Composition operators on Hardy spaces on Lavrentiev domains

For any simply connected domain , we prove that a Littlewood type inequality is necessary for boundedness of composition operators on , , whenever the symbols are finitely-valent. Moreover, the corresponding ``little-oh' condition is also necessary for the compactness. Nevertheless, it is shown that such an inequality is not sufficient for characterizing bounded composition operators even induced by univalent symbols. Furthermore, such inequality is no longer necessary if we drop the extra assumption on the symbol of being finitely-valent. In particular, this solves a question posed by Shapiro and Smith (2003). Finally, we show a striking link between the geometry of the underlying domain and the symbol inducing the composition operator in , and in this sense, we relate both facts characterizing bounded and compact composition operators whenever is a Lavrentiev domain.

     

Study of interactions of concentrated marine dissolved organic matter with copper and zinc by pseudopolarography

The interaction of dissolved organic matter (DOM) with copper and zinc in a concentrated seawater sample was characterised by pseudopolarography. Measurements performed at increased concentrations of copper(II) ions showed successive saturation of active DOM sites which indicate possible partition of copper between (i) free or labile complexes, (ii) reduced and released within the potential window of the method, and (iii) electroinactive copper complexes. Pseudopolarograms measured at pH 4 indicate a release of copper which was bound to the active sites of DOM that formed non-labile complexes. Variation of the peak position and half-peak width along the scanned deposition potentials and with the increasing concentration of copper bear the information about the complex electrochemical processes at the electrode surface and in the bulk of the solution. Pseudopolarograms of zinc showed a strong dependence of the peak current and the peak position along the scanned deposition potentials on pH values, indicating preferentially complexation of zinc with carboxylic-like active sites of DOM in the measured sample. Pseudopolarography is a valuable method in the trace metal complexation and speciation studies, serving as a fingerprint of the analysed sample.     

Surface hydrophobicity modulates the operation of actomyosin-based dynamic nanodevices

We studied the impact of surface hydrophobicity on the motility of actin filaments moving on heavy-meromyosin (HMM)-coated surfaces. Apart from nitrocellulose (NC), which is the current standard for motility assays, all materials tested are good candidates for microfabrication: hydrophilic and hydrophobic glass, poly(methyl methacrylate) (PMMA), poly(tert-butyl methacrylate) (PtBuMA), and a copolymer of O-acryloyl acetophenone oxime with a 4-acryloyloxybenzophenone (AAPO). The most hydrophilic (hydrophilic glass, contact angle 35 degrees) and the most hydrophobic (PtBuMA, contact angle 78 degrees) surfaces do not maintain the motility of actin filaments, presumably because of the low density of adsorbed HMM protein or its high levels of denaturation, respectively. The velocity of actin filaments presents higher values in the middle of this "surface hydrophobicity motility window" (NC, PMMA), and a bimodal distribution, which is more apparent at the edges of this motility window (hydrophobic glass and AAPO). A molecular surface analysis of HMM and its S1 units suggests that the two very different, temporally separated conformations of the HMM heads could exacerbate the surface-modulated protein behavior, which is common to all microdevices using surface-immobilized proteins. An explanation for the above behavior proposes that the motility of actin filaments on HMM-functionalized surfaces is the result of the action of three populations of motors, each in a different surface-protein conformation, that is, HMM with both heads working (high velocities), working with one head (low velocities), and fully denatured HMM (no motility). It is also proposed that the molecularly dynamic nature of polymer surfaces amplifies the impact of surface hydrophobicity on protein behavior. The study demonstrates that PMMA is a good candidate for the fabrication of future actomyosin-driven dynamic nanodevices because it induces the smoothest motility of individual nano-objects with velocities comparable with those obtained on NC.     

Electrical impedance spectroscopy of epoxy systems: The case of 1,4-butanediol diglycidyl ether/cis-1,2-cyclohexanedicarboxylic anhydride and triethylamine as initiator

A series of epoxy cured samples, with different molar composition of 1,4-butanediol diglycidyl ether (EP), cis-1,2-cyclohexanedicarboxylic anhydride (CH) and triethylamine (TEA) as initiator, was studied by Electrical Impedance Spectroscopy (EIS) in the frequency range 10⁻²-10⁵ Hz. The resistivity of the system was evaluated by using the complex impedance analysis method. Resistivity values in the range between 10⁷ and 10¹³ Ω cm were obtained and related to the composition (molar fraction x_EP or x_CH) of the epoxy system. The gel formation characteristics of the samples were obtained as theoretically described by Flory.     

Characterization of Cellulolytic Extract from <Emphasis Type="Italic">Pycnoporus sanguineus</Emphasis> PF-2 and Its Application in Biomass Saccharification

The aim of this work was to evaluate the biochemical features of the white-rot fungi Pycnoporus sanguineus cellulolytic complex and its utilization to sugarcane bagasse hydrolysis. When cultivated under submerged fermentation using corn cobs as carbon source, P. sanguineus produced high FPase, endoglucanase, β-glucosidase, xylanase, mannanase, α-galactosidase, α-arabinofuranosidase, and polygalacturonase activities. Cellulase activities were characterized in relation to pH and temperature. β-Glucosidase and FPase activities were higher at 55 °C, pH 4.5, and endoglucanase activity was higher at 60 °C, in a pH range of 3.5–4.0. All cellulase activities were highly stable at 40 and 50 °C through 48 h of pre-incubation. Crude enzymatic extract from P. sanguineus was applied in a saccharification experiment using acid-treated and alkali-treated sugarcane bagasse as substrate, and the hydrolysis yields were compared to that obtained by a commercial cellulase preparation. Reducing sugar yields of 60.4% and 64.0% were reached when alkali-treated bagasse was hydrolyzed by P. sanguineus extract and commercial cellulase, respectively. Considering the glucose production, it was observed that P. sanguineus extract and commercial cellulase ensured yields of 22.6% and 36.5%, respectively. The saccharification of acid-treated bagasse was lower than that of alkali-treated bagasse regardless of the cellulolytic extract. The present work showed that P. sanguineus has a great potential as an enzyme producer for biomass saccharification.     

Study of free volume and crystallinity in polybithiophene and poly(3-methylthiophene)

Compressed pellets of partly crystalline, chemically synthesized, doped (Cl^? and FeCl) polybithiophene (PBTd), poly(3-methylthiophene) (P3MTd), and their neutral (dedoped) forms (PBTn and P3MTn) were studied by wide-angle x-ray diffraction and positron annihilation lifetime spectroscopy. As synthesized, PBTd and P3MTd polymers have a helical syn conformation they crystallize in the hexagonal system. On dedoping, PBT macromolecules change their helical syn conformation in a rodlike anti conformation and crystallize in the orthorhombic or monoclinic system, whereas P3MT macromolecules retain their helical syn conformation. Chemical doping–dedoping cycles lead to amorphous PBT and P3MT in either doped or dedoped states. The P3MT helical macromolecule behaves like a spiral spring; by doping, it becomes axially compressed. The unit-cell volume of P3MTd is smaller than that of P3MTn. The positron lifetime spectra for all polymers were resolved, without constraint, into three components. The τ₁ lifetime is attributed to free-positron annihilation events, the τ₂ lifetime to positrons annihilating trapped in voids, and the τ₃ lifetime to positrons annihilating as o-Ps trapped in cavities located inside the polymer grains for P3MTn and at the surface of the grains for PBTd, PBTn, and P3MTd. Most positrons annihilate when trapped in voids, both in doped and dedoped PBT and P3MT. The doping apparently increases the concentration of the voids and their mean diameter in P3MT, and probably also in PBT. Cavities anchored in the bulk are produced by dedoping. © 1993 John Wiley & Sons, Inc.     

Extremal solutions of Nevanlinna-Pick problems and certain classes of inner functions

Consider a scaled Nevanlinna-Pick interpolation problem and let ∏ be the Blaschke product whose zeros are the nodes of the problem. It is proved that if ∏ belongs to a certain class of inner functions, then the extremal solutions of the problem or most of them are in the same class. Three different classical classes are considered: inner functions whose derivative is in a certain Hardy space, exponential Blaschke products and the well-known class of α-Blaschke products, for 0 < α < 1.