On norms of composition operators acting on Bergman spaces

For arbitrary composition operators acting on a general Bergman space we improve the known lower bound for the norm and also generalize a related recent theorem of D.G. Pokorny and J.E. Shapiro. Next, we obtain a geometric formula for the norms of composition operators with linear fractional symbols, thus extending a result of C. Cowen and P. Hurst and revealing the meaning of their computation. Finally, we obtain a lower bound for essential norm of an arbitrary composition operator related to the well-known criterion of B. MacCluer and J.H. Shapiro. As a corollary, norms and essential norms are obtained for certain univalently induced noncompact composition operators in terms of the minimum of the angular derivative of the symbol.     

A study on the applications of the acoustic design sensitivity analysis of vibrating bodies

The determination of the sensitivity of the acoustical characteristics of vibrating systems with respect to the variation of the design parameters predicting these characteristics is a necessary and important step of the acoustic design and optimization process. Acoustic design sensitivity analysis includes the computation and evaluation of the sensitivity information required for this procedure. In this study, a boundary element code performing the sensitivity analysis of the acoustic pressure by using the matrix sensitivities with respect to different design variables has been developed. The effect of the precision of boundary element discretization on the acoustic pressure sensitivity is examined via this code. The formulation is applied to a multi-source system and the dimension sensitivity analysis of near field pressures of two-dilating-spherical source is performed. The last application is devoted to a real sound source: a washing machine sitting on the floor. Sensitivity of the field pressures to the machine’s dimensions (size), surface velocity and frequency is examined on the bases of the boundary element model of the machine and half-space condition. The impacts of these variables are compared; and a limiting speed for the machine responding both the acoustical and operational requirements is determined.     

Simultaneous determination of cloramphenicol, salicylic acid and resorcinol by capillary zone electrophoresis and its application to pharmaceutical dosage forms

This study demonstrates the separation of active ingredients in acne formulations (salicylic acid, cloramphenicol and resorcinol in presence of azulene) by capillary zone electrophoresis. Factors affecting their separations were the buffer pH and concentration, applied voltage, sample preparation, and presence of additives. Optimun results were obtained with a 50 mM sodium tetraborate-50 mM sodium phosphate, pH 9.0. The carrier electrolyte gave baseline separation with good resolution, short migration times (<6 min), great reproducibility and accuracy. Calibration plots were linear over at least three orders of magnitude of analyte concentrations, the lower limits of detection being within the range 0.39-1.25 μg ml⁻¹. The procedure was fast and reliable and commercial pharmaceuticals could be analysed without prior sample clean-up procedure.     

On existence and asymptotic stability of solutions of a nonlinear integral equation

We prove an existence theorem for a nonlinear integral equation being a Volterra counterpart of an integral equation arising in the traffic theory. The method used in the proof allows us to obtain additional characterization in terms of asymptotic stability of solutions of an equation in question.     

Comparison of Several Calibration Procedures for Glass Electrodes in Proton Concentration

Several reported procedures for calibrating glass electrodes in proton concentration are compared. Some recommendations for non-experts are also given. The examined procedures can be classified into two broad categories, namely: those based on direct potential difference measurements of solutions of known proton concentration and those that use one or several pH standards to calibrate the electrode and subsequently measure the pH of solutions containing known proton concentrations. With a single buffer, the two types of procedures lead to equivalent results. However, if two pH buffers are used, the slope of the calibration graph in proton concentration will differ from the real electrode slope to an extent proportional to the difference between the liquid junction potentials of the two buffers. Therefore, any other method is preferable under these circumstances.     

On the spectral picture of an irreducible subnormal operator II

In this paper we show that the spectral picture of an irreducible subnormal operator may be arbitrarily prescribed subject only to certain natural necessary conditions. This completes work begun by the second author.

     

Invariant Subspaces for Semigroups of Algebraic Operators

T. Laffey showed (Linear and Multilinear Algebra6(1978), 269–305) that a semigroup of matrices is triangularizable if the ranks of all the commutators of elements of the semigroup are at most 1. Our main theorem is an extension of Hthis result to semigroups of algebraic operators on a Banach space. We also obtain a related theorem for a pair {A, B} of arbitrary bounded operators satisfying rank (AB−BA)=1 and several related conditions. In addition, it is shown that a semigroup of algebraically unipotent operators of bounded degree is triangularizable.     

Bounded sets in topological groups and embeddings

We show that the existence of a non-metrizable compact subspace of a topological group G often implies that G contains an uncountable supersequence (a copy of the one-point compactification of an uncountable discrete space). The existence of uncountable supersequences in a topological group has a strong impact on bounded subsets of the group. For example, if a topological group G contains an uncountable supersequence and K is a closed bounded subset of G which does not contain uncountable supersequences, then any subset A of K is bounded in G?(K?A). We also show that every precompact Abelian topological group H can be embedded as a closed subgroup into a precompact Abelian topological group G such that H is bounded in G and all bounded subsets of the quotient group G/H are finite. This complements Ursul's result on closed embeddings of precompact groups to pseudocompact groups.