Synthesis of the first nonmetalated triazolephthalocyanine derivatives

The synthesis of nonmetalated triazolephtahlocyanines is described for the first time. These compounds have been prepared by both one-step and stepwise procedures. Their spectroscopic data reveal a nonaromatic cross-conjugated 18pi-electron structure in contrast to their aromatic metalated derivatives.     

Stability of compact actions of ℝ n of codimensional oneof codimensional one

In this paper we study theC ^r stability of locally free compact actions of ℝ ⁿ with compact orbits over manifolds of dimensionn+1. More precisely, we show that in many cases aC ¹ perturbation of an action with all orbits compact must also have all orbits compact and aC ⁰ perturbation usually has many compact orbits.     

Interpolating Blaschke products solving Pick-Nevanlinna problems

We study when a Pick-Nevanlinna problem with more than one solution can be solved by an interpolating Blaschke product. Supported in part by the grant PB85-0374 of the CYCIT, Ministerio de Educación y Ciencia, Spain.     

On some geometrical properties of Seifert bundles

In this paper we use the integration along the leaves introduced by Haefliger in 1980 to obtain a differentiable version of the Gysin sequence and Euler class for compact Hausdorff orientable foliations with generic leaf the sphereS ^p. From this we give a geometrical significance to the vanishing of the Euler class on Seifert bundles. We also obtain an integral formula on Seifert bundles similar to the Gauss-Bonnet one.     

Inner Functions, Bloch Spaces and Symmetric Measures

Schwarz's lemma asserts that analytic mappings from the unitdisc into itself decrease hyperbolic distances. In this paper,inner functions which decrease hyperbolic distances as muchas possible, when one approaches the unit circle, are constructed.Actually, it is shown that a quadratic condition governs thebest decay of the hyperbolic derivative of an inner function.This is related to a result of L. Carleson on the existenceof singular symmetric measures. As a consequence, some resultson composition operators are obtained, bringing out the importanceof the Bloch spaces in this connection. Another consequenceis a uniform way of producing singular measures which are simultaneouslysymmetric and Kahane. 1991 Mathematics Subject Classification:primary 30D50; secondary 30D45, 26A30, 47B38.     

Closures of finitely generated ideals in Hardy spaces

LetH ^∞ be the algebra of bounded analytic functions in the unit diskD. LetI=I(f ₁,...,f _N) be the ideal generated byf ₁,...,f _N∈H ^∞ andJ=J(f ₁,...,f _N) the ideal of the functionsf∈H ^∞ for which there exists a constantC=C(f) such that |f(z)|≤C(|f ₁ (z)|+...;+|f _N (z)|),z∈D. It is clear that , but an example due to J. Bourgain shows thatJ is not, in general, in the norm closure ofI. Our first result asserts thatJ is included in the norm closure ofI ifI contains a Carleson-Newman Blaschke product, or equivalently, if there existss>0 such that

Staleya guttiformis attachment on poly(tert-butylmethacrylate) polymeric surfaces

The attachment behaviour of Staleya guttiformis DSM 11458^T on poly(tert-butyl methacrylate) (P(tBMA)) polymeric surfaces has been studied. The electrostatic charge of the S. guttiformis cell surface (measured as zeta potential via microelectrophoresis) was −43.18 mV. S. guttiformis cells appeared weakly hydrophilic as the water contact angle measured on lawns of bacterial cells was found to be 55 ± 4.9°. It was found that while attaching on P(tBMA) surfaces, S. guttiformis cells produced extracellular polymeric substances (EPS) as observed from atomic force microscopy (AFM) and scanning electron microscopy (SEM) analysis. The AFM high resolution imaging revealed the nano-topography of the ‘free’ (the EPS that is produced by the bacterial cells, but no longer directly attached to the cells) EPS associated on the cell surface and also found on P(tBMA) surface. The ‘free’ EPS exhibited granular structure with lateral dimensions of 30–50 nm and a vertical nano-roughness of 7–10 nm. Another type of the EPS secreted by S. guttiformis cells appeared as a hydogel substance, presumably polysaccharide that formed a biopolymer network that facilitated bacterial attachment.