New theory of spatio-temporal chaos in nonlinear systems of partial differential equations

It is shown that there exists one universal scenario of transition to chaos in three considered systems of nonlinear partial differential equations of diffusion type. It is the subharmonic cascade of bifurcations of two-dimensional tori along one or both frequencies. So, it is shown that the new universal Feigenbaum-Sharkovskii-Magnitskii theory of dynamical chaos in nonlinear differential equations is applicable also for nonlinear partial differential equations of diffusion type. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Local ν-Euler Derivations and Deligne's¶Characteristic Class of Fedosov Star Products¶and Star Products of Special Type

In this paper we explicitly construct local ν-Euler derivations , where the ξ_α are local, conformally symplectic vector fields and the are formal series of locally defined differential operators, for Fedosov star products on a symplectic manifold (M,ω) by means of which we are able to compute Deligne's characteristic class of these star products. We show that this class is given by , where is a formal series of closed two-forms on M the cohomology class of which coincides with the one introduced by Fedosov to classify his star products. Moreover, we consider star products that have additional algebraic structures and compute the effect of these structures on the corresponding characteristic classes of these star products. Specifying the constituents of Fedosov's construction we obtain star products with these special properties. Finally, we investigate equivalence transformations between such special star products and prove existence of equivalence transformations being compatible with the considered algebraic structures. Dedicated to the memory of Moshé Flato Received: 28 June 1999 / Accepted: 11 April 2002?Published online: 11 September 2002     

Damping lateral vibrations in rotary machinery using motor speed modulation

This paper outlines a new principle for damping lateral vibrations of rotary systems. According to this principle, no changes in the visco-elastic properties of the system to be damped are required. The method is based on the generation of a harmonic additive to the constant speed of rotation that provides significant damping of lateral vibrations at critical speeds of rotation. This concept is validated analytically using the method of averaging and additionally with the help of direct numerical integration. The solution is shown to represent Fourier series containing Bessel functions. Consequently, proper choice of the parameters of the additional harmonic component ensuring that the Bessel functions have minimum values results from a minimization of the solution itself. Thus, the analytical solution and numerical results prove this concept by showing an essential decrease of the amplitudes of lateral vibrations of the damped system compared with those of the undamped system. The physical explanation of this effect is presented.     

The $${\bar\mu}$$-invariant of Seifert fibered homology spheres and the Dirac operator

We derive a formula for the [`(m)]{\bar\mu}-invariant of a Seifert fibered homology sphere in terms of the η-invariant of its Dirac operator. As a consequence, we obtain a vanishing result for the index of certain Dirac operators on plumbed 4-manifolds bounding such spheres.     

A Bohr Phenomenon For Elliptic Equations

In 1914 Bohr proved that there is an r (0,1) such that if apower series converges in the unit disk and its sum has modulusless than 1 then, for |z| < r, the sum of absolute valuesof its terms is again less than 1. Recently, analogous resultshave been obtained for functions of several variables. The aimof this paper is to place the theorem of Bohr in the contextof solutions to second-order elliptic equations satisfying themaximum principle. 2000 Mathematics Subject Classification: 35J15, 32A05, 46A35.     

Interatomic electronic decay driven by nuclear motion

The interatomic electronic decay after inner-valence ionization of a neon atom by a single photon in a neon-helium dimer is investigated. The excited neon atom relaxes via interatomic Coulombic decay and the excess energy is transferred to the helium atom and ionizes it. We show that the decay process is only possible if the dimer's bond stretches up to 6.2 ?, i.e., to more than twice the equilibrium interatomic distance of the neutral dimer. Thus, it is demonstrated that the electronic decay, taking place at such long distances, is driven by the nuclear motion.     

Sharp Hardy Inequalities in Star-shaped Domains with Double Singular Kernels

Improved Hardy inequality with double singular kernel in bounded, star-shaped domains \(\Omega \subset R^n\) is proved. The case of singularity at an interior point and on the boundary of the domain is considered. The Hardy constant is optimal and the inequality is sharp due to the additional term.     

Probing Absolute Electronic Energy Levels in Hg‐Doped CdTe Semiconductor Nanocrystals by Electrochemistry and Density Functional Theory

The absolute electronic energy levels in Hg‐doped CdTe semiconductor nanocrystals (CdHgTe NCs) with varying sizes/volumes and Hg contents are determined by using cyclic voltammetry (CV) measurements and density functional theory (DFT) ‐based calculations. The electrochemical measurements demonstrate several distinct characteristic features in the form of oxidation and reduction peaks in the voltammograms, where the peak positions are dependent on the volume of CdHgTe NCs as well as on their composition. The estimated absolute electronic energy levels for three different volumes, namely 22, 119 and 187 nm³ with 2.7±0.3 % of Hg content, show strong volume dependence. The volume‐dependent shift in the characteristic reduction and oxidation peak potential scan can be attributed to the alteration in the energetic band positions owing to the quantum confinement effect. Moreover, the composition (Cd/Hg=98.3/1.7 and 97.0/3.0) ‐dependent alteration in the electronic energy levels of CdHgTe NCs for two different samples with similar volumes (ca. 124±5 nm³) are shown. Thus obtained electronic energy level values of CdHgTe NCs as a function of volume and composition demonstrate good congruence with the corresponding absorption and emission spectral data, as well as with DFT‐based calculations. DFT calculations reveal that incorporation of Hg into CdTe NCs mostly affects the energy levels of conduction band edge, whereas the valence band edge remains almost unaltered.     

Copper (II) complexes of sterically hindered o-diphenol derivatives: synthesis, characterization and microbiological studies

Cu (II) complexes with the sterically hindered diphenol derivatives 3,5-di(tert-butyl)-1,2-benzenediol (I), 4,6-di(tert-butyl)-1,2,3-benzenetriol (II) and the sulfur-containing 4,6-di(tert-butyl)-3-(2-hydroxyethylsulfanyl)-1,2-benzenediol (III) and 2-[4,6-di(tert-butyl)-2,3-dihydroxyphenylsulfanyl]acetic acid (IV) have been synthesized and characterized by elemental analysis, TG/DTA, FT-IR, ESR, XPS, XPD and conductivity measurements. Compounds I–III can coordinate in their singly deprotonated forms and act as bidentate ligands. These compounds yield Cu (II) complexes of the stoichiometry Cu(L)₂, which have square planar geometry (g_| > g_⊥ > g_e). Unlike them, compound IV behaves as a terdentate ligand, and its complex Cu(L^IV)₂ has distorted octahedral geometry. According to ESR data, only the Cu(L^II)₂ complex contains a very small amount of phenoxyl radicals. Antimicrobial activities of these ligands and their respective Cu (II) complexes have been determined with respect to Gram-positive and Gram-negative bacteria, as well as on yeasts. Their phytotoxic properties against Chlorella vulgaris 157 were also examined.     

High resolution 1H detected 1H,13C correlation spectra in MAS solid-state NMR using deuterated proteins with selective 1H,2H isotopic labeling of methyl groups

MAS solid-state NMR experiments applied to biological solids are still hampered by low sensitivity and resolution. In this work, we employ a deuteration scheme in which individual methyl groups are selectively protonated. This labeling scheme allows the acquisition of proton carbon correlation spectra with a resolution comparable to that in solution-state NMR experiments. We observe an increase in resolution by a factor of 10-15 compared to standard heteronuclear correlation experiments using PMLG for 1H,1H dipolar decoupling in the indirect dimension. At the same time, the full sensitivity of the proton-based experiment is retained. In comparison to the heteronuclear detected version of the experiment, a gain in sensitivity of a factor of approximately 4.7 is achieved.