The effective potential of interactions in crystals

This paper contains a study of the effective potential of the electron-electron interaction in a periodic crystal lattice, using the Hamiltonian of a system of ions and electrons in interaction [1], in which an effective mass is used, calculated in a many-electron approximation, and also the electron-plasmon and electron-phonon coupling constants. The smallest value is obtained for the energy and the effective potential which, besides the electron-phonon interaction, also includes the electron-plasmon interaction. It is shown that Hrivnák's results [2] are particular cases of this potential.     

Dinuclear Zn(II) catalysts as biomimics of RNA and DNA phosphoryl transfer enzymes: changing the medium from water to alcohol provides enzyme‐like rate enhancements

Phosphodiesters are notoriously hydrolytically inert compounds that are demonstrated to have large accelerations of P‐OR cleavage promoted by transition and lanthanide metal ions in methanol and ethanol media. This review commentary describes recent findings of how a simple mononuclear and a dinuclear Zn(II) complex promote the cleavage of a series of RNA models and DNA models in alcohol media. The discussion centers on the analysis of the mechanisms of cleavage, energetics of the catalytic process, on recent findings of electrophilic assistance of leaving group departure, and the observation of a rapid hydrolytic reaction of a DNA model promoted by the dinuclear Zn(II) complex in ethanol containing less than 2% water. Copyright © 2009 John Wiley & Sons, Ltd.     

Dealing with a local heating effect when measuring catalytic solids in a reactor with Raman spectroscopy

In continuation of our previous work on the applicability of the G(R(infinity)) correction factor for the quantification of Raman spectra of coke during propane dehydrogenation experiments (Phys. Chem. Chem. Phys., 2005, 7, 211), research has been carried out on the potential of this correction factor for the quantification of supported metal oxides during reduction experiments. For this purpose, supported chromium oxide catalysts have been studied by combined in situ Raman and UV-Vis spectroscopy during temperature programmed reduction experiments with hydrogen as reducing agent. The goal was to quantify on-line the amount of Cr(6+) in a reactor based on the measured in situ Raman spectra. During these experiments, a significant temperature effect was observed, which has been investigated in more detail with a thermal imaging technique. The results revealed a temperature 'on the spot' that can exceed 100 degrees C. It implies that Raman spectroscopy can have a considerable effect on the local reaction conditions and explains observed inconsistencies between the in situ UV-Vis and Raman data. In order to minimize this heating effect, reduction of the laser power, mathematical matching of the spectroscopic data, a different cell design and a change in reaction conditions has been evaluated. It is demonstrated that increasing the reactor temperature is the most feasible method to solve the heating problem. Next, it allows the application of in situ Raman spectroscopy in a reliable quantitative way without the need of an internal standard.     

Quantum measure theory

We first present some basic properties of a quantum measure space. Compatibility of sets with respect to a quantum measure is studied and the center of a quantum measure space is characterized. We characterize quantum measures in terms of signed product measures. A generalization called a super-quantum measure space is introduced. Of a more speculative nature, we show that quantum measures may be useful for computing and predicting elementary particle masses.     

On a new method for the study of the spatial behavior in a homogeneous elastic arch-like region

We consider a two-dimensional homogeneous elastic state in the arch-like region a?≤?r?≤?b, 0?≤?θ?≤?α, where (r,θ) denotes plane polar coordinates. We assume that three of the edges are traction-free, while the fourth edge is subjected to a (in plane) self-equilibrated load. The Airy stress function ‘?’ satisfies a fourth-order differential equation in the plane polar coordinates with appropriate boundary conditions. We develop a method which allows us to treat in a unitary way the two problems corresponding to the self-equilibrated loads distributed on the straight and curved edges of the region. In fact, we introduce an appropriate change for the variable r and for the Airy stress functions to reduce the corresponding boundary value problem to a simpler one which allows us to indicate an appropriate measure of the solution valuable for both the types of boundary value problems. In terms of such measures we are able to establish some spatial estimates describing the spatial behavior of the Airy stress function. In particular, our spatial decay estimates prove a clear relationship with the Saint-Venant's principle on such regions.     

Symmetric vortices for two-component Ginzburg–Landau systems

We study Ginzburg–Landau equations for a complex vector order parameter Ψ=(_ψ+,_ψ−)∈C²$\Psi =({\psi }_{+},{\psi }_{-})\in {\mathbb{C}}^2$. We consider symmetric vortex solutions in the plane R²${\mathbb{R}}^2$, ψ(x)=_f±(r)e^i_n±θ$\psi (x)=f_{\pm }(r)e^{i{n}_{\pm }\theta }$, with given degrees _n±∈Z$n_{\pm }\in \mathbb{Z}$, and prove the existence, uniqueness, and asymptotic behavior of solutions as r→∞$r\to \infty$. We also consider the monotonicity properties of solutions, and exhibit parameter ranges in which both vortex profiles _f+$f_{+}$, _f−$f_{-}$ are monotone, as well as parameter regimes where one component is non-monotone. The qualitative results are obtained by means of a sub- and super-solution construction and a comparison theorem for elliptic systems.