Approximating dominant singular triplets of large sparse matrices via modified moments

A procedure for determining a few of the largest singular values and corresponding singular vectors of large sparse matrices is presented. Equivalent eigensystems are solved using a technique originally proposed by Golub and Kent based on the computation of modified moments. The asynchronicity in the computations of moments and eigenvalues makes this method attractive for parallel implementations on a network of workstations. Although no obvious relationship between modified moments and the corresponding eigenvectors is known to exist, a scheme to approximate both eigenvalues and eigenvectors (and subsequently singular values and singular vectors) has been produced. This scheme exploits both modified moments in conjunction with the Chebyshev semi-iterative method and deflation techniques to produce approximate eigenpairs of the equivalent sparse eigensystems. The performance of an ANSI-C implementation of this scheme on a network of UNIX workstations and a 256-processor Cray T3D is presented.This research was supported in part by the National Science Foundation under grant numbers NSF-ASC-92-03004 and NSF-ASC-94-11394.     

The electrochemistry of cephalosporin C derivatives: Part II. Cephalothin,sodium salt

The electrochemical behavior of cephalothin has been studied by a.c. and d.c. polarography, cyclic voltammetry, and coulometry in both aqueous and nonaqueous media in order to gain a greater understanding of the reaction pathways involved in cephalosporin reduction. The reductive allylic cleavage of the 3′-acetoxy function has been found to produce Δ³-deacetoxy and 3-exomethylene cephalothin compounds (geometric isomers) and stereochemical isomers of the 3′-exomethylene compound at the 4-position. The ratio of these compounds to one another is dependent on the experimental conditions used, with adsorption playing an important role. The reductive allylic cleavage of the S₁?C₂ bond is a competitive reaction pathway. Δ³-Deacetoxy cephalothin may undergo further reduction, depending on the electrolysis potential selected.     

Analysis of electronically nonadiabatic chemical reactions: An information theoretic approach

A practical procedure for the determination of branching ratios for reactions which lead to either excited or electronically ground state products is outlined. The method is applied to four reactions which could (on energetic grounds) produce an electronically excited iodine atom. No case of a complete inversion is found, but one reaction (F + HI) is predicted to yield a statistical, (one half), I^*(²P_1/2) to I(²P_3/2) ratio.     

Search for [corrected] B0(s) --> mu+ mu- and B0(d) [corrected] --> mu + mu- decays in pp collisions with CDF II

We report on a search for B0(s) --> mu+ mu- and B0(d) --> mu + mu- decays in pp collisions at square root(s) = 1.96 TeV using 364 pb(-1) of data collected by the CDF II detector at the Fermilab Tevatron Collider. After applying all selection requirements, we observe no candidates inside the B0(s) or B0(d) mass windows. The resulting upper limits on the branching fractions are B(B0(s) --> mu+ mu-) < 1.5 x 10(-7) and B(B0(d) --> mu+ mu-) < 3.9 x 10(-8) at 90% confidence level.     

Network information and connected correlations

Entropy and information provide natural measures of correlation among elements in a network. We construct here the information theoretic analog of connected correlation functions: irreducible N-point correlation is measured by a decrease in entropy for the joint distribution of N variables relative to the maximum entropy allowed by all the observed N-1 variable distributions. We calculate the "connected information" terms for several examples and show that it also enables the decomposition of the information that is carried by a population of elements about an outside source.     

Lewis acid mediated cyclisations of silylated methylenecyclopropyl hydrazones

Silylated methylenecyclopropyl hydrazones on treatment with BF3 x Et2O cyclise to give heterocyclic products involving a novel sequence of hydride and silyl shifts via a series of increasingly stable cationic intermediates.     

Metal-directed self-assembly of bimetallic dithiocarbamate transition metal cryptands and their binding capabilities

A novel family of redox-active dinuclear transition metal based cryptands self-assembled from dithiocarbamate ligands has been synthesised; depending upon the nature of the spacer groups these new cryptand systems have been shown to electrochemically recognise the binding of cations or anions.     

Knotted Zeros in the Quantum States of Hydrogen

Complex superpositions of degenerate hydrogen wavefunctions for the n th energy level can possess zero lines (phase singularities) in the form of knots and links. A recipe is given for constructing any torus knot. The simplest cases are constructed explicitly: the elementary link, requiring n6, and the trefoil knot, requiring n7. The knots are threaded by multistranded twisted chains of zeros. Some speculations about knots in general complex quantum energy eigenfunctions are presented.     

Investigation of active structural intensity control in finite beams: theory and experiment

An investigation of structural intensity control is presented in this paper. As opposed to previous work, the instantaneous intensity is completely taken into account in the control algorithm, i.e., all the terms are considered in the real-time control process and, in particular, the evanescent waves are considered in this approach. A finite difference approach using five accelerometers is used as the sensing scheme. A feedforward filtered-X least mean square algorithm is adapted to this energy-based control problem, involving a nonpositive definite quadratic form in general. In this respect, the approach is limited to cases where the geometry is such that the intensity component will have the same sign for the control source and the primary disturbance. Results from numerical simulations are first presented to illustrate the benefit of using a cost function based on structural intensity. Experimental validation of the approach is conducted on a free-free beam covered with viscoelastic material. A comparison is made between classical acceleration control and structural intensity control and the performance of both approaches is presented. These results confirm that using intensity control allows the error sensors to be placed closer to the control source and the primary disturbance, while preserving a good control performance.