Condensation in Nongeneric Trees

We study nongeneric planar trees and prove the existence of a Gibbs measure on infinite trees obtained as a weak limit of the finite volume measures. It is shown that in the infinite volume limit there arises exactly one vertex of infinite degree and the rest of the tree is distributed like a subcritical Galton-Watson tree with mean offspring probability m<1. We calculate the rate of divergence of the degree of the highest order vertex of finite trees in the thermodynamic limit and show it goes like (1−m)N where N is the size of the tree. These trees have infinite spectral dimension with probability one but the spectral dimension calculated from the ensemble average of the generating function for return probabilities is given by 2β−2 if the weight w _n of a vertex of degree n is asymptotic to n ^−β .     

Free-knot spline approximation of stochastic processes

We study optimal approximation of stochastic processes by polynomial splines with free knots. The number of free knots is either a priori fixed or may depend on the particular trajectory. For the s-fold integrated Wiener process as well as for scalar diffusion processes we determine the asymptotic behavior of the average L_p-distance to the splines spaces, as the (expected) number of free knots tends to infinity.     

On the production of \pi^{+}_{} \pi^{+}_{} pairs in pp collisions at 0.8 GeV

Data accumulated recently for the exclusive measurement of the pp $ \rightarrow$ pp $ \pi^{+}_{}$ $ \pi^{-}_{}$ reaction at a beam energy of 0.793GeV using the COSY-TOF spectrometer have been analyzed with respect to possible events from the pp $ \rightarrow$ nn $ \pi^{+}_{}$ $ \pi^{+}_{}$ reaction channel. The latter is expected to be the only $ \pi$ $ \pi$ production channel, which contains no major contributions from resonance excitation close to threshold and hence should be a good testing ground for chiral dynamics in the $ \pi$ $ \pi$ production process. No single event has been found, which meets all conditions for being a candidate for the pp $ \rightarrow$ nn $ \pi^{+}_{}$ $ \pi^{+}_{}$ reaction. This gives an upper limit for the cross-section of 0.16μb (90% C.L.), which is more than an order of magnitude smaller than the cross-sections of the other two-pion production channels at the same incident energy.     

Charge-carrier density collapse in La0.67Ca0.33MnO3and La0.67Sr0.33MnO3 epitaxial thin films

We measured the temperature dependence of the linear high field Hall resistivity of ( K) and ( K) thin films in the temperature range from 4 K up to 360 K in magnetic fields up to 20 T. At low temperatures we find a charge-carrier density of 1.3 and 1.4 holes per unit cell for the Ca- and Sr-doped compound, respectively. In this temperature range electron-magnon scattering contributes to the longitudinal resistivity. At the ferromagnetic transition temperature a dramatic drop in the number of charge-carriers n down to 0.6 holes per unit cell, accompanied by an increase in unit cell volume, is observed. Corrections of the Hall data due to a non saturated magnetic state will lead a more pronounced charge-carrier density collapse. Received 22 July 1999 and Received in final form 7 October 1999     

A nonalgebraic attractor in

We construct a nonalgebraic attractor for a holomorphic mapping on . The construction uses ideas from one-dimensional complex dynamics.

     

Valuations and multiplier ideals

We present a new approach to the study of multiplier ideals in a local, two-dimensional setting. Our method allows us to deal with ideals, graded systems of ideals and plurisubharmonic functions in a unified way. Among the applications are a formula for the complex integrability exponent of a plurisubharmonic function in terms of Kiselman numbers, and a proof of the openness conjecture by Demailly and Kollár. Our technique also yields new proofs of two recent results: one on the structure of the set of complex singularity exponents for holomorphic functions; the other by Lipman and Watanabe on the realization of ideals as multiplier ideals.

     

On the anomalous temperature dependence of cellulose aqueous solubility

The solubility of cellulose in water-based media is promoted by low temperature, which may appear counter-intuitive. An explanation to this phenomenon has been proposed that is based on a temperature-dependent orientation of the hydroxymethyl group. In this paper, this hypothesis is investigated using molecular dynamics computer simulations and NMR spectroscopy, and is discussed in conjunction with alternative explanations based on solvent–solute and solvent–solvent hydrogen bond formation respectively. It is shown that neither simulations nor experiments lend support to the proposed mechanism based on the hydroxymethyl orientation, whereas the two alternative explanations give rise to two distinct contributions to the hydration free energy of cellooligomers.