On the structure of quantum permutation groups

The quantum permutation group of the set corresponds to the Hopf algebra . This is an algebra constructed with generators and relations, known to be isomorphic to for , and to be infinite dimensional for . In this paper we find an explicit representation of the algebra , related to Clifford algebras. For the representation is faithful in the discrete quantum group sense.

     

Formation of sp3 hybridized bonds and stability of CaCO3 at very high pressure

By performing ab initio electronic structure calculations, we observed a new high-pressure phase transition within the Pmcn structure of CaCO3. This transition is characterized by the change of the carbon's sp hybridization state and is driven by the intrinsic property of the carbon atom to form tetrahedral covalent bonds at high pressure. The formation of sp(3) hybridized bonds explains the stability of MgCO3 and CaCO3 at Earth's lower mantle pressure conditions and may serve as a criterion for searching new possible high-pressure phases of carbon bearing minerals.     

250 µm long anodic TiO2 nanotubes with hexagonal self‐ordering

In this work we show that the growth of more than 250 µm thick self‐organized TiO₂ nanotube layers is possible, using an electrochemical approach in organic electrolytes. The tubes can grow as a hexagonal close packed pore array. Crucial parameters that decide on the dimensions are the fluoride ion concentration, the voltage and the anodization time. Self‐organized tube formation is restricted to a critical parameter range. Highest aspect ratio tubes can be achieved under a set of very optimized conditions. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

     

Catenation control in the two-dimensional coordination polymers based on tritopic carboxylate linkers and azamacrocyclic nickel(II) complexes

Four new coordination polymer frameworks, namely [(NiL(1))(3)(BTB)(2)]·6H(2)O, [(NiL(2))(3)(BTB)(2)]·6H(2)O, [(NiL(3))(3)(BTB)(2)]·6H(2)O and [(NiL(2))(3)(BTC)(2)]·10.25H(2)O (L(1) = 1,4,8,11-tetraazacyclotetradecane, L(2) = 3-methyl-1,3,5,8,12-pentaazacyclotetradecane, L(3) = 3,10-dimethyl-1,3,5,8,10,12-hexaazacyclotetradecane, BTC(3-) = benzene-1,3,5-tricarboxylate, BTB(3-) = 4,4',4'-benzene-1,3,5-triyl-tribenzoate) were prepared in water-N,N-dimethylformamide solutions. The molecular and crystal structures of these compounds are compared to the related coordination polymers formed by nickel(II) macrocyclic cations to examine the effect of carboxylate linker size on the framework architecture. Luminescent properties of the complexes based on the BTB(3-) bridging ligand are also discussed.     

Surface‐enhanced Raman spectroscopy of DNA from leaves of in vitro grown apple plants

Ultrasensitive Raman measurements of nucleic acids are possible by exploiting the effect of surface‐enhanced Raman scattering (SERS). In this work, the vibrational spectra of eight genomic DNAs from in vitro grown apple leaf tissues (Malus domestica Borkh., Fam Rosaceae, cvs. Florina, Idared, Rebra, Goldrush, Romus 3, Romus 4 and the rootstocks M9 and M26) were analyzed using surface‐enhanced Raman spectroscopy, in the wavenumber range 200–1800 cm⁻¹. SERS signatures, spectroscopic band assignments and structural interpretations of these plant genomic DNAs are reported. Strong dependences of the SERS spectra on genomic DNA amount in the measured sample volume and on time were observed. Similarities of the SERS signals of DNAs from Rebra and Romus 3 leaves were detected. To our knowledge, this is the first SERS study on genomic DNA from leaf tissues. The present work provides a basis for future use of surface‐enhanced Raman spectroscopy to analyze specific plant DNA–ligand interactions or DNA structural changes induced by plants' stress conditions associated with their natural environment. Besides, this study will generate information that is valuable in the development of low‐level plant DNA‐based analytical sensors. Copyright © 2010 John Wiley & Sons, Ltd.     

The Influence of the Magnetic Impurity Content on the Pore Size Distribution Determination via the DDIF Technique

The pore size distribution of porous media can be determined in a completely non-invasive manner using a new nuclear magnetic resonance (NMR) technique which monitors the magnetization decay due to diffusion in internal fields (DDIF). However, using of the DDIF technique is restricted to the low-phase encoding limit when only the relaxation mode and the first-order diffusion mode are excited. In the present work the fulfillment of such a limit is verified for a progressive increase of the magnetic impurity content of the porous media. If the higher order diffusion modes are excited they lead both to a stronger attenuation of the echo signal and to the appearance of ripples in the DDIF spectra which cannot be related to a pore size distribution. The samples used in this study are porous ceramics prepared using the replication technique and the magnetic impurity is iron (III) oxide which is introduced in an increasing concentration inside the porous matrix. All NMR experiments were done on water filling such porous ceramics using a low-field instrument operating at a proton resonance frequency of 20 MHz. The average pore dimension obtained with the DDIF technique in the weak encoding limit indicates a satisfactory agreement with that observed in optical microscopy images.     

On p-superlinear equations with a nonhomogeneous differential operator

We consider a nonlinear elliptic equation driven by a nonhomogeneous differential operator and with a (p?1)-superlinear Carathéodory reaction. Our formulation incorporates as a special case equations monitored by the p-Laplacian. Using variational methods coupled with truncation techniques and comparison principles, we show that the problem has at least five nontrivial smooth solutions.     

Cascade reactions for constructing heterocycles containing a pyrimidino-pyrazino-pyrimidine core using 1,2,4-triazole scaffolds

The regioselective cyclocondensation of aminoethyl-1,2,4-triazoles and glyoxal provides pentacyclic heterocycles in which two 7,8-dihydro-5H-6λ²-[1,2,4]triazolo[1,5-c]pyrimidine systems are connected through CH(OH) bridges generating a central piperazine-2,5-diol ring. The structure of the new compounds was elucidated based on ¹H, ¹³C and ¹⁵N NMR spectroscopic methods. The molecular structure of the parent compound generated from aminoethyl-1,2,4-triazole was established by single crystal X-ray diffraction.     

Crystal smectic E revisited for(E)-N-(biphenyl-4-ylmethylene)-4-butylaniline – mesomorphism,crystal structure and FTIR study

This paper recalls the attention to an interesting compound having aromatic azomethine structure, namely: (E)-N-(biphenyl-4-ylmethylene)-4-butylaniline (PB4A). The molecular structure of PB4A was determined by X-ray single-crystal diffraction analysis. Besides the enantiotropic smectic B and nematic phases, this compound exhibits a monotropic crystal E phase. By polarising optical microscopy and differential scanning calorimetry, we confirmed the existence of these phases. FTIR measurements in attenuated total reflection configuration have been performed to investigate the evolution of significant absorption bands during phase transitions.