Experimental study of light diffraction by standing ultrasonic wave with cylindrical symmetry

We report a new acousto-optic arrangement based on ultrasonic wave with cylindrical symmetry. The theory of light interaction with standing cylindrical ultrasonic wave is experimentally verified in the Fraunhofer region. A very good agreement of experimental results with numerical calculations based on the proposed theory is found. The diffraction pattern consists of ring-shaped diffraction orders which posses a fine structure. The time average light intensity of the whole zeroth diffraction order as a function of the Raman-Nath parameter is investigated. The modulation properties of presented system are examined by means of single photon counting technique. Finally, some potentially useful applications in the laser and fibre technology are suggested.     

Conversion of single-stranded oligonucleotides into cloned duplexes and its consecutive application to short artificial genes.

A general method to convert single-stranded, chemically synthesized oligonucleotides into cloned duplexes is described. Oligonucleotides supplied with 3'-terminal extensions that are complementary to 3'-protruding ends obtained by certain restriction enzymes can be cloned either directly or with the help of an adapter molecule into double-stranded vectors. Two methods have also been developed for consecutive cloning applications. According to these methods, the synthetic oligonucleotides (and their enzymatically prepared complementary strands) are joined, one after the other, inside a cloning vector, each joining requiring one cloning step. Synthetic genes are thus built up from oligonucleotides corresponding to only one strand of the DNA. The sequential assembly of the cloned duplex takes place in the 5' to 3' direction. Each oligonucleotide is supplied with a four-nucleotide-long 3'-terminal extension, but this sequence is eliminated when the joining takes place, leaving no limiting sequence between the oligonucleotides. The two consecutive cloning methods, the adapter and the polycloning site methods, are illustrated by the assembly of short artificial genes.     

On exactness and isoperimetric profiles of discrete groups

We introduce a quasi-isometry invariant related to Property A and explore its connections to various other invariants of finitely generated groups. This allows to establish a direct relation between asymptotic dimension on one hand and isoperimetry and random walks on the other. We apply these results to reprove sharp estimates on isoperimetric profiles of some groups and to answer some questions in dimension theory.     

Interpolation of Bilinear Operators Between Quasi-Banach Spaces

We study interpolation, generated by an abstract method of means, of bilinear operators between quasi-Banach spaces. It is shown that under suitable conditions on the type of these spaces and the boundedness of the classical convolution operator between the corresponding quasi-Banach sequence spaces, bilinear interpolation is possible. Applications to the classical real method spaces, Calderón-Lozanovsky spaces, and Lorentz-Zygmund spaces are presented. The author is supported by the National Science Foundation under grant DMS 0099881. The author is supported by KBN Grant 1 P03A 013 26.     

Jacobians of Symmetric Polynomials

Annals of Combinatorics - We give the Jacobian of any family of complete symmetric functions, or of power sums, in a finite number of variables.     

Neocompact Sets and the Fixed Point Property

We use a newly introduced concept of neocompactness to study problems from metric fixed point theory. In particular, we give a sufficient condition for a superreflexive Banach space X to have the fixed point property and obtain shorter proofs of some well-known results in that theory.     

Initiation process of L‐lactide polymerization carried out with zirconium(IV) acetylacetonate

Lactide polymerization using zirconium(IV) acetylacetonate [Zr(acac)₄] as an initiator was investigated. In the reaction between Zr(acac)₄ and the monomer molecule, lactide deprotonation and the release of acetylacetone occurred. The structures of the obtained complexes were analyzed with high‐resolution NMR spectroscopy. A computational method was used to calculate the hypothetical structures. The role of the obtained complexes in the initiation of polymerization and the reaction of chain growth was proposed. The influence of the reaction temperature on the structures of the complexes was investigated. Polylactide chain growth proceeded by an insertion‐coordination mechanism. The polymer chain grew on one ligand, which was formed in advance from a deprotonated lactide. The molecular masses of the obtained polymers were the same as the theoretical masses and were directly proportional to the reaction conversion. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 1886–1900, 2004     

Copper-D-penicillamine complex as potential contrast agent for MRI.

In vitro and in vivo proton T1 data are reported that demonstrate that the paramagnetic copper-D-penicillamine complex can be applied as a potential contrast agent to magnetic resonance imaging.