The Padé-Rayleigh-Ritz method for solving large hermitian eigenproblems

We make use of the Padé approximants and the Krylov sequencex, Ax,,...,A ^m–1 x in the projection methods to compute a few Ritz values of a large hermitian matrixA of ordern. This process consists in approaching the poles ofR _x()=((I–A)^–1 x,x), the mean value of the resolvant ofA, by those of [m–1/m]_Rx(), where [m–1/m]_Rx() is the Padé approximant of orderm of the functionR _x(). This is equivalent to approaching some eigenvalues ofA by the roots of the polynomial of degreem of the denominator of [m–1/m]_Rx(). This projection method, called the Padé-Rayleigh-Ritz (PRR) method, provides a simple way to determine the minimum polynomial ofx in the Krylov subspace methods for the symmetrical case. The numerical stability of the PRR method can be ensured if the projection subspacem is sufficiently small. The mainly expensive portion of this method is its projection phase, which is composed of the matrix-vector multiplications and, consequently, is well suited for parallel computing. This is also true when the matrices are sparse, as recently demonstrated, especially on massively parallel machines. This paper points out a relationship between the PRR and Lanczos methods and presents a theoretical comparison between them with regard to stability and parallelism. We then try to justify the use of this method under some assumptions.     

The asymptotic behavior of queueing systems: Large deviations theory and dominant pole approximation

This paper presents the exact asymptotics of the steady state behavior of a broad class of single-node queueing systems. First we show that the asymptotic probability functions derived using large deviations theory are consistent (in a certain sense) with the result using dominant pole approximations. Then we present an exact asymptotic formula for the cumulative probability function of the queue occupancy and relate it to the cell loss ratio, an important performance measure for service systems such as ATM networks. The analysis relies on a new generalization of the Taylor coefficients of a complex function which we call characteristic coefficients. Finally we apply our framework to obtain new results for the M/D/1 system and for a more intricate multiclass M/D/n system.     

The law of the solution to a nonlinear hyperbolicSPDE

Let { _s,t ,(s,t ₊ ² } be a white noise on ₊ ² . We consider the hyperbolic stochastic partial differential equation {ie863-3} The purpose of this paper is to study the law of the solution to this equation. We analyze the existence and smoothness of the density using the tools of Malliavin Calculus. Finally we prove a large deviation principle on the space of continuous functions, for the family of probabilities obtained by perturbation of the noise in the equation.This work has been partially supported by the grant of the DGICYT No. PB 930052 and the EU Science project CT 910459.     

Evolution of the structural stability of large Cu,Ni, Pd,and Ag clusters with size: An analysis within the embedded atom method

A study of the structural stability of clusters made up of a single component has been carried out within the Embedded Atom Method. Perfect icosahedral and cuboctahedral Cu, Ni, Pd, and Ag clusters with up to 5083 atoms have been compared. The icosahedron is found to be the stable structure for small clusters, and a change of structure from icosahedral to cuboctahedral is found as the cluster size increases. A contraction of the interatomic distances results when the cluster size decreases.     

苯并[b]萘并[2'''',3'''':5,6][1,4]二噻英并[2,3-i]噻蒽-5,7,9,14,16,18-六酮的合成及其三阶非线性光学性能

以1,4-萘醌为原料,合成了含硫的醌构稠杂环化合物苯并[b]萘并[2',3':5,6][1,4]二噻英并[2,3-i]噻蒽-5,7,9,14,16,18-六酮(4),其结构经1H NMR和IR确证.采用波长为800 nm,脉宽为80 fs的Ti:Sapphire飞秒激光,运用双光束简并四波混频法测定了4的三阶非线性光学性能,结果表明,4的三阶非线性光学极化率χ(3),非线性折射率n2,分子二阶超极化率γ和响应时间分别为2.89×10-13 esu, 5.31×10-12 esu, 3.14×10-31 esu和101 fs.并分析了4的分子结构对其三阶非线性光学性能的影响.     

Consequences of the ‘Pedersen papers’ on crown type chemistry at Würzburg and Bonn Universities: From heteroaromatic crowns and podands to large molecular and crystalline cavities including multisite receptors,cascade molecules,chromoionophores, siderophores,surfactant-type,and extreme ligands

We thank the editors of this issue for the opportunity to present the historic development of crown chemistry at the Universities of Wurzburg and Bonn in memory of C. J. Pedersen, the originator of the crown ethers. His legacy of science has tremendously stimulated research at both universities.This paper is dedicated to the memory of the late Dr C. J. Pedersen.     

The pockels coefficient of new polymers for nonlinear optics and its time dependence after poling,compared with dielectric measurements

Epoxy polymers with donor–acceptor type side groups were synthesized for application in nonlinear optics. The stability of the Pockels coefficient was measured in thin films after poling. The relaxation times and their temperature dependence seem to be correlated with dielectric measurements. Guest–host systems (polystyrene and polymethylmethacrylate with dimethylaminonitrostilbene) were investigated for comparison.     

Synthesis of Calix[4]arene Derivatives with NLO Properties

The new chromophore compounds with NLO properties were prepared by Knoevenagel condensation from forrnyl or diformyl calix[4/arene and isophorone derivatives in the presence of piperidine and acetic acid, respectively. In these chromophore calix[4]arenes, the ring locked trienes were employed as the conjugation bridge and electron acceptor in D-π-A units. The NMR spectra demonstrated that they existed in a cone conformation and consequently non-conjugated D-π-A units could be oriented at nearly the same direction.     

The Synthesis of Third—order Optical Nonlinear Organic Polyheterocyclic Materials

Synthesis of the third-order nonlinear materials:bis (1,4-dihydroxynaphthalene) tetrathiafulvalene and bis (1,4-dialkoxylnaphthalene) tetrathiafulvalene has been achieved in four steps, starting from 2,3-dichloro-1,4-naphthaquinone. The materials exhibit larger third-order nonlinear optical susceptibilities χ.