Plane brownian motion in a region with holes

We consider a fixed family of balls with decreasing radii in the plane. We establish a relationship between a Dirichlet problem in a region without the balls and the solution of a Schroedinger equation in the complete region. Then we find upper bounds for the probability that a brownian motion exits the region without touching these balls. This is used to study harmonic measure and entire functions.     

Sidelobe decline in single-photon 4Pi microscopy by Toraldo rings

We demonstrate theoretically the feasibility of single-photon 4Pi-confocal microscopy. By inserting a pair of properly designed multi-ring phase-only pupil filters in the illumination path of a 4Pi microscope the height of the sidelobes of the point spread function substantially reduced, so that there is no ambiguity in the 3D image. Then, an axial resolution up to four times higher than that of single-photon confocal microscope can be effectively achieved.     

List of Contributors

Authors Index

List of Contributors     

Synthesis and Characterization of Ethylene/Propylene Copolymers in the Whole Composition Range

Summary: The incorporation of comonomer molecules in the backbone of a homopolymer can influence the final properties of the material, decreasing its crystallinity and the melting and glass transition temperatures, and increasing its impact resistance and transparency. In the present work, ten ethylene/propylene copolymers have been synthesized using a supported metallocene catalytic system covering the whole composition range. Any desired composition was obtained by controlling the feed composition during the reaction. These synthesized copolymers have been characterized by different techniques in order to study the effect of the comonomer incorporation onto their final properties. When the comonomer content is low, the behaviour of the copolymer is similar to that of the corresponding homopolymer. Nevertheless, if the comonomer content increases, the copolymer becomes more amorphous (low crystallization temperature and soft XRD signals) and easily deformable, reaching a behaviour close to that corresponding to an elastomeric material. In order to corroborate these results the samples have been characterized by TREF and GPC-MALS. TREF analysis showed that copolymers containing less than 10% and more than 80% of ethylene are semicrystalline, with elution temperatures typical of this kind of polymers. Molecular weights are higher for homopolymers and they decrease as the comonomer concentration increases, whereas the polydispersity index keeps almost constant at the expected value for this kind of samples.     

2‐(4‐Methoxyphenyl­azo)‐4‐phenyl­phenol

The crystal structure of the title compound, C₁₉H₁₆N₂O₂, displays a trans configuration of the azo moiety, which forms an intramolecular O—H?N=N hydrogen bond. The H?N and O?N distances are 1.81 (3) and 2.581 (4) Å, respectively. The azo­benzene moiety is approximately planar, and has a dihedral angle of ca 23° with the substituted phenyl group.     

The Toxicity of Silver Nanoparticles Depends on Their Uptake by Cells and Thus on Their Surface Chemistry

A set of three types of silver nanoparticles (Ag NPs) are prepared, which have the same Ag cores, but different surface chemistry. Ag cores are stabilized with mercaptoundecanoic acid (MUA) or with a polymer shell [poly(isobutylene‐alt‐maleic anhydride) (PMA)]. In order to reduce cellular uptake, the polymer‐coated Ag NPs are additionally modified with polyethylene glycol (PEG). Corrosion (oxidation) of the NPs is quantified and their colloidal stability is investigated. MUA‐coated NPs have a much lower colloidal stability than PMA‐coated NPs and are largely agglomerated. All Ag NPs corrode faster in an acidic environment and thus more Ag(I) ions are released inside endosomal/lysosomal compartments. PMA coating does not reduce leaching of Ag(I) ions compared with MUA coating. PEGylation reduces NP cellular uptake and also the toxicity. PMA‐coated NPs have reduced toxicity compared with MUA‐coated NPs. All studied Ag NPs were less toxic than free Ag(I) ions. All in all, the cytotoxicity of Ag NPs is correlated on their uptake by cells and agglomeration behavior.