Anomalous postcritical refraction behavior for certain transversely isotropic media

Snell's law at the boundary between two transversely isotropic media with a vertical axis of symmetry (VTI media) can be solved by setting up a fourth order polynomial for the sine of the reflection/transmission angles. This approach reveals the possible presence of an anomalous postcritical angle for certain transversely isotropic media. There are thus possibly three incident angle regimes for the reflection/refraction of longitudinal or transverse waves incident upon a VTI medium: precritical, postcritical/preanomalous, and postanomalous. The anomalous angle occurs for certain strongly anisotropic media where the required root to the phase velocity equation must be switched in order to obey Snell's law. The reflection/transmission coefficients, polarization directions, and the phase velocity are all affected by both the anisotropy and the incident angle. The incident critical angles are also effected by the anisotropy.     

Synthesis of new chiral amines with a cyclic 1,2-diacetal skeleton derived from (2R, 3R)-(+)-tartaric acid

The syntheses of new chiral cyclic 1,2-diacetals from (2R, 3R)-( )-tartaric acid are described. C(2)-symmetrical diamines were prepared via direct amidation of the tartrate or from the corresponding bismesylate via reaction with sodium azide. For C1-symmetrical compounds, the Appel reaction was used to form the key intermediate, a monochlorocarbinol, from the diol. Some of the new chiral compounds, produced in good to high yields, may be potentially useful as asymmetric organocatalysts or as nitrogen and sulfur chelating ligands for asymmetric metal catalyzed reactions. Thus, a bis-N-methyl-methanamine derivative, used in substoichiometric amounts, was found to catalyze the enantioselective addition of cyclohexanone to (E)-beta-nitrostyrene with high diastereoselectivity (syn / anti = 92:8), albeit giving moderate optical purity (syn: 30 %).     

The deformed twisted Heisenberg–Virasoro type Lie bialgebra

Abstract

In this article, we investigate Lie bialgebra structures on the deformed twisted Heisenberg–Virasoro Lie algebra. Sufficient and necessary conditions for this type Lie bialgebra structures to be triangular coboundary are given.

Communicated by K. C. Misra     

Stability of Jensen functional equation on semigroups

In this paper we introduce a Jensen type functional equation on semigroups and study the Hyers-Ulam stability of this equation. It is proved that every semigroup can be embedded into a semigroup in which the Jensen equation is stable.     

CBMO estimates for multilinear Hardy operators

The purpose of this paper is to study the multilinear Hardy operators in higher dimensional cases and establish the CBMO estimates for multilinear Hardy operators on some function spaces, such as the Lebesgue spaces, the Herz spaces and the Morrey-Herz spaces.     

Some contributions to the model order reduction of large scale non-linear electric circuits

Model order Reduction (MOR) has become an ubiquitous technique in the simulation of large-scale dynamical systems (i.e. 10⁴ and more equations). One technique for non-linear MOR is the trajectory piecewise-linear approach (TPWL) [1]. TPWL approximates a non-linear differential system by a weighted sum of linear systems which have a significantly reduced number of equations. One open question is which weight representations provide physical meaning of the weighted sum [2]. In this article we propose two representations. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Charged particles detection: The graft-and-dye method

Charged particles travelling through an organic medium leave a trail of highly concentrated active, stable chemical radicals. These functions are able to initiate copolymerization reactions of unsaturated molecules. Such a reagent is made to reach the trail; polymerization occurs. If the new polymer formed either absorbs or emits light the track of the charged particle is made visible. This technique and results are discussed: the efficiency of those detectors has been increased, they do not exhibit any critical dip angle for the registration of particle tracks, they may offer a way to reveal tracks originating in the detector itself.     

Electrochemical Monitoring of ROS/RNS Homeostasis Within Individual Phagolysosomes Inside Single Macrophages

The existence of a homeostatic mechanism regulating reactive oxygen/nitrogen species (ROS/RNS) amounts inside phagolysosomes has been invoked to account for the efficiency of this process but could not be unambiguously documented. Now, intracellular electrochemical analysis with platinized nanowire electrodes (Pt‐NWEs) allowed monitoring ROS/RNS effluxes with sub‐millisecond resolution from individual phagolysosomes impacting onto the electrode inserted inside a living macrophage. This shows for the first time that the consumption of ROS/RNS by their oxidation at the nanoelectrode surface stimulates the production of significant ROS/RNS amounts inside phagolysosomes. These results establish the existence of the long‐postulated ROS/RNS homeostasis and allows its kinetics and efficiency to be quantified. ROS/RNS concentrations may then be maintained at sufficiently high levels for sustaining proper pathogen digestion rates without endangering the macrophage internal structures.     

Scaled‐Up Synthesis of Amorphous NiFeMo Oxides and Their Rapid Surface Reconstruction for Superior Oxygen Evolution Catalysis

The anode oxygen evolution reaction (OER) is known to largely limit the efficiency of electrolyzers owing to its sluggish kinetics. While crystalline metal oxides are promising as OER catalysts, their amorphous phases also show high activities. Efforts to produce amorphous metal oxides have progressed slowly, and how an amorphous structure benefits the catalytic performances remains elusive. Now the first scalable synthesis of amorphous NiFeMo oxide (up to 515 g in one batch) is presented with homogeneous elemental distribution via a facile supersaturated co‐precipitation method. In contrast to its crystalline counterpart, amorphous NiFeMo oxide undergoes a faster surface self‐reconstruction process during OER, forming a metal oxy(hydroxide) active layer with rich oxygen vacancies, leading to superior OER activity (280 mV overpotential at 10 mA cm^?2 in 0.1 m KOH). This opens up the potential of fast, facile, and scale‐up production of amorphous metal oxides for high‐performance OER catalysts.     

Dimers on the kagome lattice II: Correlations and the Grassmannian approach

In this paper we continue our consideration of closed-packed dimers on the kagome lattice. Using the Pfaffian approach we evaluate the correlation between dimers on two lattice edges. It is found that the correlation is extremely short-ranged in the case of symmetric dimers weights. Explicit expressions for the nonvanishing correlations are obtained for two dimers in the interior of a large lattice. We also describe a Grassmannian functional integral approach, and use it to evaluate the dimer generating function and correlation functions.