On a theorem of Burnside on fixed-point-free automorphisms

We prove that a finite group having a fixed-point-free automorphism in the Fitting subgroup of its automorphism group must be abelian of rather restricted structure. As a consequence, no finite nonabelian group could have a fixed-point-free automorphism in the Frattini subgroup of its automorphism group. Received: 21 April 2007, Revised: 18 May 2007     

Subcritical and fatigue crack growth in anti-plane strain state

Assuming elastic-plastic material behavior the slow growth of Mode III crack under both monotonic and pulsating loadings is considered. Rice's idea of universal R-curve is employed while the mathematical analysis is based on the one-dimensional plasticity model suggested by Kostrov and Nikitin. Motion of a quasi-static Mode III crack is studied and the stable/unstable transition points are found through application of the final stretch failure condition proposed in 1972 by Wnuk. A logarithmic formula for fatigue crack extension rate is derived. Results are compared to other well-known solutions.     

Diverse chemical behaviour of 2-hydroxy-functionalized pyrroline-1-oxide

The reactivity of 2-hydroxy-3,3,5-trimethyl-3,4-dihydro-2H-pyrrole 1-oxide was investigated. The title compound showed unexpected reactivity with several different types of reagents.     

Spectroelectrochemical Study of 9‐Substituted Acridines with Potential Antitumor Activity

The electrochemical and spectroelectrochemical behavior of 9‐substituted with ? CN and ? COOH acridine N‐oxides with potential antitumor activity was investigated. In SER spectra of the investigated compounds, the ring stretching vibration at 1568 cm^?1 for 9‐CN‐substituted compound respectively 1639 cm^?1 for 9‐COOH‐substituted compound was analyzed. Cyclic voltammograms indicates that the reduction potential ?0.766 V for ? CN substituted compound increase towards ?0.745 V for ? COOH substituted compound. The proposed theoretical method in the electrochemical impedance spectroscopy uses a reference redox dielectrode and a multielectrode containing the compound. To account for the change of electrochemical impedance we have considered two theoretical quantities: a pseudocapacitance and a pseudo inductance. Two possible arrangements of them: in series, respective in parallel can be used like criteria of drug classification.     

Supramolecular dimer formation through hydrogen bond extensions of carboxylate ligands – Path for magnetic exchange

A new complex of unusual composition [Cu(3-O₂Nbz)₂(nia)(H₂O)₂] (1) (nia = nicotinamide, 3-O₂Nbz = 3-nitrobenzoate) has been prepared and studied together with two other complexes of composition [Cu(4-O₂Nbz)₂(nia)₂(H₂O)₂] (2) and [Cu(4-O₂Nbz)₂(nia)₂]?(4-O₂NbzH)₂ (3) (4-O₂Nbz = 4-nitrobenzoate). The composition of all complexes has been determined by elemental analysis, the complexes have been studied by electronic, infrared and EPR spectroscopy, as well as by magnetization measurements over the temperature range 1.8–300 K, and their structures have been solved. The structure of complex (1) consists of molecules, where Cu(II) atom is monodentately coordinated by the pair of 3-nitrobenzoato anions in trans  -positions together with water and nicotinamide molecules, forming nearly tetragonal basal plane, and by another water molecule in axial position of tetragonal-pyramidal coordination polyhedron. The neighboring molecule coordination polyhedron basal planes are coplanar and allow formation of supramolecular dimers with strong H-bonds between hydrogen atoms from equatorially coordinated water molecules and uncoordinated carboxylate oxygen atoms thus giving the nearest Cu?$?$Cu distance of 4.886(2) Å. Magnetization measurements showed that complex (1) exhibits maximum of magnetic susceptibility at 6.5 K and a fit to Bleaney-Bowers equation gave singlet–triplet energy gap 2J = −6.25 cm⁻¹, and zJ′ = −0.03 cm⁻¹. This might be an experimental proof that the carboxylate bridges extended with hydrogen bonds are the pathway of the spin–spin interactions. The temperature dependence of changes in EPR spectra of (1) and the spectrum at 4.2 K have confirmed its hydrogen bonded dimeric structure. The calculated Cu?$?$Cu distance 4.8 Å is in very good agreement with the value obtained from crystal structure. The complexes (2) and (3) at 300 K exhibit magnetic moment μ_eff = 1.98 B.M. and μ_eff = 1.84 B.M., respectively. These values practically do not change with lowering the temperature up to 5 K and only small drops to μ_eff = 1.87 B.M. (for (2)) and μ_eff = 1.79 B.M. (for (3)) at 1.8 K have been observed. The EPR spectra of complex (2) at room temperature as well as at 77 K are of axial type with g_⊥ = 2.062 and g_|| = 2.285 and exhibit resolved parallel hyperfine splitting with A_|| = 160 Gauss. The EPR spectra of complex (3) at room temperature as well as at 77 K are of axial type with g_⊥ = 2.065 and g_|| = 2.235 and exhibit unresolved parallel hyperfine splitting. EPR spectra of (2) and (3) are consistent with the X-ray structure.     

QM/MM calculation of solvent effects on absorption spectra of guanine

Electronic spectra of guanine in the gas phase and in water were studied by quantum mechanical/molecular mechanical (QM/MM) methods. Geometries for the excited‐state calculations were extracted from ground‐state molecular dynamics (MD) simulations using the self‐consistent‐charge density functional tight binding (SCC‐DFTB) method for the QM region and the TIP3P force field for the water environment. Theoretical absorption spectra were generated from excitation energies and oscillator strengths calculated for 50 to 500 MD snapshots of guanine in the gas phase (QM) and in solution (QM/MM). The excited‐state calculations used time‐dependent density functional theory (TDDFT) and the DFT‐based multireference configuration interaction (DFT/MRCI) method of Grimme and Waletzke, in combination with two basis sets. Our investigation covered keto‐N7H and keto‐N9H guanine, with particular focus on solvent effects in the low‐energy spectrum of the keto‐N9H tautomer. When compared with the vertical excitation energies of gas‐phase guanine at the optimized DFT (B3LYP/TZVP) geometry, the maxima in the computed solution spectra are shifted by several tenths of an eV. Three effects contribute: the use of SCC‐DFTB‐based rather than B3LYP‐based geometries in the MD snapshots (red shift of ca. 0.1 eV), explicit inclusion of nuclear motion through the MD snapshots (red shift of ca. 0.1 eV), and intrinsic solvent effects (differences in the absorption maxima in the computed gas‐phase and solution spectra, typically ca. 0.1–0.3 eV). A detailed analysis of the results indicates that the intrinsic solvent effects arise both from solvent‐induced structural changes and from electrostatic solute–solvent interactions, the latter being dominant. © 2009 Wiley Periodicals, Inc. J Comput Chem 2010     

Thermal desorption/gas chromatography/mass spectrometry approach for characterization of the volatile fraction from amber specimens: A possibility of tracking geological origins

Research on the chemical composition of fossil resins has evolved during the last decades as a multidisciplinary field and is strongly oriented toward the correlation with their geological and botanical origin. Various extraction procedures and chromatographic techniques have been used together for identifying the volatile compounds contained in the fossil resin matrix. Hyphenation between thermal desorption (TD), gas chromatography (GC) and mass spectrometry detection (MS) has been chosen to investigate the volatile compounds fraction from ambers with a focus on Romanite (Romanian amber) and Baltic amber species. A data analysis procedure was developed for the main purpose of fingerprinting ambers based on the MS identity of the peaks generated by the volatile fraction, together with their relative percentual area within the chromatogram. Chromatographic data analysis was based entirely on Automated Mass Spectral Deconvolution & Identification System (AMDIS) software to produce deconvoluted mass spectra which were used to build-up a mixed mass spectra and relative retention scale library. Multivariate data analysis was further applied on AMDIS results with successful discrimination between Romanite and Baltic ambers. A special trial was conducted to generate pyrolysis “like” macromolecular structure breakdown to volatile compounds by gamma irradiation with a high absorbed dose of 500 kGy. Contrary to our expectations the volatile fraction fingerprints were not modified after irradiation experiments. A complementary non-destructive new approach by ESR spectroscopy was also proposed for discriminating between Romanite and Baltic ambers.     

The Landau–Hall problem on canal surfaces

In this note we study the Landau–Hall problem on a generalized canal surface and classify all uniform magnetic trajectories of a charged particle moving on such a surface under the action of a uniform magnetic field.     

A Variational Characterization of the Effective Yield Set for Ionic Polycrystals

The effective yield set of ionic polycrystals is characterized by means of variational principles in $L^\infty $ associated to supremal functionals acting on matrix-valued divergence-free fields.