Castelnuovo-Mumford regularity by approximation

The Castelnuovo-Mumford regularity of a module gives a rough measure of its complexity. We bound the regularity of a module given a system of approximating modules whose regularities are known. Such approximations can arise naturally for modules constructed by inductive combinatorial means. We apply these methods to bound the regularity of ideals constructed as combinations of linear ideals and the module of derivations of a hyperplane arrangement as well as to give degree bounds for invariants of finite groups.     

Julia lines of random Dirichlet series

For the random entire functions defined by some random Dirichlet series almost surely every horizontal line is a Julia line without exceptional values. These results contain and generalize partially a theorem of P.L. Davies. The proofs are different.     

Sur la R-équivalence de torseurs sous un groupe fini

We give criteria for R-equivalence of torsors under finite constant group schemes over a field. In particular, using bitorsors, we obtain a Galois dévissage result which formalises and generalises a theorem of Philippe Gille in the case of local fields; for instance, Gille's theorem is shown to extend to higher local fields.     

Optimal prediction for linear regression with infinitely many parameters

The problem of optimal prediction in the stochastic linear regression model with infinitely many parameters is considered. We suggest a prediction method that outperforms asymptotically the ordinary least squares predictor. Moreover, if the random errors are Gaussian, the method is asymptotically minimax over ellipsoids in ?₂. The method is based on a regularized least squares estimator with weights of the Pinsker filter. We also consider the case of dynamic linear regression, which is important in the context of transfer function modeling.     

The representation type of Hecke algebras of type B

This paper determines the representation type of the Iwahori-Hecke algebras of type B when q≠±1. In particular, we show that a single parameter non-semisimple Iwahori-Hecke algebra of type B has finite representation type if and only if q is a simple root of the Poincaré polynomial, confirming a conjecture of Uno's (J. Algebra 149 (1992) 287).     

An analytical proof of Hardy-like inequalities related to the Dirac operator

We prove some sharp Hardy-type inequalities related to the Dirac operator by elementary, direct methods. Some of these inequalities have been obtained previously using spectral information about the Dirac-Coulomb operator. Our results are stated under optimal conditions on the asymptotics of the potentials near zero and near infinity.     

Le saut en zéro de la fonction de décalage spectral

We give a formula for the jump at zero of the spectral shift function associated with Schrödinger operator on manifolds with conical ends. We show that, according to its decay, a zero energy resonant state has a non-integer contribution.     

A remark on the moduli field of a curve

We give a purely algebro-geometric proof of the fact that every nonsingular projective curve can be defined over a finite extension of its moduli field. This extends a result byWolfart [7] to curves over fields of arbitrary characteristic. Received: 30 November 2001     

GI／G／1单重休假随机服务系统的马氏骨架方法

文献[1]引入一类具有广泛应用前景的随机过程-Markov骨架过程。借助Markov骨架过程的方法研究GI/G/1单重休假服务系统队长，及t时刻到达顾客等待时间的瞬时概率分布。