Nontrivial Solutions for Resonant Hemivariational Inequalities

We study a resonant semilinear elliptic hemivariational inequality. Under some assumptions of strong resonance on the Clarke subdifferential of the superpotential, and using nonsmooth critical point theory, the existence of a nontrivial solution of the problem is shown. This paper has been partially supported by the State Committee for Scientific Research of Poland (KBN) under research grants no. 2 P03A 003 25 and no. 4 T07A 027 26.     

Structural studies of Cr-doped mullite derived from single-phase precursors

Cr-doped mullites were prepared from single-phase precursors containing up to 9.60 wt% Cr₂O₃ using a sol-gel technique followed by thermal treatment. Particle induced X-ray emission spectroscopy and X-ray powder diffraction were used to characterize the samples. Mullites were orthorhombic, space group Pbam. Cr doping caused the increase of unit-cell parameters. Strongest expansion was noticed along c-axis followed by a and b (Δc/c=0.089, Δa/a=0.061, Δb/b=0.045% per mole Cr₂O₃). A second phase, namely θ-(Al,Cr)₂O₃, was revealed by XRD in the sample containing 9.60 wt% Cr₂O₃. The structure of mullites was refined by the Rietveld method, location of Cr³⁺ was performed by the EPR spectroscopy. At low chromium doping level (Cr₂O₃ content less than ∼5 wt%) Cr³⁺ ions were substituted for Al³⁺ in the AlO₆ octahedra of the mullite structure (M1 site). For higher doping level, Cr³⁺ ions were additionally substituted for Al³⁺ in the AlO₆ octahedra of the second phase [θ-(Al,Cr)₂O₃ at 1400 °C, or α-(Al,Cr)₂O₃ at 1600 °C] which segregated in the system. Substitution of Cr³⁺ for Al³⁺ on M1 site in the mullite structure resulted in increase of average distances in (M1)O₆ octahedron and decrease of average distances in T*O₄ tetrahedron, while average distances in TO₄ tetrahedron stayed almost constant.     

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.     

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.     

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.     

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.     

Specific carbon-13 labelling of leucine residues in human growth hormone.

Biosynthetic human growth hormone specifically 13C-labelled in the carbonyl positions of all 26 leucine residues has been obtained by recombinant DNA techniques using 13C-labelled leucine and an E. coli strain that requires leucine. It is shown that, on the whole, the labelling is specific with no significant mislabelling as would have been the case had the 13C-labelled leucine been metabolized.     

Analysis of fragrance compounds in blood samples of mice by gas chromatography, mass spectrometry, GC/FTIR and GC/AES after inhalation of sandalwood oil.

After inhalation experiments with sandalwood oil and the pure fragrance compounds coumarin and alpha-terpineol, substances were detected and measured in the blood samples of test animals (mice) using gas chromatography/mass spectrometry (GC/MS) (MID) in connection with GC/FTIR (SWC), GC/AES (carbon and oxygen trace) and flame ionization detection/gas chromatography. Using tiglinic acid benzyl ester as the internal standard the following concentrations in serum could be found: alpha-santalol 6.1 ng/mL, beta-santalol 5.3 ng/mL and alpha-santalene 0.5 ng/mL. In separate inhalation experiments with coumarin and with alpha-terpineol the corresponding concentrations were 7.7 ng/mL and 6.9 ng/mL, respectively.     

Crystallization-induced asymmetric transformation. Application to conjugate addition of benzylamine to amides of benzoylacrylic acid

Adducts of the conjugate addition of benzylamine to enantiopure amides of aroylacrylic acid possess high enantiomeric and diastereomeric purity. A high degree of stereoselectivity has been achieved by means of crystallization-induced asymmetric transformation. A practical synthesis leading to dipeptides containing homophenylalanine is depicted.