Polymerization of 4‐methylpentene and vinylcyclohexane by amine bis(phenolate) titanium and zirconium complexes

The polymerization of the substituted olefins 4‐methylpentene and vinylcyclohexane by dibenzyl titanium and zirconium complexes of three amine bis(phenolate) ligands is reported. The ligands featured a dimethylamino side‐arm donor and either electron‐withdrawing (Cl and Br) or methyl phenolate substituents. After activation with B(C₆F₅)₃, the zirconium catalysts exhibited a higher activity than the titanium catalysts toward these bulky olefins. Very high weight‐average molecular weight poly(4‐methylpentene) was obtained with the zirconium catalysts. The zirconium catalysts were employed in 1‐hexene polymerization, and their activity was found to be the highest ever reported for catalysts of the amine bis(phenolate) family. The catalysts featuring methyl phenolate substituents showed a higher activity toward these substituted olefins than the electron‐poor catalysts; this trend was opposite to their activity toward 1‐hexene. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 1136–1146, 2006     

Optical fiber based radial polarizer

In this paper we present a new type of optical fiber aiming to radially polarize the electrical field. This special device is composed of a tapered fiber having a classical core while on top of its external surface, radially oriented nanorods are disposed. The tails of the propagated wave are interacting with those radially oriented nanorods. This interaction performs the polarization of the propagated mode into a radial polarization.     

Iron porphyrins catalyze the synthesis of non-protected amino acid esters from ammonia and diazoacetates

Iron complexes of porphyrins (and corroles to a lesser extent) are the first catalysts to utilize ammonia for the synthesis of N-free amino acid esters.     

Synthesis and application of quantum dots FRET-based protease sensors

Preparation of FRET-based quantum dots as protease sensors-RGDC peptide molecules are bound to the surface of CdSe/ZnS quantum dots. The peptide molecules are then labeled with rhodamine dye molecules. The emission color of the quantum dots change from green to orange due to fluorescence resonance energy transfer (FRET) between the quantum dots and the bound rhodamine molecules. Cleavage of the peptide by selective proteases releases the rhodamine molecules from the quantum dots surface, which results in decreasing FRET efficiency between the quantum dots and the rhodamine molecules. The emission color of the quantum dots changes back to green.     

Superresolved imaging of remote moving targets

We present a superresolving approach that allows one to exceed the diffraction limit and recover highly resolved contours of moving targets from a sequence of low-resolution images. The presented approach is suitable for remote sensing applications. The resolution decoding algorithm that is used to recover the high-resolution features of the target can be run partially via optical means and that way can be used to reduce the required computational complexity.     

New electronic and magnetic properties emerging from adsorption of organized organic layers

New electronic and magnetic properties are induced by the adsorption of closed packed monolayers on solid substrates. For many thiolated molecules self-assembled on gold, a surprisingly large paramagnetism is observed. In the case where the layers are made from chiral molecules, in addition an unexpectedly large electronic dichroism is observed, which manifests itself as spin specific electron transmission. This dichroism was observed for monolayers made from polyalanine and from DNA. Self-assembled monolayers of double-stranded DNA oligomers on gold interact with polarized electrons similarly to a strong and oriented magnetic field. The direction of the field for right-handed DNA is away from the substrate. Moreover, the layer shows very high paramagnetic susceptibility. Interestingly, thiolated single-stranded DNA oligomers on gold do not show this effect. All the observations can be rationalized by assuming organization induced charge transfer between the substrate and the organic layer. The charge transfer results in spin alignment of the transferred electrons/holes. While for achiral molecules the spin alignment varies among the domains, in the case of monolayer made from chiral molecules the alignment is the same across the entire sample. When magnetic field is applied, large magnetic moment is observed that results from orbital magnetism.     

Second-order semilinear elliptic inequalities in exterior domains

We study the problem of existence and nonexistence of positive solutions of the semilinear elliptic inequalities in divergence form with measurable coefficients in exterior domains in . For W(x)?|x|^−σ at infinity we compute the critical line on the plane (p,σ), which separates the domains of existence and nonexistence, and reveal the class of potentials V that preserves the critical line. Example are provided showing that the class of potentials is maximal possible, in certain sense. The case of (p,σ) on the critical line has also been studied.     

Realization and Smoothness Related to the Laplacian

For f L _n (T ^d ) and , the modulus of smoothness

Fractional Derivatives and Best Approximation

We relate fractional derivatives of some operators to the rate of best approximation from a space of eigenfunctions of those operators. This is done via the introduction of "fractional" K-functionals and appropriate Riesz means. Continuous simultaneous approximations and fractional Kolmogorov-type inequalities are also achieved.