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.     

Depth-adaptive regularized reconstruction for reflection diffuse optical tomography

We study reflection diffuse optical tomography using two-dimensional (2D) continuous-wave source-detector arrays on the surface of semi-infinite medium, aiming at imaging the perfusion and the hemoglobin oxygen saturation variation of human cerebral cortex with brain activation. We had previously formulated the inverse problem with Moore-Penrose inversion. When we use simple regularization in this inverse problem, the reconstruction sensitivity decreases markedly with the depth so that the signal in the deep range may be masked by an unwanted signal in the shallow range. In this paper, we propose a depth-adaptive regularized reconstruction, in which we assign a smaller regularization parameter with the depth. We demonstrate improvement of the three-dimensional (3D) reconstruction uniformity using the proposed scheme.     

Brownian Approximation and Monte Carlo Simulation of the Non-Cutoff Kac Equation

The non-cutoff Boltzmann equation can be simulated using the DSMC method, by a truncation of the collision term. However, even for computing stationary solutions this may be very time consuming, in particular in situations far from equilibrium. By adding an appropriate diffusion, to the DSMC-method, the rate of convergence when the truncation is removed, may be greatly improved. We illustrate the technique on a toy model, the Kac equation, as well as on the full Boltzmann equation in a special case.     

Time Evolution of Spontaneous Emission Rate of Two Undistinguished Radiators

The behavior of the system of radiators at short and long time intervals in comparison with the retardation between them is studied. The entanglement behavior of atomic states in the process of spontaneous emission is determined. It is demonstrated that at a short time interval the rate of spontaneous emission in an oscillatory manner tends to the exponential law of spontaneous emission. The simple kinetic equation, which describes this stage of system evolution, is obtained.     

Grafting of PMMA brushes on titania nanoparticulate surface via surface-initiated conventional radical and “controlled” radical polymerization (ATRP)

Stable dispersion of titania nanoparticles in organic solvents are obtained by grafting poly(methyl methacrylate) layer on to the surface. Titania nanoparticles are synthesized through the hydrolysis of titanium (IV) isopropoxide. The average size of the titania particles is found to be 15 ± 2 nm. The polymer layer was introduced onto the surface by immobilizing the initiating moiety. Azo initiator moiety required for surface-initiated conventional free radical polymerization and a tertiary bromide initiator moiety required for ATRP are attached covalently to the titania nanoparticulate surface through the surface hydroxyl groups. The “encapsulation” of PMMA layer results in the steric stabilization of the titania nanoparticles. Another important finding is that it is possible to grow polymer layer in a controlled fashion.     

Evolution in shapes of a series of (111)-based In<Subscript>2</Subscript>O<Subscript>3</Subscript> particles

In₂O₃ particles with different morphology were controllably synthesized on silicon substrates by thermal evaporation of In grains at 900 °C. The structure and morphology of the In₂O₃ particles were evaluated using X-ray diffraction, and scanning and transmission electron microscopies. The evolution in shapes as the ratio of {100} relative to {111} increases is clearly observed. The photoluminescence spectrum of the obtained In₂O₃ structures exhibits UV emission centered at about 378 nm and wide-band emission covering the green and orange regions with three peaks around 525, 572, and 604 nm. PACS 81.05.Hd; 81.07.Bc; 81.16.-c; 61.46.-w; 81.40.Gh