Jacobi matrices for measures modified by a rational factor

This paper describes how, given the Jacobi matrixJ for the measure d(t), it is possible to produce the Jacobi matrix for the measurer(t)d(t) wherer(t) is a quotient of polynomials. The method uses a new factoring algorithm to generate the Jacobi matrices associated with the partial fraction decomposition ofr(t) and then applies a previously developed summing technique to merge these Jacobi matrices. The factoring method performs best just where Gautschi's minimal solution method for this problem is weakest and vice versa. This suggests a hybrid strategy which is believed to be the most powerful yet for solving this problem. The method is demonstrated on a simple example and some numerical tests illustrate its performance characteristics.     

Performance analysis of a hybrid switching system where voice messages can be queued

In the classical model of a hybrid switching system with movable boundary it is assumed that blocked voice messages are lost and do not affect the further functioning of the system. We describe a more realistic model where blocked voice messages are queued and then are served once a channel becomes free. The main mathematical difficulty in the analysis of such models lies in the fact that the underlying stochastic process has as state space the whole quadrant ₊ ² . We reduce the problem to a set of equations defined over the lattice semi-strip {1,...,N} × ₊. This in turn allows us to use available general mathematical theories.     

Analysis of preconditioning and multigrid for Euler flows with low-subsonic regions

For subsonic flows and upwind-discretized, linearized 1-D Euler equations, the smoothing behavior of multigrid-accelerated point Gauss-Seidel relaxation is analyzed. Error decay by convection across domain boundaries is also discussed. A fix to poor convergence rates at low Mach numbers is sought in replacing the point relaxation applied to unconditioned Euler equations, by locally implicit time-stepping applied to preconditioned Euler equations. The locally implicit iteration step is optimized for good damping of high-frequency errors. Numerical inaccuracy at low Mach numbers is also addressed.The work reported was performed in the framework of the BRITE-EURAM Aeronautics R&D Programme of the European Communities (Contract No. AER2-CT92-0040). The work was started during the second author's visit to CWI in 1993.     

Nonlinear coordinate representations of smooth optimization problems

Nonlinear coordinate representations of smooth optimization problems are investigated from the point of view of variable metric algorithms. In other words, nonlinear coordinate systems, in the sense of differential geometry, are studied by taking into consideration the structure of smooth optimization problems and variable metric methods.Both the unconstrained and constrained cases are discussed. The present approach is based on the fact that the nonlinear coordinate transformation of an optimization problem can be replaced by a suitable Riemannian metric belonging to the Euclidean metric class. In the case of equality and inequality constraints, these questions are related closely to the right inverses of full-rank matrices; therefore, their characterization is a starting point of the present analysis. The main results concern a new subclass of nonlinear transformations in connection with the common supply of coordinates to two Riemannian manifolds, one immersed in the other one. This situation corresponds to the differentiable manifold structure of nonlinear optimization problems and improves the insight into the theoretical background of variable metric algorithms. For a wide class of variable metric methods, a convergence theorem in invariant form (not depending on coordinate representations) is proved. Finally, a problem of convexification by nonlinear coordinate transformations and image representations is studied.This research was supported by the Hungarian National Research Foundation, Grant Nos. OTKA-2568 and OTKA-2116, and by the Project Trasporti of the Italian National Research Council (CNR).     

On the multifractal analysis of Bernoulli convolutions. II. Dimensions

We show how the formalism developed in a previous paper allows us to exhibit the multifractal nature of the infinitely convolved Bernoulli measures for the golden mean. In this second part we show how the Hausdorff dimension of the set where the measure has a power law singularity of strength is related to the large-deviation function given in Part I.     

On the multifractal analysis of Bernoulli convolutions. I. Large-deviation results

We show how the formalism developed in a previous paper allows us to exhibit the multifractal nature of the infinitely convolved Bernoulli measures , for the golden mean. In this first part we establish some large-deviation results for random products of matrices, using perturbation theory of quasicompact operators.     

Solution of the generalized eigenvalue equation perturbed by a generalized low rank perturbation

Summary The problem of finding eigenvalues and eigenstates of the generalized perturbed eigenvalue equation = g3(+) is considered. The eigenvalues and the eigenstates of the unperturbed eigenvalue equation = are assumed to be known. Matrices , and can be arbitrary, except for the requirement that be nonsingular and that the eigenstates of the unperturbed equation be complete. It is shown that the eigenvalues and the eigenstates of the perturbed equation can be easily obtained if the rank of the generalized perturbation , is small. A special case of low rank perturbations are piecewise local perturbations which are common in physics and chemistry. If the perturbation is piecewise local with fixed localizability, the operation count for the derivation of a single eigenvalue and/or a single eigenstate is (n). If the perturbation has a fixed rank, the operation count for the derivation of all eigenvalues and/or all eigenstates is (n ²).Research supported by the Welch Foundation of Houston, Texas, and by the Yugoslav Ministry for Development (Grant P-96)     

Synthesis and application of doxorubicin-loaded silica gels as solid materials for spectral analysis

A new approach to synthesis and the possibility of application of solid gel matrices containing the target analyte, a cancer drug—doxorubicin for the calibration of UV-vis spectrometers is presented. The doxorubicin-loaded gels were prepared by the acid-catalyzed sol-gel pre-doping method. The efficiency of doxorubicin encapsulation in gels by the sol-gel process was 100 ± 1.2% (w/w). The amount of doxorubicin encapsulated per unit mass of the gel (1 g) was found to be independent of the mass of the gel taken for analysis, which demonstrates the homogeneity of encapsulation of the drug in the gel matrix. The gelation process of doxorubicin in the sol was found to be both repeatable (R.S.D. = 11.2% for n = 80, confidence level P = 95%) and reproducible (largest value of R.S.D. = 4.8% for n = 27, P = 95%).The prepared doxorubicin-loaded gel matrices are characterized primarily by their lack of toxicity as compared to the toxic free form of doxorubicin as well as by high stability over a long-time span.     

Some basic properties of the correlation matrices

On the basis of the properties of correlation matrices, it is shown here that the set of all the first‐order transition reduced density matrices of a system provide complete information about that system. Also, the interrelation between the properties of the correlation matrix and the 2‐RDM N‐representability conditions is studied. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002     

Palladium catalysts supported on oligomeric aramides in the liquid-phase hydrogenation of phenylacetylene

The catalytic behaviour of palladium supported on oligomeric aramides has been investigated in the liquid phase selective hydrogenation of phenylacetylene to styrene, by comparison with conventional Pd-supported systems, such as Pd/carbon. Pd/Al₂O₃ and Pd/SiO₂. The influences of the reduction temperature and metal loading on the activity/selectivity behaviour of the title reaction are explained in terms of different reducibility patterns of the catalysts, as well as in the light of a peculiar support effect of the organic matrix on Pd particles.