Some exact equivalents for the Brownian motion in Hölder norm

Summary Some exact equivalents of small probabilities are given for the Wiener measure on spaces of Hölder paths. It turns out that most of them are easier to derive than their counterparts in the uniform norm because of a classical result of Z. Ciesielski which makes the Brownian motion on these spaces easy to handle. In particular we study the equivalents of the probability of B in a fixed ball, ofB in a small ball and we give applications to the speed of clustering in Strassen law.     

Limiting laws for long Brownian bridges perturbed by their one-sided maximum, III

Summary Results of penalization of a one-dimensional Brownian motion ]]>]]>]]>]]>]]>]]>]]>(X_t) $, by its one-sided maximum $\big(S_t=\sup_{0 \leq u \leq t}X_u\big)$, which were recently obtained by the authors are improved with the consideration - in the present paper - of the asymptotic behaviour of the likewise penalized Brownian bridges of length $t$, as $t\rightarrow \infty$, or penalizations by functions of $(S_t,X_t)$, and also the study of the speed of convergence, as $t\rightarrow \infty$, of the penalized distributions at time $t$.     

Determination of theQ-value dependence of charged particle emission in the40Ca+40Ca reaction at 10 MeV/nucleon

An iterative method for the determination of the charged particle loss as a function of the reactionQ-value is developped. The analysis is based on experimental data resulting from 400 MeV⁴⁰Ca+⁴⁰Ca collisions.Z distributions are obtained at different calculatedQ-values corrected for evaporation and show rather good agreement — in the strongly damped case — with the ones derived from the OVERLAID ALICE code. Mean numbers of evaporated particles exhibit a linear increase as a function of these correctedQ-values; this corresponds to the evolution from quasi-direct to fully relaxed reactions.     

Contribution of decay products of transfer reactions to heavy-ion inelastic and transfer spectra

A study of decay product contributions to inclusive ejectile kinetic energy spectra is presented. Analytical formulae for the positions and widths of these contributions are derived from kinematical considerations. A formal integral expression for the double-differential cross section $\text{d}{}^2\text{σ/}\text{d}\text{Ω}\text{d}\text{E}$ is given in the case of one-particle emission from an excited state of the ejectile. The effects of anisotropic angular distributions are studied. The differential cross sections are then computed by a Monte Carlo method and compared to experimental spectra over a large range of measured systems. The transfer-evaporation mechanism is shown to contribute strongly to the background of the spectra but not to be responsible for the narrow structure observed in some reactions.     

Boundedness and convergence of some self-attracting diffusions

 We consider some self-attracting diffusions and study the behaviour of their paths when time tends to infinity. We prove that, in case the interaction is nonlocal, the paths are bounded a.s. even if they don't converge. Otherwise, we generalize the convergence result of M. Cranston and Y. Le Jan. Received: 5 March 2001 / Revised version: 3 June 2002 / Published online: 2 December 2002 Mathematics Subject Classification (2000): 60G17, 60J60, 60K35     

Une loi du logarithme itéré pour le groupe d'Heisenberg

Sans résumé     

Ten penalisation results of Brownian motion involving its one-sided supremum until first and last passage times, VIII

We penalise Brownian motion by a function of its one-sided supremum considered up to the last zero before t, respectively first zero after t, of that Brownian motion. This study presents some analogy with penalisation by the longest length of Brownian excursions, up to time t.     

Transfer and fragmentation reactions of14N at 60 MeV/u

Inclusive energy spectra and cross sections of reaction products close to the¹⁴N projectile (¹¹C,¹²C,¹³C,¹⁵N and¹⁵O) have been measured in the angular rangeθ _L =1.2°–4.2° at an incident energy of 60 MeV/u for five different target nuclei (¹²C,²⁷Al,⁵⁸Ni,⁹⁰Zr and²⁰⁸Pb). Two components are found to be systematically present in the energy spectra of the carbon isotopes, the first similar to that observed at relativistic energies and the second shifted down in energy characteristic for a very dissipative process. The dependence of the differential and integrated cross sections on the target mass indicates that the two-body final channels (¹⁴N,¹³C), (¹⁴N,¹⁵N) and (¹⁴N,¹⁵O) are strongly correlated to the fragmentation channels.