Hankel Operators on Bounded Analytic Functions

For a domain in the complex plane and a bounded measurable function on , the generalized Hankel operator on is the operator of multiplication by followed by projection into . Under certain conditions on we show that either is compact or there is an embedded on which is bicontinuous. We characterize those 's for which is compact in the case that is a Behrens roadrunner domain.

     

Two new characterizations of carleson-newman Blaschke products

We present an extension of a result of Vasyunin by giving a characterization of finite products of interpolating Blaschke products B in terms of the minorization of B(z) by the distance of z to the zeros of B. We also characterize those Blaschke products that satisfy the hereditary weak embedding property.     

Cluster sets of interpolating Blaschke products

We construct interpolating Balschke products whose radial cluster sets at a given point of the unit circle can be prescribed to be one of the following: the closed unit disk; an arbitrary closed arc on the unit circle; an arbitrary interval of the form [x, y], wherexy ≠ 0 and −1≤1x≤y≤1. We also show that there does not exist an interpolating Blaschke product having [0,y] or [x, 0] as a radial cluster set. On the other hand, there do exist finite products of interpolating Blaschke products that have [0, 1] as a radial cluster set. Research supported by the RIP-program Oberwolfach, 2002/2003.     

Value Distribution of Interpolating Blaschke Products

A Blaschke product B with zero-sequence (a_n) is called almostinterpolating if the inequality lim inf_n(1 – |a_n|²)|B'(a_n)|     

Electrical conductivity,impedance, and percolation behavior of carbon nanofiber and carbon nanotube containing gellan gum hydrogels

The electrical impedance behavior of gellan gum (GG), GG–carbon nanotube, and GG–carbon nanofiber hydrogel composites is reported. It is demonstrated that the impedance behavior of these gels can be modeled using a Warburg element in series with a resistor. Sonolysis (required to disperse the carbon fillers) does not affect GG hydrogel electrical conductivity (1.2 ± 0.1 mS/cm), but has a detrimental effect on the gel's mechanical characteristics. It was found that the electrical conductivity (evaluated using impedance analysis) increases with increasing volume fraction of the carbon fillers and decreasing water content. For example, carbon nanotube containing hydrogels exhibited a six‐ to sevenfold increase in electrical conductivity (to 7 ± 2 mS/cm) at water content of 82%. It is demonstrated that at water content of 95 ± 2% the electrical behavior of multiwalled nanotube containing hydrogels transitions (percolates) from transport dominated by ions (owing to GG) to transport dominated by electrons (owing to the carbon nanotube network). © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2014 , 52, 864–871     

Norms and essential norms of linear combinations of endomorphisms

We compute norms and essential norms of linear combinations of endomorphisms on uniform algebras.

     

Electroinduced thermal lens spectrometry

A new technique for the generation of a thermal lens effect is considered. In this technique, the action of focused radiation from an inducing laser is replaced by an analogous action of electric current, which forms a thermal lens at a certain site of a liquid by the generation of a high local current density in a small liquid volume. The main regularities of this technique for thermal lens signal generation are considered, and an expression is derived to relate the detected signal (a relative change in probing radiation intensity at the detector) and the electrolyte concentration. A cell is proposed for electroinduced thermal lens detection. The dependence of the thermal lens signal on the applied voltage and on the concentration of the test electrolyte is determined for a model electrolyte (NaCl), and sensitivity characteristics are found to be consistent with theoretical estimations made in this work.