Cauchy-Born Rule and the Stability of Crystalline Solids： Dynamic Problems

We study continuum and atomistic models for the elastodynamics of crystalline solids at zerotemperature.We establish sharp criterion for the regime of validity of the nonlinear elastic wave equationsderived from the well-known Cauchy-Born rule.     

Trace element concentrations from São Francisco River - PR analyzed with PIXE technique

Summary Kulcsszavak (angolul, ha nem azonos az elozovel)     

A new approach towards peptidosulfonamides: synthesis of potential inhibitors of bacterial peptidoglycan biosynthesis enzymes MurD and MurE

Peptidosulfonamides are an emerging group of peptidomimetics with a variety of applications in medicinal chemistry. We present a novel approach to the synthesis of peptidosulfonamides, and apply it to a series of new potential inhibitors of the bacterial peptidoglycan biosynthesis enzymes MurD and MurE. The synthesis was conducted via N-phthalimido β-aminoethanesulfonyl chlorides, which are new building blocks for the synthesis of peptidosulfonamides. In the most crucial step, sulfonic acids or their sodium salts were converted into the corresponding sulfonyl chlorides using an excess of either SOCl₂ or SOCl₂/DMF, and then coupled to the C-protected amino acid. None of the compounds significantly inhibited MurD, however, some inhibited MurE; one had an IC₅₀ below 200 μM, which constitutes a promising starting point for further development. Molecular modelling simulations were performed on two analogues to investigate the absence of inhibitory activity of the sulfonamide compounds on MurD.     

Regioselectivity in the ene-reaction of singlet oxygen with cyclic alkenes: photooxygenation of methyl-substituted 1,4-cyclohexadiene derivatives

The photooxygenation of the 1-methyl-, 2,3-dimethyl-, and 1,4-dimethylcyclohexa-1,4-dienes, which are readily available through Birch reduction, yielded the corresponding ene-products. The formed endocyclic dienes were trapped by the addition of singlet oxygen to give the corresponding bicyclic endoperoxy hydroperoxides. In the case of 1-methylcyclohexa-1,4-diene and 1,4-dimethylcyclohexa-1,4,-diene, the cis-effect determined the product distribution. Photooxygenation of 2,3-dimethylcyclohexa-1,4-dienes gave mainly exocyclic olefin, which was attributed to the lowered rotational barrier of the methyl group and increased reactivity of the methyl groups.     

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.     

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.