On projective group properties of the 6D pseudo-Riemannian space

We study the six-dimensional pseudo-Riemannian spaces with two time-like coordinates that admit non-homothetic infinitesimal projective transformations. The metrics are manifestly obtained and the projective group properties are determined. We also find a generic definition of projective motion in the 6-dimensional rigid h-space. Presented at the International Colloquium “Integrable Systems and Quantum Symmetries”, Prague, 16–18 June 2005.     

Galvanomagnetic study of the quantum-well valence band of germanium in the Ge<Subscript>1−x</Subscript>Si<Subscript>x</Subscript>/Ge/Ge<Subscript>1−x</Subscript>Si<Subscript>x</Subscript> potential well

The structure of the quantum-well valence band in a Ge(111) two-dimensional layer is calculated by the self-consistent method. It is shown that the effective mass characterizing the motion of holes along the germanium layer is almost one order of magnitude smaller than the mass for the motion of heavy holes along the [111] direction in a bulk material (this mass is responsible for the formation of quantum-well levels). This creates a unique situation in which a large number of subbands appear to be populated at moderate values of the layer thickness d _w and the hole concentration p _s . The depopulation of two or more upper subbands in a 38-nm-thick germanium layer at a hole concentration p _s = 5 × 10¹⁵ m^?2 is revealed from the results of measuring the magnetoresistance in a strong magnetic field aligned parallel to the germanium layers. The destruction of the quantum Hall state at a filling factor ν = 1 indicates that the two lower subbands merge together in a self-formed potential profile of the double quantum well. It is demonstrated that, in a quasi-two-dimensional hole gas, the latter effect should be sensitive to the layer strain.     

Phase-sensitive scattering of a continuous wave on a soliton

Using cross-correlation frequency-resolved optical gating, we observe the phase-sensitive resonance in the interaction of a soliton with a continuous wave in a photonic crystal fiber. This interaction strongly depends on the difference in the phase velocities of the orthogonally polarized fiber modes and leads to generation of a new spectral peak. The spectral and temporal structure of this signal is revealed in our measurements, which are supported by analytical theory and numerical simulations.     

Exploring structure–selectivity relationships of biogenic amine GPCR antagonists using similarity searching and dynamic compound mapping

We design and analyze compound selectivity sets of antagonists with differential selectivity against seven biogenic amine G-protein coupled receptors. The selectivity sets consist of a total of 267 antagonists and contain a spectrum of in part closely related molecular scaffolds. Each set represents a different selectivity profile. Using these com- pound sets, a systematic computational analysis of structure-selectivity relationships is carried out with different 2D similarity methods including fingerprints, recursive partitioning, clustering, and dynamic compound mapping. Screening calculations are performed in a background database containing nearly four million molecules. Fingerprint searching and compound mapping are found to enrich target-selective antagonists over family-selective ones. Dynamic compound mapping effectively discriminates database compounds from GPCR antagonists and consistently retains target-selective antagonists during the final dimension extension levels. Furthermore, the widely used MACCS key fingerprint displays a strong tendency to distinguish between target- and family-selective GPCR antagonists. Taken together, the results indicate that different types of 2D similarity methods are capable of distinguishing closely related molecules having different selectivity. The reported compound benchmark system is made freely available in order to enable selectivity-oriented analyses using other computational approaches.     

Pd-Si binary bulk metallic glass

Pd_80+x Si_20−x (x = 0, 1, and 2) binary metallic glasses with the diameter ranging from 7 to 8 mm were prepared by a combination of fluxing and water quenching or air cooling. Thermal analysis results show that with increasing Si content, the glass transition temperature T _g, the initial crystallization temperature T _x and the onset crystallization temperature T _p of Pd-Si binary glassy alloys increase. Moreover, the supercooled liquid region reaches 61 K. It indicates that Pd-Si binary alloys possess large glass forming ability, which can be greatly improved by fluxing treatment. Supported by the National Basic Research Program of China (Grant No. 2007CB613905) and the National Natural Science Foundation of China (Grant Nos. 50671050 and 50431030)     

The Automorphism Group of a Simple Tracially AI Algebra

The structure of the automorphism group of a simple TAI algebra is studied. In particular, we show that is isomorphic (as a topological group) to an inverse limit of discrete abelian groups for a unital, simple, AH algebra with bounded dimension growth. Consequently, is totally disconnected. Another consequence of our results is the following: Suppose A is the transformation group C*-algebra of a minimal Furstenberg transformation with a unique invariant probability measure. Then the automorphism group of A is an extension of a simple topological group by the discrete group .     

Comparative study of different Schlieren diffracting elements

This paper presents an analysis of diffraction effects taking place at different Schlieren diffracting elements. Two types of diffraction effects are prominent in the Schlieren schemes. One is diffraction of direct light (source image) at the Schlieren element, which limits the sensitivity and resolution of Schlieren systems. The second type is the diffraction of light deflected from the test object at the Schlieren-diffracting element. This second type of diffraction degrades the quality of Schlieren results. Experimental results showing the effect of diffraction of light deflected from the test object at a phase knife-edge, corner of a square phase aperture and an optical fiber tip as Schlieren diffracting elements have been presented and discussed.      

Two-frequency mutual coherence function and its applications to pulse scattering by random rough surface

An analytic expression of the two-frequency mutual coherence function (MCF) was derived for a two-dimensional random rough surface. The scattered field was calculated by the Kirchhoff approximation, which is valid in the case that the radius of curvature of the surface is much larger than the incident wave length. The scattering problem of narrowband pulse was investigated to simplify the analytic expression of the two-frequency MCF. Numerical simulations show that the two-frequency MCF is greatly dependent on the root-mean-square (RMS) height, while less dependent on the correlation length. The analytic solutions were compared with the results of Monte Carlo simulation to assess the accuracy and computational efficiency. Supported by the National Natural Science Foundation of China (Grant No. 60571058) and the National Defense Foundation of China (Grant No. 51403020505DZ0111)     

Synthesis and photoluminescent properties of silica-coated LaCeF<Subscript>3</Subscript>:Tb nanocrystals

La_0.45Ce_0.45F₃:Tb (10 mol% Tb) nanoparticles was synthesized via sonochemical method and then coated with silica (SiO₂) shells through a microemulsion process, resulting in the formation of core/shell structured LaCeF₃:Tb/SiO₂ nanoparticles. The obtained core/shell LaCeF₃:Tb/SiO₂ nanoparticles are spherical and uniform in size (average size about 60 nm), strongly fluorescent, and long fluorescence lifetime (1.87 ms). This kind of nanoparticles was water-soluble, which could be applied in biological labeling and other fields.     

Explicit cosmological coarse graining via spatial averaging

The present matter density of the Universe, while highly inhomogeneous on small scales, displays approximate homogeneity on large scales. We propose that whereas it is justified to use the Friedmann–Lemaître–Robertson–Walker (FLRW) line element (which describes an exactly homogeneous and isotropic universe) as a template to construct luminosity distances in order to compare observations with theory, the evolution of the scale factor in such a construction must be governed not by the standard Einstein equations for the FLRW metric, but by the modified Friedmann equations derived by Buchert (Gen Relat Gravit 32:105, 2000; 33:1381, 2001) in the context of spatial averaging in Cosmology. Furthermore, we argue that this scale factor, defined in the spatially averaged cosmology, will correspond to the effective FLRW metric provided the size of the averaging domain coincides with the scale at which cosmological homogeneity arises. This allows us, in principle, to compare predictions of a spatially averaged cosmology with observations, in the standard manner, for instance by computing the luminosity distance versus red-shift relation. The predictions of the spatially averaged cosmology would in general differ from standard FLRW cosmology, because the scale-factor now obeys the modified FLRW equations. This could help determine, by comparing with observations, whether or not cosmological inhomogeneities are an alternative explanation for the observed cosmic acceleration.