Product Integration Rules at Clenshaw-Curtis and Related Points: A Robust Implementation

Product integration rules generalizing the Fej?r, Clenshaw-Curtis,and Filippi quadrature rules respectively are derived for integralswith trigonometric and hyperbolic weight factors. The Chebyshevmoments of the weight functions are found to be given by well-conditionedexpressions, in terms of hypergeometric functions ₀F₁. An a priori error estimator is discussed which is shown bothto avoid wasteful invocation of the integration rule and toincrease significantly the robustness of the automatic quadratureprocedure. Then, specializing to extended Clenshaw-Curtis (ECC) rules,three types of a posteriori error estimates are considered andthe existence of a great risk of their failure is demonstratedby large scale validation tests. An empirical error estimator,superseding them for slowly varying integrands, is found toresult in a spectacular increase in the output reliability. Finally, enhancements in the control of the interval subdivisionstrategy aiming at increasing code robustness is discussed.Comparison with the code DQAWO of QUADPACK, with about a hundredthousand solved integrals, is illustrative of the increasedrobustness and error estimate reliability of our computer codeimplementation of the ECC rules.     

Asynchronous two-stage iterative methods

Summary. Parallel block two-stage iterative methods for the solution of linear systems of algebraic equations are studied. Convergence is shown for monotone matrices and for -matrices. Two different asynchronous versions of these methods are considered and their convergence investigated. Received September 7, 1993 / Revised version received April 21, 1994     

Direct modulation and optical confinement factor modulation of semiconductor lasers

Abstract

A method for modulation of semiconductor lasers is demonstrated. The method is based on the modulation of the optical confinement factor. Using this method an enhanced—3-dB bandwidth is observed in agreement with the small signal rate equation analysis. A modulation response that drops at high frequencies slower than the conventional direct current modulation response is achieved. This supports the theoretical predictions, showing an intrinsic 1/f decay rate for the optical confinement factor modulation scheme versus an intrinsic 1/f² decay for direct modulation.     

Thermodynamic Complexation of Dopamine with Zinc(II) in Media with Different Dielectric Constants

The complexation of zinc(II) with dopamine has been investigated by spectrophotometric measurements in mixed solvent system at an ionic strength of 0.2 mol•dm－3 sodium chloride, employed at at (15±0.1), (25±0.1), (35±0.1) ℃ at inin a pH range of ca. 6 to ca. 7 with a high ratio of ligand to metal. The effect of solvent systems on protonation and complexation are was was discussed. Linear relationships are werewere observed by plotting lg K versus 1/D, where K and D show stability and dielectric constants, respectively.     

A deflated conjugate gradient method for multiple right hand sides and multiple shifts

We consider the task of computing solutions of linear systems that only differ by a shift with the identity matrix as well as linear systems with several different right-hand sides. In the past, Krylov subspace methods have been developed which exploit either the need for solutions to multiple right-hand sides (e.g. deflation type methods and block methods) or multiple shifts (e.g. shifted CG) with some success. In this paper we present a block Krylov subspace method which, based on a block Lanczos process, exploits both features—shifts and multiple right-hand sides—at once. Such situations arise, for example, in lattice quantum chromodynamics (QCD) simulations within the Rational Hybrid Monte Carlo (RHMC) algorithm. We present numerical evidence that our method is superior compared to applying other iterative methods to each of the systems individually as well as, in typical situations, to shifted or block Krylov subspace methods.     

Determination of C60/C70 ratios in fullerene mixtures and film characterization by scanning tunneling microscopy

Fullerene powder mixtures with different C₆₀/C₇₀ ratios have been analyzed by a variety of techniques, and results have been compared. The fullerence mixtures have been characterized as solutions in n-hexane by high-pressure liquid chromatography (HPLC) and UV-VIS spectroscopy. Thin films of fullerenes on Au(111) have been prepared from the mixtures by sublimation. The sublimation process has been studied by simultaneous thermogravimetric and differential thermal analyses. Thin fullerene films on Au(111) have been investigated by scanning tunneling microscopy (STM). The STM images show primarily two types of ballshaped molecules arranged in a lattice with hexagonal symmetry (fcc(111) face, nearest neighbour distance: 1 nm). The two species differ in diameter. STM images of films made of mixtures of different C₆₀/C₇₀ ratios show that C₇₀ molecules display a larger apparent diameter (0.8 nm) and corrugation than C₆₀ molecules (0.7 nm). The C₆₀/C₇₀ ratios obtained by counting the corresponding molecular species in the STM images of the thin films are compared to the C₆₀/C₇₀ ratios determined by HPLC on hexane solutions of the mixtures. The observed differences might be explained by different rates of sublimation for the two species. The STM images reveal film defects (vacancies and boundaries) and dynamic processes (displacement of C₇₀ molecules and vacancies). In films prepared to have a C₆₀ coverage of less than one monolayer, stable structural units of the C₆₀(111) surface consisting of three or seven C₆₀ molecules are revealed by STM. Occasionally, substructure within individual fullerene molecules is observed.     

Diamagnetic susceptibility effects in NMR measurements of the properties of water in polymeric membranes

The NMR spectra of water adsorbed at various relative humidities on various cellulose ester membranes have been studied. Membranes of cellulose acetate (CA), cellulose triacetate (CTA), and cellulose acetate butyrate (CAB) were investigated. It was found that the resonance peak of a liquid imbibed in or adsorbed on membranes from high relative humidity is very sensitive to the angle between the membrane plane and the direction of the magnetic field, shifting 5–7 ppm to higher fields as the membrane plane is rotated from a perpendicular to a parallel position with respect to the direction of the external magnetic field. This phenomenon was found to be independent of the nature of the polymeric material (namely CA, CTA, or CAB), porosity of the membrane (varying from an “all bulk” dense sheet to an 80% porosity and 0.2 μm average pore size membrane), nature of the magnetic nuclei (H₂O or D₂O), intensity of the external magnetic field (60 Mcps or 100 Mcps), and nature of the liquid in the membrane (water, methanol, or n-hexane). It is therefore concluded that the dependence of the position of the resonance peak on the position of the membrane plane with respect to the external magnetic field, is a geometrical phenomenon due to the magnetic “bulk susceptibility” of the medium. Quantitative estimations of the magnitude of the diamagnetic susceptibility effect in a cylindrically rolled sheet are given. These estimates agree well with the experimentally observed “splittings.”     

On the absence of an s-band energy gap in niobium

No evidence for a superconducting tunneling s-band energy gap in single crystal Nb has been observed for any of the main symmetry directions investigated in Nb-oxide-Pb_0.7Bi_0.3 and Nb-oxide-In junctions.