Arithmetic expressions of Selberg's zeta functions for congruence subgroups

In [P. Sarnak, Class numbers of indefinite binary quadratic forms, J. Number Theory 15 (1982) 229-247], it was proved that the Selberg zeta function for SL₂(Z) is expressed in terms of the fundamental units and the class numbers of the primitive indefinite binary quadratic forms. The aim of this paper is to obtain similar arithmetic expressions of the logarithmic derivatives of the Selberg zeta functions for congruence subgroups of SL₂(Z). As applications, we study the Brun-Titchmarsh type prime geodesic theorem and the asymptotic formula of the sum of the class number.     

A robust and efficient adaptive reweighted estimator of multivariate location and scatter

This article proposes a reweighted estimator of multivariate location and scatter, with weights adaptively computed from the data. Its breakdown point and asymptotic behavior under elliptical distributions are established. This adaptive estimator is able to attain simultaneously the maximum possible breakdown point for affine equivariant estimators and full asymptotic efficiency at the multivariate normal distribution. For the special case of hard-rejection weights and the MCD as initial estimator, it is shown to be more efficient than its non-adaptive counterpart for a broad range of heavy-tailed elliptical distributions. A Monte Carlo study shows that the adaptive estimator is as robust as its non-adaptive relative for several types of bias-inducing contaminations, while it is remarkably more efficient under normality for sample sizes as small as 200.     

An estimate for symmetric square <Emphasis Type="Italic">L</Emphasis>-functions on weight aspect

We establish a mean square estimate on the weight aspect for symmetric square L-functions at every point on the critical line. Received: 15 February 2002     

Completely empty pyramids on integer lattices and two-dimensional faces of multidimensional continued fractions

In this paper we develop an integer-affine classification of three-dimensional multistory, completely empty convex marked pyramids. We apply it to obtain the complete lists of compact two-dimensional faces of multidimensional continued fractions lying in planes at integer distances 2, 3, 4, …  to the origin. The faces are considered up to the action of the group of integer-linear transformations.     

Equivariant fixed-point indices of iterated maps

We describe an equivariant version (for actions of a finite group G) of Dold’s index theory, [10], for iterated maps. Equivariant Dold indices are defined, in general, for a G-map U → X defined on an open G-subset of a G-ANR X (and satisfying a suitable compactness condition). A local index for isolated fixed-points is introduced, and the theorem of Shub and Sullivan on the vanishing of all but finitely many Dold indices for a continuously differentiable map is extended to the equivariant case. Homotopy Dold indices, arising from the equivariant Reidemeister trace, are also considered.      

Higher order bad loci

Zero-schemes on smooth complex projective varieties, forcing all elements of ample and free linear systems to be reducible, are studied. Relationships among the minimal length of such zero-schemes, the positivity of the line bundle associated with the linear system, and the dimension of the variety are established. Bad linear spaces are also investigated.     

关于非光滑不变凸多目标规划的Wolfe型对偶

本文讨论定义在Banach空间上的,既具有等式约束又具有不等式约束的,非光滑(F,P)不变凸多目标规划的Wolfe对偶性,Mond-Weir型对偶性可类似讨论之。     

Echo planar imaging of perfluorocarbons

Emulsions of perfluorotributylamine (FTBA) and perflubron were evaluated for their utility in ¹⁹F echo planar imaging. Fluorine images of the emulsions were obtained in a phantom and two mice that had been predosed. Both agents, but particularly perflubron, show potential for fluorine echo planar studies because of the long spin-spin relaxation times of the CF₃ resonances. High resolution thin slice images obtained in as little as 26.6 ms are presented.