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.     

Low frequency longitudinal lattice modes in graphite intercalation compounds

Results of inelastic neutron scattering experiments on a stage 2 graphite-FeCl₃ intercalation compound are reported. A one-dimensional Born-von Kármán model is formulated and applied to interpret the data. The application of this model to other recently reported neutron data for donor compounds suggests systematic trends in the magnitudes of the interactions, dependent on the intercalate sandwich thickness.     

Bounds for the round-off errors in the richardson second order method

The application of the Richardson second order iterative method to positive definite, symmetric linear equations is investigated. Absolute and statistical bounds for the round-off error are derived. The statistical theory agrees well with numerical experiments, until the accumulated round-off error becomes of the order of magnitude of the error in the computed solution. After this point the statistical dependence between the local round-off errors makes the observed variances larger than the theoretical variances.This paper (and the Appendix) describe research carried out while both authors were employed by Space Technology Laboratories, Inc., Los Angeles, California.Presented at the IFIP Congress, 1962, under a National Science Foundation travel grant.     

Atomic-scale imaging of wall-by-wall breakdown and concurrent transport measurements in multiwall carbon nanotubes

We report the atomic-scale imaging with concurrent transport measurements of the breakdown of individual multiwall carbon nanotubes inside a transmission electron microscope equipped with a piezomanipulator. We found unexpectedly three distinct breakdown sequences: namely, from the outermost wall inward, from the innermost wall outward, and alternatively between the innermost and the outmost walls. Remarkably, a significant amount of current drop was observed when an innermost wall is broken, proving unambiguously that every wall is conducting. Moreover, the breakdown of each wall in any sequence initiates in the middle of the nanotube, not at the contact, proving that the transport is not ballistic.     

Strain-induced interference effects on the resonance Raman cross section of carbon nanotubes

In this Letter, we report the effects of strain on the electronic properties of single-wall carbon nanotubes. When we normalize the electronic transition energies to the corresponding values obtained for unstrained tubes, we obtain that, regardless of the tube diameter, all the data collapse onto universal curves following an n - m = constant family pattern. In the case of metallic tubes, quantum interference effects on the Raman cross section are predicted for strained tubes when the energies of the lower and the upper components have nearly the same values. Experimental evidence for the strain-induced Raman cross section changes is observed in single nanotube spectroscopy.     

Preconditioned Hermitian and skew-Hermitian splitting methods for non-Hermitian positive semidefinite linear systems

Summary. For the positive semidefinite system of linear equations of a block two-by-two structure, by making use of the Hermitian/skew-Hermitian splitting iteration technique we establish a class of preconditioned Hermitian/skew-Hermitian splitting iteration methods. Theoretical analysis shows that the new method converges unconditionally to the unique solution of the linear system. Moreover, the optimal choice of the involved iteration parameter and the corresponding asymptotic convergence rate are computed exactly. Numerical examples further confirm the correctness of the theory and the effectiveness of the method.Mathematics Subject Classification: 65F10, 65F50, CR: G1.3Subsidized by The Special Funds For Major State Basic Research Projects G1999032803Research supported, in part, by DOE-FC02-01ER4177Revised version received November 5, 2003     

Real and Rational Forms of Certain O<Subscript>2</Subscript>(ℂ)-actions,and a Solution to the Weak Complexification Problem

The main result of this paper is that there is a non-linearizable real algebraic action of the circle S¹ on ⁴, an action which becomes linearizable over . This solves the Weak Complexification Problem. We also show that for any field k of characteristic zero, there are non-linearizable algebraic actions of the group O₂(k) on four-dimensional affine k-space, and if k contains a square root of 3, then this action restricts to a non-linearizable action of the symmetric group S₃ on four-dimensional affine k-space.     

Embeddings of Danielewski surfaces

A Danielewski surface is defined by a polynomial of the form P=x ^nz –p(y). Define also the polynomial P =x ^nz –r(x)p(y) where r(x) is a non-constant polynomial of degree n–1 and r(0)=1. We show that, when n2 and deg p(y)2, the general fibers of P and P are not isomorphic as algebraic surfaces, but that the zero fibers are isomorphic. Consequently, for every non-special Danielewski surface S, there exist non-equivalent algebraic embeddings of S in ³. Using different methods, we also give non-equivalent embeddings of the surfaces xz=(y ^d _n >–1) for an infinite sequence of integers d _n . We then consider a certain algebraic action of the orthogonal group on ⁴ which was first considered by Schwarz and then studied by Masuda and Petrie, who proved that this action could not be linearized. This was done by comparing the strata of this action to those of the induced tangent space action. Inequivalent embeddings of a certain singular Danielewski surface S in ³ are found. We generalize their result and show how this leads to an example of two smooth algebraic hypersurfaces in ³ which are algebraically non-isomorphic but holomorphically isomorphic. Partially supported by NSF Grant DMS 0101836.     

A note on triangular derivations of

For a field of characteristic zero, and for each integer , we construct a triangular derivation of whose ring of constants, though finitely generated over , cannot be generated by fewer than elements.

     

A Facile Synthesis and Structural Verification of Etorphine and Dihydroetorphine from Codeine

In this study, an improved process for the synthesis of etorphine and dihydroetorphine from codeine with an overall yield of 2.7% and 1.5% respectively is described. The structure of 19‐propylthevinol 7 was verfied by X‐ray structure analysis. This result is promising for synthesizing various morphine‐based drugs.