Three-step iterations for nonlinear accretive operator equations

In this paper, we suggest and analyze a three-step iterative scheme for solving nonlinear strongly accretive operator equation Tx=f without continuous condition in a uniformly smooth Banach space. Our results include the Ishikawa, Mann and Noor iterations as special cases. The results presented in this paper improve and extend almost all the current results in the more general setting.     

Some Remarks on Complex Crowns of Riemannian Symmetric Spaces

We discuss several results and problems in which complex geometric constructions appear in the geometry of real pseudo Riemannian symmetric spaces in connection with analysis on such spaces.     

Picosecond time-resolved nonresonant ionization detected IR spectroscopy on 7-azaindole dimer

The picosecond time-resolved IR spectrum of the 7-azaindole dimer has been measured by picosecond time-resolved nonresonant ionization detected IR spectroscopy. This new time-resolved technique was developed by combining nonresonant ionization detected IR (NID-IR) spectroscopy with tunable picosecond IR and UV lasers. The time-resolved NID-IR spectrum from 2 600 cm^-1 to 3 800 cm^-1 shows a drastic change from 1.5 ps to 11 ps time evolution. A mode-specific vibrational redistribution has been suggested. Received 14 May 2002 / Received in final form 11 June 2002 Published online 13 September 2002     

Ultrafast dynamics in the excited hydrogen atom transfer states of ammonia clusters

Neutral ammonia clusters (NH₃)_m are photo-excited to the electronic state by a deep UV femtosecond laser pump pulse. Within a few hundred femtoseconds a significant fraction of the clusters rearrange to form an H-transfer state (NH₃)_m-2NH₄(3s)NH₂ with the subunit NH₄ in its 3s electronic ground state. This state is then electronically excited by a time-delayed infrared control pulse of variable wavelength. Finally, a third (probe) pulse in the UV ionizes the clusters for detection. The lifetime of the excited (NH₃)_m-2NH₄(3p)NH₂ states is found to vary between 2.7 and 0.13 ps depending on cluster size and excitation energy. It increases drastically upon deuteration. The corresponding cluster size-dependent photoelectron spectra allow us to disentangle the underlying energetics of the excitation and ionization process and reveal additional processes, such as nonresonant ionization or dissociative ionization. The experimental findings suggest that the excited H-transfer ammonia complexes with m > 2 are deactivated by an internal conversion process back to the electronically lowest H-transfer state followed by fast dissociation. Received 22 September 2001 and Received in final form 31 January 2002     

实对称五对角矩阵逆特征值问题

1 引 言 对于n阶实对称矩阵A=(aij),r是一个正整数,且1≤r≤n-1,当|i-j|>r时,aij=0(i,j=1,2,…,n),至少有一个i使得ai,i+r≠0,则称矩阵A是带宽为2r+1的实对称带状矩阵.特别地,当r=1时,称A为实对称三对角矩阵;当r=2时,称A为实对称五对角矩阵. 实对称带状矩阵逆特征值问题应用十分广泛,这类问题不仅来自微分方程逆特征值问     

A Statistic for Testing the Null Hypothesis of Elliptical Symmetry

We present and study a procedure for testing the null hypothesis of multivariate elliptical symmetry. The procedure is based on the averages of some spherical harmonics over the projections of the scaled residual (1978, N. J. H. Small, Biometrika65, 657–658) of the d-dimensional data on the unit sphere of ^d. We find, under mild hypothesis, the limiting null distribution of the statistic presented, showing that, for an appropriate choice of the spherical harmonics included in the statistic, this distribution does not depend on the parameters that characterize the underlying elliptically symmetric law. We describe a bivariate simulation study that shows that the finite sample quantiles of our statistic converge fairly rapidly, with sample size, to the theoretical limiting quantiles and that our procedure enjoys good power against several alternatives.     

一类对称函数的Schur凸性及其应用

给出一类对称函数 Schur凸性的推广 ,运用该结果并结合控制不等式理论建立若干对称函数不等式及 n维欧氏空间 En中的单形不等式 ,所得结果是以往某些结果的推广或补充 .     

扩散过程代数式收敛定性的判别准则

本文定性地讨论非紧空间中可逆扩散过程的代数式收敛的判定 .使用分裂空间的方法 .将全空间分裂成两个部分 :紧的子空间与非紧的余子空间 .在紧子空间中考虑边界反射的Neumann过程 ,它必然是代数式收敛的 .而在非紧子空间中考虑边界吸收的Dirichlet过程 ,如果这一Dirichlet过程以代数式的速度击中边界 ,那么就有原过程在全空间代数式收敛 ;反之 ,原过程代数式收敛 ,非紧子空间中的Dirichlet过程也是代数式收敛的 .因此过程在紧子空间的任意摄动不会影响在全空间的代数式收敛性 .     

Quantum Dynamics in the Fermi–Pasta–Ulam Problem

We study a quantum chain of oscillators with nonlinear quartic interactions, under the “narrow packet” approximation. We analyse the dynamics of quantum corrections and the conditions at which the quantum solution for average complex amplitude converges to the corresponding classical unstable solution which describes the four-wave decay processes of phonons. We develop an asymptotic theory by using a small quasiclassical parameter, and determine the characteristic time scale for which the evolution of decay processes is essentially specified by quantum effects. AMS Subject classification: Primary: 35F10 Secondary: 35Q40, 35B40     

Improved Lower Bounds for the Critical Probability of Oriented Bond Percolation in Two Dimensions

We present a coupled decreasing sequence of random walks on Z that dominate the edge process of oriented bond percolation in two dimensions. Using the concept of random walk in a strip, we describe an algorithm that generates an increasing sequence of lower bounds that converges to the critical probability of oriented percolation p_c. From the 7th term on, these lower bounds improve upon 0.6298, the best rigorous lower bound at present, establishing 0.63328 as a rigorous lower bound for p_c. Finally, a Monte Carlo simulation technique is presented; the use thereof establishes 0.64450 as a non-rigorous five-digit-precision (lower) estimate for p_c. Mathematics Subject Classification (1991): 60K35 Supported by CNPq (grant N.301637/91-1). Supported by a grant from CNPq.