In addition, we provide a systematic classification scheme for Brownian motor models and review historical landmark contributions to the field. Received: 9 November 2001 / Accepted: 14 January 2002 / Published online: 22 April 2002     

Exclusive charge exchange reaction pD↦n(pp) within the Bethe-Salpeter formalism

The exclusive charge exchange reaction pD↦n(pp) at intermediate and high energies is studied within the Bethe-Salpeter formalism. The final-state interaction in the detected pp pair at nearly zero excitation energy is described by the ¹ S ₀ component of the Bethe-Salpeter amplitude. Results of numerical calculations of polarization observables and differential cross-section persuade that, as in the non-relativistic case, this reaction i) can be utilized as a “relativistic deuteron polarimeter” and ii) delivers further information about the elementary nucleon-nucleon charge exchange amplitude. Received: 26 November 2002 / Accepted: 30 January 2003 / Published online: 29 April 2003     

Bose-Einstein and colour interference in W-pair decays

We study effects on the W mass measurements at LEP2 from non-perturbative interference effects in the fully hadronic decay channel. Based on a model for Bose-Einstein interference, which is in agreement with LEP1 data, we argue that there are no Bose-Einstein correlations between bosons coming from the different W's. For small reconnection probabilities we rule out the possible experimental signal of colour interference at LEP2, suggested in [1]. The conclusions from this paper are that the theoretical uncertainties in the W mass determination should be smaller than the experimental statistical error. Received: 3 November 1997 / Published online: 10 March 1998     

Accuracy of optical frequency comb generators and optical frequency interval divider chains

We compared two methods for measuring large optical frequency differences: an optical frequency comb generator, which creates a large number of sidebands from a single-mode laser through electro-optic modulation, and an optical frequency interval divider chain, which divides a frequency gap successively by two until it becomes accessible to a radio-frequency counter. By locking two diode lasers to two modulation sidebands of a comb generator, ~1 THz apart, and measuring this interval with a chain of four phase-locked interval dividers, we demonstrate for the first time to our knowledge the accuracy of both techniques within an experimental limit of 6.8 x 10(-15).     

Proton double quantum coherence and cross-relaxation in (NH4)2SnBr6

A proton double quantum coherence signal can be observed exclusively from the T species NH4 groups (with the total spin I = 1) in ammonium compounds at low temperatures by the three-pulse sequence 90x degrees - tpr - 90x degrees - tev - 90x degrees - ta, where tpr and ta are of the magnitude of the inverse line width and tev very short. The usefulness of this pulse sequence, preceded by the additional pulse sequence 90x degrees - t1 -90(-x) degrees - t2 for creating an unbalance between the A and T species magnetizations, was demonstrated by applying it to cross-relaxation studies in (NH4)2SnBr6.     

Nuclear spin relaxation of 8Li adsorbed on surfaces

Nuclear spin relaxation experiments with ⁸Li adsorbed on various surfaces provide new information in surface science which is not obtainable othervise. Both dipolar (Korringa) and quadrupolar relaxation due to diffusion are observed. However, in addition, a fast and presently not understood spin relaxation mechanism is present while dosing during the first 0.5 s the surface with polarized ⁸Li. Most strange in this respect is the fact that those ⁸Li atoms which survive depolarization through this mechanism depolarize afterwards with modest spin lattice relaxation rates. The origin of the fast spin lattice relaxation mechanism is presently unknown. This revised version was published online in July 2006 with corrections to the Cover Date.     

Real structures of Teichmüller spaces, Dehn twists, and moduli spaces of real curves

An orientation reversing involution of a topological compact genus surface induces an antiholomorphic involution of the Teichmüller space of genus g Riemann surfaces. Two such involutions and are conjugate in the mapping class group if and only if the corresponding orientation reversing involutions and of are conjugate in the automorphism group of . This is equivalent to saying that the quotient surfaces and are homeomorphic. Hence the Teichmüller space has distinct antiholomorphic involutions, which are also called real structures of ([7]). This result is a simple fact that follows from Royden's theorem ([4]) stating that the the mapping class group is the full group of holomorphic automorphisms of the Teichmüller space (). Let and be two real structures that are not conjugate in the mapping class group. In this paper we construct a real analytic diffeomorphism such that This mapping d is a product of full and half Dehn–twists around certain simple closed curves on the surface . This has applications to the moduli spaces of real algebraic curves. A compact Riemann surface admitting an antiholomorphic involution is a real algebraic curve of the topological type . All fixed–points of the real structure of the Teichmüller space , are real curves of the above topological type and every real curve of that topological type is represented by an element of the fixed–point set of . The fixed–point set is the Teichmüller space of real algebraic curves of the corresponding topological type. Given two different real structures and , let d the the real analytic mapping satisfying (1). It follows that d maps onto and is an explicit real analytic diffeomorphism between these Teichmüller spaces. Received 8 December 1997; accepted 12 August 1998     

Efficient J=0-1 soft-X-ray lasing in neon-like ions at pump powers below 250 GW

2 . By using a 0.7% prepulse that precedes the main pulse by 5 ns and applying a total pump energy of 100 J or less, the J=0-1 lasing is at least one order of magnitude higher than the non-lasing background. For the 32.6-nm line of Ti, the 25.5-nm line of Fe, and the 23.1-nm line of Ni, gain coefficients of (±) 4.20.4cm^-1, (±) 3.90.3cm^-1, and (±) 3.60.6cm^-1, respectively, were measured for 2.4-cm-long curved targets, resulting in gain–length products of ∼10. Angle-resolved spectra indicate a beam divergence of 3 mrad (FWHM), typically. The space-resolved spectra show that the J=0-1 lasing lines are emitted from an approximately 60-μm-wide (FWHM) plasma region, whereas the nearby continuum emission is produced in a considerably broader plasma region of ∼250 μm. Lasing at 25.5 nm in neon-like iron was observed at a pump power as low as 180 GW (∼9 TW/cm²), with, however, considerable shot-to-shot scatter in the absolute laser output. Received: 5 September 1997/Revised version: 10 November 1997     

U-branes and T fibrations

We describe eight-dimensional vacuum configurations with varying moduli consistent with the U-duality group . Focusing on the latter less-well understood properties, we construct a class of fivebrane solutions living on lines on a three-dimensional base space. The resulting U-manifolds, with five scalars transforming under SL(3), admit a Ricci-flat Kähler metric. Based on the connection with special Lagrangian T³ fibered Calabi-Yau three-folds, this construction provides a simple framework for the investigation of Calabi-Yau mirrors.