Elliptic boundary value problems in hybrid domains

We derive asymptotic transmission conditions at points where segments are attached to a three-dimensional body. These conditions result in a formally self-adjoint problem on a hybrid set with properties similar to those of standard boundary value problems. In particular, the problem has a zero index and possesses a variational statement. If the systems of differential equations have a special form, then the operator of the problem is realized as a self-adjoint extension of the decoupled operators of the problems on the body and the segments. From this viewpoint, we interpret the results of asymptotic analysis of coupled thin and solid bodies.Dedicated to Victor Borisovich Lidskii on the occasion of his jubileeTranslated from Funktsionalnyi Analiz i Ego Prilozheniya, Vol. 38, No. 4, pp. 55–72, 2004Original Russian Text Copyright © by S. A. NazarovSupported by the Russian Foundation for Basic Research (grant No. 00-01-00835).     

Uniform bounds on the number of rational points of a family of curves of genus 2

We exhibit a genus-2 curve defined over which admits two independent morphisms to a rank-1 elliptic curve defined over . We describe completely the set of -rational points of the curve and obtain a uniform bound on the number of -rational points of a rational specialization of the curve for a certain (possibly infinite) set of values . Furthermore, for this set of values we describe completely the set of -rational points of the curve . Finally, we show how these results can be strengthened assuming a height conjecture of Lang.     

p-Adic multi-zeta values

Let X be the projective line minus 0,1, and ∞ over . The aim of the following is to give a series representations of the p-adic multi-zeta values in the depth two quotient. The approach is to use the lifting of the frobenius which is not a good choice near 1, but which gives simple formulas away from 1, and to relate the action of frobenius on the de Rham path from 0 to ∞ and on the one from 0 to 1. Also some relations between the p-adic multi-zeta values of depth two are obtained.     

Detecting Change Points in Polynomial Regression Models with an Application to Cable Data Sets

In this paper, the Schwarz Information Criterion (SIC) is used to detect the change points in polynomial regression models. Switching quadratic regression models with same amount of model deviation and switching polynomial regression models with different amount of model deviation for different segments of regression are considered. The number of separate regimes and their corresponding regression orders are assume to be known. The method is then applied to cable data sets and the change points are successfully detected.     

Descriptive properties of the set of exposed points of compact convex sets in

We construct a compact convex subset of such that the set of its exposed points is not the intersection of an set and a set. The existence of such a set answers a question posed by G. Choquet, H.H. Corson and V.L. Klee.

     

两个渐近非扩张映射公共不动点的迭代程序

在一致凸Banach空间中,研究了迭代序列逼近收敛于两个渐近非扩张映射的公共不动点。所得结果推广了已有的一些结果。     

自反Banach空间算子闭值域的若干性质

本文讨论自反Banach空间算子T－正则点,证明了T及其共轭算子T^*在闭值域区域上的T－正则点集的关系,ρb（T）与ρb(T)的若干结构表示。     

Multiplicities of fixed points of holomorphic maps in several complex variables

Let Δ^υ be the unit ball in ℂ^υ with center 0 (the origin of υ) and let F:Δ^υ→ℂ^υbe a holomorphic map withF(0) = 0. This paper is to study the fixed point multiplicities at the origin 0 of the iteratesF ⁱ =F∘⋯∘F (i times),i = 1,2,.... This problem is easy when υ = 1, but it is very complicated when υ > 1. We will study this problem generally.