Singer-Thorpe bases for special Einstein curvature tensors in dimension 4

Let (M, g) be a 4-dimensional Einstein Riemannian manifold. At each point p of M, the tangent space admits a so-called Singer-Thorpe basis (ST basis) with respect to the curvature tensor R at p. In this basis, up to standard symmetries and antisymmetries, just 5 components of the curvature tensor R are nonzero. For the space of constant curvature, the group O(4) acts as a transformation group between ST bases at T _p M and for the so-called 2-stein curvature tensors, the group Sp(1) ? SO(4) acts as a transformation group between ST bases. In the present work, the complete list of Lie subgroups of SO(4) which act as transformation groups between ST bases for certain classes of Einstein curvature tensors is presented. Special representations of groups SO(2), T ², Sp(1) or U(2) are obtained and the classes of curvature tensors whose transformation group into new ST bases is one of the mentioned groups are determined.     

Reactivity of Alkyne-Substituted Transition Metal Clusters: An Overview

In this work we present a summary of reactivity studies of alkyne substituted transition metal clusters towards different nucleophilic and electrophilic reagents. This work is not comprehensive but includes some of the most representative types of reactions of this type of compounds.     

Thermal properties and the structure of amorphous Sb2Se3 thin film

The amorphous Sb₂Se₃ film with a thickness ~0.9 µm was prepared by thermal evaporation and its composition was confirmed using an energy-dispersive X-ray analysis. The amorphous state was checked by an X-ray diffraction analysis. The optical gap E _g ^opt was determined to be 1.32 eV. The glass transition temperature could not be found by either a differential scanning calorimetry or a thermomechanical analysis. The film was crystallized and characterized using the quasi-isothermal method. The temperature dependence of the isobaric heat capacity was raised monotonously and no drop over the course of the crystallization was observed. The temperature-modulated thermomechanical analysis determined a temperature T = 133 °C which can be assumed to be the temperature of the structural reorganization beginning. Raman spectra of amorphous Sb₂Se₃ revealed that the vibrations of both the amorphous and crystalline phase are close to one other. Raman scattering revealed that both the short and the medium-range order of amorphous and crystalline phases are similar.     

Monitoring stabilizing procedures of archaeological iron using electrochemical impedance spectroscopy

A methodology for monitoring washing procedures applied to stabilize archaeological iron is described. It is based on the combination of voltammetry of microparticles (VMP) with electrochemical impedance spectroscopy (EIS). A semi-empirical approach is used where the impedances at low and high frequencies were related with the fraction areas of passive and corrosion layers generated during the stabilizing treatment, the thickness, and the porosity of the corrosion layer. The variation of such parameters with the time of washing was determined from EIS data for four types of desalination procedures using concentrated NaOH and/or Na₂SO₃ aqueous solutions on archaeological iron artifacts. After 2 months of treatment, EIS data indicate that an essentially identical “stable” state was attained in all cases, as confirmed by the formation of a passive magnetite layer identified in VMP measurements while the rate of variation of corroded surface and porosity at short washing times varied significantly from one stabilization procedure to another.     

Palladium‐Catalyzed Stereoselective Intramolecular Oxidative Amidation of Alkenes in the Synthesis of 1,3‐ and 1,4‐Amino Alcohols and 1,3‐Diamines

An efficient and practical Pd‐catalyzed intramolecular oxidative allylic amidation provides facile access to derivatives of 1,3‐ and 1,4‐amino alcohols and 1,3‐diamines. The method operates under mild reaction conditions (RT) with molecular oxygen (1 atm) as the sole reoxidant of Pd. Excellent diastereoselectivities were attained with substrates bearing a secondary stereogenic center     

Synthesis and characterization of palladium(II) complexes [PdX2(p-diben)] (X = Cl,Br, I,N3, or NCO; p-diben = N,N′-bis(4-dimethylaminobenzylidene)ethane-1,2-diamine): crystal structure of [Pd(N3)2(p-diben)]

Five new complexes of general formula [PdX₂(p-diben)], where p-diben = N,N′-bis(4-dimethylaminobenzylidene)ethane-1,2-diamine) (1) and X = Cl (2), Br (3), I (4), N₃ (5), or CNO (6), were synthesized and characterized by physicochemical and spectroscopic methods. The crystal structure of compound (5) was determined by single-crystal X-ray diffraction. Complexes 2–6 were characterized as N,N-chelated products. The crystal structure confirmed this formulation for [Pd(N₃)₂(p-diben)], besides showing the isomerism inversion of one of the C=N bonds, caused by Pd(II) coordination.     

Asymmetric deformation of bubble shape: cause or effect of vortex-shedding?

Two perpendicular projections of rising bubbles were observed in counter-current downstream diverging flow. Evidently, the bubbles did not enter the boundary layer at the channel wall and a plug liquid flow assumption was acceptable in our experimental equipment. This confirmed that the experiment was appropriate for simulation of bubble rises in a quiescent liquid column. Recent data obtained by a high-speed camera permitted recording over a period of 60 s. Image analysis by a tailor-made program provided a time-series of quantities related to the position, size, and shape of bubbles. In addition to determination of the aspect ratio of the equivalent oblate ellipsoid, deviation from this shape was investigated in respect of the difference between the bubble’s centre of mass and the geometrical centre of bubble projection. Autocorrelation of the data indicated that the bubble inclination oscillated harmonically with a frequency of 5–10 Hz; cross correlation showed that the horizontal shift of the centre of mass, as well as the horizontal velocity, increased with increasing bubble inclination, and the vertical shift of the centre of mass increased with an increases in the absolute value of the bubble inclination. There is no significant phase shift in the oscillation of these quantities. The bulky bottom side of the bubbles is in accordance with the model of bubble oscillation induced by instability of the equilibrium of gravity and surface tension forces. The oscillation frequency dependence on surface forces (Eötvös number) is evident, while viscosity does not play a significant role in low-viscosity liquids. Therefore, vortex-shedding is more likely to be an effect of the oscillation and not its cause.