Tribute to Endre Csáki and Pál Révész

Summary This article provides a glimpse of some of the highlights of the joint work of Endre Csáki and Pál Révész since 1979. The topics of this short exploration of the rich stochastic milieu of this inspiring collaboration revolve around Brownian motion, random walks and their long excursions, local times and additive functionals, iterated processes, almost sure local and global central limit theorems, integral functionals of geometric stochastic processes, favourite sites--favourite values and jump sizes for random walk and Brownian motion, random walking in a random scenery, and large void zones and occupation times for coalescing random walks.     

Nonextensive Statistical Mechanics Application to Vibrational Dynamics of Protein Folding

The vibrational dynamics of protein folding is analyzed in the framework of Tsallis statistics. We employ exact expressions for classical harmonic oscillators by considering the unnormalized constraints. As q→1, we show that these approximations agree with the result of Gaussian network model.     

Some applications of polarized inelastic neutron scattering in magnetism

A brief account of applications of polarized inelastic neutron scattering in condensed matter research is given. We show that full polarization analysis is the only tool allowing to discriminate unambiguously between different magnetic modes in various magnetic materials. We show by means of recent results in the Heisenberg ferromagnet EuS that the effects of dipolar interactions can be studied on a microscopic scale. Moreover, we have found for the first time indications for the divergence of the longitudinal fluctuations belowT _c. In the itinerant antiferromagnet chromium we demonstrate that the dynamics of the longitudinal and transverse excitations are very different, resolving a long standing puzzle concerning the slope of their dispersion. Finally, we show that a measurement of the polarization-dependent part of the cross section of non-centrosymmetric MnSi proves directly that the chirality of the magnetic fluctuations is left-handed.     

Investigations of low- and high-spin states of <Superscript>132</Superscript>La

The fusion evaporation reaction ¹²²Sn(¹⁴N, 4n)¹³²La was used to populate the high-spin states of ¹³²La at the beam energy of 60 MeV. A new band consisting of mostly E2 transitions has been discovered. This band has the interesting links to the ground state 2^- and the isomeric state 6^-. A new transition of energy 351 keV connecting the low-spin states of the positive-parity band based on the πh _11/2 ⊗ νh _11/2 particle configuration, has been found. This has played a very important role in resolving the existing ambiguities and inconsistencies in the spin assignment of the band head. Received: 12 August 2002 / Accepted: 18 March 2003 / Published online: 7 May 2003     

Numerical study of the effects of the rupture process of a secondary diaphragm in expansion tubes

The results of a numerical study are described in which the interactions of a primary shock wave with a secondary diaphragm in expansion tubes are taken into account. The developing wave pattern in the interacting process of the shock with a secondary diaphragm are visualized by many kinds of figures (e.g., the time-distance diagrams of the wave phenomena on the axis, the acoustic impedance contours, and the time histories of the pitot pressure on the axis), and the influences of the shape and rupture process of the diaphragm on the quality of the test gas are explored.     

Investigating buyer and seller strategies in online auctions

The annual turnover of online auctions is already in tens of billions of dollars and this amount is predicted to grow substantially over the next few years. Hence, it is important to know how buyers and sellers can influence their chances of success. Therefore, data were collected from eBay auctions for three different categories of collectible items, namely those with a published guide price, those with a rough guide price and those having no easily obtainable guide price. The options available to buyers and sellers of items were then analysed. It was found that it was hard for the seller to influence an item's achieved price significantly, apart from items with no guide price where the starting price could have an effect. Most bidders bid close to the current value and so there were insufficient data to determine the consequences of timing on the placing of high bids. For low bids, delaying a bid was found to improve significantly the chances of winning for one of the data sets.     

Smoothing estimation of rate function for recurrent event data with informative censoring

This paper proposes kernel estimation of the occurrence rate function for recurrent event data with informative censoring. An informative censoring model is considered with assumptions made on the joint distribution of the recurrent event process and the censoring time without modeling the censoring distribution. Under the validity of the informative censoring model, we also show that an estimator based on the assumption of independent censoring becomes inappropriate and is generally asymptotically biased. To investigate the asymptotic properties of the proposed estimator, the explicit form of its asymptotic mean squared risk and the asymptotic normality are derived. Meanwhile, the empirical consistent smoothing estimator for the variance function of the estimator is suggested. The performance of the estimators are also studied through Monte Carlo simulations. An epidemiological example of intravenous drug user data is used to show the influence of informative censoring in the estimation of the occurrence rate functions for inpatient cares over time.     

An algorithm to locate perinatal facilities in the municipality of Rio de Janeiro

In order to reduce infant mortality in the municipality of Rio de Janeiro it is desired to encourage all mothers-to-be to attend the appropriate health care facilities. A 3-level hierarchical prenatal–neonatal health care system is described together with a basic model for optimising accessibility to facilities. A genetic algorithm to solve the basic model is developed and some numerical experience reported. Extensions to the basic model and planned future research are briefly indicated.     

Inversion of adjunction for non-degenerate hypersurfaces

 We prove a precise inversion of adjunction formula for the log variety (ℂ ^{d +1},X), where X is a non-degenerate hypersurface. As a corollary, the minimal log discrepancies of non-degenerate normal hypersurface singularities are bounded by dimension. Received: 17 September 2002 / Revised version: 22 November 2002 Published online: 14 February 2003 Current address: DPMMS, CMS, University of Cambridge, Wilberforce Road, Cambridge CB3 0WB, England. e-mail: f.ambro@dpmms.cam.ac.uk Mathematics Subject Classification (2000): Primary 14B05; Secondary 14M25, 52B20