Rectifiability of harmonic measure

In the present paper we prove that for any open connected set \({\Omega\subset\mathbb{R}^{n+1}}\), \({n\geq 1}\), and any \({E\subset \partial \Omega}\) with \({\mathcal{H}^n(E)<\infty}\), absolute continuity of the harmonic measure \({\omega}\) with respect to the Hausdorff measure on E implies that \({\omega|_E}\) is rectifiable. This solves an open problem on harmonic measure which turns out to be an old conjecture even in the planar case \({n=1}\).     

Biocompatible polymer vesicles from biamphiphilic triblock copolymers and their interaction with bovine serum albumin

The self-assembly of the biamphiphilic triblock copolymer poly(ethylene oxide)-b-poly(caprolactone)-b-poly(acrylic acid) into polymer vesicles is studied. The vesicles provide both biocompatibility and biodegradability. Moreover, the biamphiphilic nature of the triblock copolymer provides different surface properties in the interior and in the outer interface of the vesicles. Preparation of the aggregates by direct dissolution of the copolymer in a solution of albumin does not alter the morphology of the aggregates, and thus, they have the potential to immobilize protein molecules. Since a part of the protein is encapsulated in the interior of the vesicles, they can be used as nanocontainers. A further fraction of the protein is bound to the outer interface, which is primarily composed of the poly(acrylic acid) tails. Immobilization of protein on the outer interface can stabilize the colloidal particles and also provide them with a biofunctional component.     

Crystallization kinetics of ZnS precipitation; an experimental study using the mixed‐suspension‐mixed‐product‐removal (MSMPR) method

The precipitation kinetics of zinc sulfide were studied using a lab scale mixed‐suspension‐mixed‐product‐removal (MSMPR) precipitation reactor. The vessel was operated at different feed concentrations, molar ratios, stirrer speeds, pH‐values, feed injection positions and residence times. Primary nucleation and volume average crystal growth rates as well as agglomeration kernel were determined. Relationships were found between the rates of the different crystallization steps on the one hand and supersaturation, stirrer speeds, pH‐values, Zn²⁺ to S^2‐ ratio, feed positions on the other. These show that larger crystals are obtained at high supersaturation, moderate stirrer speeds, small residence times, a pH‐value of around 5 and high Zn²⁺ to S^2‐ ratios. One should realize though that the applied MSMPR method is not the most optimal technique for examining fast precipitation reactions. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Dextran-spermine conjugate: an efficient vector for gene delivery

Cationic Polysaccharides based on oligoamine-dextran conjugates were synthesized and tested as vectors for gene transfection. Dextran with 40 kDa in average molecular weight was oxidized under mild conditions by potassium periodate to obtain the respective polyaldehydes in relatively high yields (∼90%). The oxidized dextran was reacted by reductive animation with various oligoamines of 2 to 4 amino groups to obtain the corresponding imine-conjugates. These water-soluble polymers were then reduced by excess of sodium borohydride to obtain the corresponding amine-conjuagtes in 30-40% overall yield. The electrostatic interactions of the representative polycations with plasmid DNA were evaluated as a function of charge ratio (+/−, polymer/DNA) and ionic strength of the medium applying the ethidium-bromide quenching assay. Although most synthetic polycations formed stable complexes with Plasmid DNAs, only the dextran-spermine conjugate of a defined amino content and molecular weight was able to transfect cells with high efficiency.     

Synthesis of some novel pyrazoline‐thiazole hybrids and their antimicrobial activities

A series of novel thiazolyl pyrazolines 7a‐h , 9a‐f , and 11a‐f have been synthesized by the reaction of thioamide derivatives 5a , b with 1‐aryl‐2‐bromoethanones 6a‐d , chloroacetones 8a‐c , and hydrazonoyl chlorides 10a‐c . Additionally, pyrazoles 15a‐c and 20 were prepared starting from enaminone 13 . These newly synthesized compounds were screened for their in vitro antibacterial activity against four bacterial species. Compound 11b showed a moderate activity against Klebsiella pneumoniae. Compounds 7c and 11c revealed a moderate activity against Pseudomonas aeruginosa. In addition, the antifungal activity of the newly synthesized compounds was determined against five fungal strains. Compounds 7e , 7g , and 11e showed a good activity against Aspergillus flavus and Penicillium expansum.     

Polar curves for transmission ellipsometry

For three-phase ambient-film-substrate systems, the ratio ?_T = T_p/T_s of the complex amplitude-transmission coefficients T_p and T_s for light polarized parallel (p) and perpendicular (s) to the plane of incidence is related to a complex exponential function of film thickness d by a bilinear transformation. This observation leads to elucidation of the nature of the complex plane polar curves of the function ?_T(d), where the film thickness is variable and the angle of incidence is fixed. In particular, the polar curve ?_T(d) for a transparent ambient-film-substrate system studied by transmission ellipsometry is shown to be exactly a circle.     

Dividing a light beam into two beams of orthogonal polarizations by reflection and refraction at a dielectric surface

Reflection and refraction of monochromatic light by an air-dielectric interface at an incidence angle below the Brewster angle can generate split beams of equal power and orthogonal polarizations under certain achievable conditions. Generation of photon streams of orthogonal polarizations, previously thought to be possible mainly by double refraction in anisotropic crystals, is achieved for an infinite set of input states that leads to a correspondingly infinite set of pairs of orthogonal output states. A bare substrate of PbTe is particularly suitable for this beam splitting function in the IR. However, use of a high-refractive-index quarter-wave layer on a low-refractive-index substrate extends the operating range of this interesting device to a much wider spectral range including the visible.