Behavior of a functional in learning theory

Let H be a Hilbert space, A ∈ L(H), y ∈ , and y ∉ R(A). We study the behavior of the distance square between y and A(B _τ), defined as a functional F(τ), as the radius τ of the ball B _τ of H tends to ∞. This problem is important in estimating the approximation error in learning theory. Our main result is to estimate the asymptotic behavior of F(τ) without the compactness assumption on the operator A. We also consider the Peetre K-functional and its convergence rates.      

Self-organized model for information spread in financial markets

A self-organized model with social percolation process is proposed to describe the propagations of information for different trading ways across a social system and the automatic formation of various groups within market traders. Based on the market structure of this model, some stylized observations of real market can be reproduced, including the slow decay of volatility correlations, and the fat tail distribution of price returns which is found to cross over to an exponential-type asymptotic decay in different dimensional systems. Received 15 March 2000     

Local order, entropy and predictability of financial time series

We consider time series of financial data as the Dow Jones Index with respect to the existence of local order. The basic idea is that in spite of the high stochasticity in average there might be special local situations where there local order exist and the predictability is considerably higher than in average. In order to check this assumption we discretise the time series and investigate the frequency of the continuation of definite words of length n first. We prove the existence of relatively long-range correlations under special conditions. The higher order Shannon entropies and the conditional entropies (dynamical entropies) are calculated, characteristic fluctuations are found. Instead of the dynamic entropies which yield mean values of the uncertainty/predictability we finally investigate the local values of the uncertainty/predictability and the distribution of these quantities. Received 19 January 2000     

汞原子6sns 3S1,6snd 3D1 Rydberg系列的寿命

利用多通道量子数亏损理论计算了汞原子6sns^3S1(n=11～25),6snd^3D1(n=12～24)两个Rydberg系列的能级和寿命,给出了这两个系列寿命所遵循的公式,6sns^3S。系列为r=0．814v^2.835(ns),6snd^3D1系列为r=0．302v^2.926ns),其中v为有效量子数。     

GENERALIZED THEORY OF NONLINEAR AND UNSTEADY MECHANICS AND APPLICATIONS TO PARTICLE PHYSICS

ＧＥＮＥＲＡＬＩＺＥＤＴＨＥＯＲＹＯＦＮＯＮＬＩＮＥＡＲＡＮＤＵＮＳＴＥＡＤＹＭＥＣＨＡＮＩＣＳＡＮＤＡＰＰＬＩＣＡＴＩＯＮＳＴＯＰＡＲＴＩＣＬＥＰＨＹＳＩＣＳＹａｎｇＷｅｎ－ｘｉｏｎｇ（杨文熊）（ＳｈａｎｇｈａｉＪｉａｏｔｏｎｙＵｎｉｖｅｒｓｉｔｙ...     

Solutions of the generaln-th order variable coefficients linear difference equation

In this paper.variable operator and its product with shifting operator are studied.The product of power series of shifting operator with variable coefficient is defined andits convergence is proved under Mikusinski’s sequence convergence.After turning ageneral variable coefficient linear difference equation of order n into a set of operatorequations.we can obtain the solutions of the general n-th order variable coefficientlinear difference equation.     

再生核希尔伯特空间连续线性泛函的范数及其应用北大核心

考虑了再生核希尔伯特空间连续线性泛函范数的表示,得到了用其范数平方等于该线性泛函连续两次作于再生核的简明表示.对于常见的Sobolev-Hibert空间而言,其再生核则可用截幂函数来表示,从而得到Sobolev-Hibert空间上连续线性泛函范数的简洁表示,以新视角解释和简化了文献中的现有结果.     

光栅横向位移遥测中的辨向和移相技术

分析在用光栅多普勒效应实现横向位移遥测过程中利用移相技术和频移技术获得９０°相移的方法以及光栅运动方向的辨别方法,得出相应的实验结果。     

积分型Hilbert定理的改进与应用

本文建立如下权函数的不等式ｗ （ｘ） ＝ ∫∞０１ｘ ＋ ｙ ＋ １（ｘ ＋ １ｙ ＋ １）１／２ｄｙ ≤π［１ － １ － ２／π（ｘ ＋ １）１／２］　（ｘ ∈［０,∞））,这里,常数１－ ２／π是最佳值,从而改进了积分型Ｈｉｌｂｅｒｔ定理,作为应用,建立一个Ｈｉｌｂｅｒｔ类积分不等式及其加强式;并改进推广了Ｈａｒｄｙ－Ｌｉｔｔｅｗ ｏｏｄ 积分不等式．     

单位圆内零级Taylor级数

我们研究了单位圆内零级Ｔａｙｌｏｒ级数的增性,得到它们的系数与增长性间的关系。