Spherical Particles of Zirconia-Titania of Hexagonal Structure from a Neutral Amine Route

Through the sol–gel process, using the so-called neutral amine route, spherical particles of 1:1 zirconia–titania were synthesized from zirconium(IV) and titanium(IV) butoxides as well as 1,12-diaminododecane as precursor species. The obtained product exhibited a hexagonal structure, as determinated by X-ray diffraction data. The obtained material was also characterized by thermogravimetry, differential scanning calorimetry, infrared spectroscopy, scanning electron microscopy, and surface area measurements. Despite the release of template molecules on heating, the spherical morphology was retained up to about 1200°C, at which the disruption of the spheres took place.     

Effects of Adsorbed Polyaniline on Redox Process on MoO3 Surface

The effects exhibited by adsorbed conducting polyaniline on the redox process on a molybdenum oxide surface were studied. Thermogravimetric results indicate a 4% polyaniline deposition. Cyclic voltammograms of the adsorbed polymer on MoO3 show that polyaniline exerts remarkable effects on the molybdenum blue oxidation-reduction process, with oxidation and reduction potentials of 0.33 and 0.18 V, respectively. This effect strongly enhances the electrode response, and can be used as an important tool in qualitative and/or quantitative determinations of molybdenum in solution as well as in any substrate. Copyright 1999 Academic Press.     

Convergence of the shifted algorithm for unitary Hessenberg matrices

This paper shows that for unitary Hessenberg matrices the algorithm, with (an exceptional initial-value modification of) the Wilkinson shift, gives global convergence; moreover, the asymptotic rate of convergence is at least cubic, higher than that which can be shown to be quadratic only for Hermitian tridiagonal matrices, under no further assumption. A general mixed shift strategy with global convergence and cubic rates is also presented.

     

On the partial realization problem

In this paper we take a unified approach to the partial realization problem in which we seek to incorporate ideas from numerical linear algebra, most of which were originally developed in other contexts. We approach the partial realization problem from several different angles and explore the connections to such topics as factoriza- tion of Hankel matrices, block tridiagonalization, generalizations of the Lanczos process for biorthogonalization, the Euclidean algorithm and the principal-part con- tinued fractions of Arne Magnus, the Padé table, and the Berlekamp-Masseyalgo- rithm. In this way we are able to clarify some previous results by Rissanen, Kalman, and others and place them in a broader context. This leads to several results and concepts which we think are new. Our analysis is restricted to the scalar case, but some definitions and formulations have been rigged to facilitate an extension to the matrix case.     

The determination of atomic force constants in cubic solid solutions: II. Experimental

The microscopic elastic theory of Matsubara-Kanzaki-Krivolglaz has been applied to the determination of the atomic force constants in disordered Cu₃Au from the diffuse scattering pattern due to local atomic order and static atomic displacements. The analysis of the effect of experimental errors and the assumptions underlying this method of analysis indicate, however, that these results may be considerably in error. A discussion of the source of these errors and their influence on the determination of the atomic force constants in solid solution alloys is presented. It will be shown that it is not possible to determine these constants from X-ray diffraction data from clustering alloys, but in some cases for ordering alloys, this may be possible.     

Small-slope simulation of acoustic backscatter from a physical model of an elastic ocean bottom

An underwater acoustic experiment with a two-dimensional rough interface, milled from a slab of PVC, was performed at a tank facility. The purpose was to verify the predictions of numerical models of acoustic rough surface scattering, using a manufactured physical model of an ocean bottom that featured shear effects, nonhomogeneous roughness statistics, and root-mean-square roughness amplitude on the order of the acoustic wavelength. Predictions of the received time series and interface scattering strength in the 100-300 kHz band were obtained from the Bottom Reverberation from Inhomogeneities and Surfaces-Small-Slope Approximation (BORIS-SSA) numerical scattering model. The predictions were made using direct measurements of scattering model inputs-specifically, the geoacoustic properties from laboratory analysis of material samples and the grid of surface heights from a touch-trigger probe. BORIS-SSA predictions for the amplitude of the received time series were shown to be accurate with a root-mean-square residual error of about 1 dB, while errors for the scattering strength prediction were higher (2-3.5 dB). The work is part of an ongoing effort to use physical models to examine a variety of acoustic scattering and propagation phenomena involving the ocean bottom.     

The numerically stable reconstruction of Jacobi matrices from spectral data

Summary We present an exposé of the elementary theory of Jacobi matrices and, in particular, their reconstruction from the Gaussian weights and abscissas. Many recent works propose use of the diagonal Hermitian Lanczos process for this purpose. We show that this process is numerically unstable. We recall Rutishauser's elegant and stable algorithm of 1963, based on plane rotations, implement it efficiently, and discuss our numerical experience. We also apply Rutishauser's algorithm to reconstruct a persymmetric Jacobi matrix from its spectrum in an efficient and stable manner.Dedicated to Professor F.L. Bauer on the occasion of his 60th birthdayThis work was supported by the National Science Foundation under grant MCS-81-02344, and by the Mathematics Research Institute of the Swiss Federal Institute of Technology, Zürich     

A divide and conquer method for unitary and orthogonal eigenproblems

Summary LetH ^{n xn} be a unitary upper Hessenberg matrix whose eigenvalues, and possibly also eigenvectors, are to be determined. We describe how this eigenproblem can be solved by a divide and conquer method, in which the matrixH is split into two smaller unitary upper Hessenberg matricesH ₁ andH ₂ by a rank-one modification ofH. The eigenproblems forH ₁ andH ₂ can be solved independently, and the solutions of these smaller eigenproblems define a rational function, whose zeros on the unit circle are the eigenvalues ofH. The eigenvector ofH can be determined from the eigenvalues ofH and the eigenvectors ofH ₁ andH ₂. The outlined splitting of unitary upper Hessenberg matrices into smaller such matrices is carried out recursively. This gives rise to a divide and conquer method that is suitable for implementation on a parallel computer.WhenH ^{n xn} is orthogonal, the divide and conquer scheme simplifies and is described separately. Our interest in the orthogonal eigenproblem stems from applications in signal processing. Numerical examples for the orthogonal eigenproblem conclude the paper.Research supported in part by the NSF under Grant DMS-8704196 and by funds administered by the Naval Postgraduate School Research Council