A note on the weak tracial Rokhlin property for finite group actions on simple unital C*-algebras

In this paper, we show that one of the conditions in the definition of weak tracial Rokhlin property for finite group actions on simple unital C*-algebras can be replaced by a seemingly weaker condition, or a seemingly stronger condition. As a corollary, this condition is redundant whenever the C*-algebra is not purely infinite. We also give a sufficient condition for the weak tracial Rokhlin property for finite group actions on simple unital C*-algebras to imply the tracial Rokhlin property.Comment: 14page

Experimental demonstration of graphene plasmons working close to the near-infrared window

Due to strong mode-confinement, long propagation-distance, and unique tunability, graphene plasmons have been widely explored in the mid-infrared and terahertz windows. However, it remains a big challenge to push graphene plasmons to shorter wavelengths in order to integrate graphene plasmon concepts with existing mature technologies in the near-infrared region. We investigate localized graphene plasmons supported by graphene nanodisks and experimentally demonstrated graphene plasmon working at 2 {\mu}m with the aid of a fully scalable block copolymer self-assembly method. Our results show a promising way to promote graphene plasmons for both fundamental studies and potential applications in the near-infrared window.Comment: 6 pages, 4 figures, a revised versio

Substrate tolerant direct block copolymer nanolithography

Sub-20 nm block copolymer films directly applied on substrates and annealed in vapors of selective solvents significantly simplify the lithographic process.</p

Relative controllability of impulsive multi-delay differential systems

In this paper, relative controllability of impulsive multi-delay differential systems in finite dimensional space are studied. By introducing the impulsive multi-delay Gramian matrix, a necessary and sufficient condition, and the Gramian criteria, for the relative controllability of linear systems is given. Using Krasnoselskii’s fixed point theorem, a sufficient condition for controllability of semilinear systems is obtained. Numerically examples are given to illustrate our theoretically results

Chandra Study of X-Ray Point Sources in the Early-Type Galaxy NGC 4552 (M89)

We present a Chandra ACIS study of the early-type galaxy NGC 4552. We detect 47 X-ray point sources, most of which are likely LMXBs, within 4 R_e. The brightest X-ray source coincides with the optical/UV/radio center of the galaxy, and shows variability on >1 hr timescales, indicating the possible existence of a LLAGN. The 46 off-center sources and the unresolved point sources contribute about 29% and 20% to the total luminosity of the galaxy, respectively. The corrected cumulative XLF of the off-center sources is best fit by a broken power-law model with a break at L_b=4.4+2.0-1.4 e38 ergs/s. We identified 210 GCs candidates in a HST WFPC2 optical image of the galaxy's central region. Of the 25 off-center LMXBs that fall within the WFPC2 FOV, 10 sources are coincident with a GC. Thus the fraction of the GCs hosting bright LMXBs and the fraction of the LMXBs associated with GCs are 4.8% and 40%, respectively. In the V and I bands, the GCs hosting bright LMXBs are typically 1-2 magnitudes brighter than the GCs with no detected LMXBs. There are about 1.9+-0.4 times as many LMXBs in the red, metal-rich GCs as there are in the blue, metal-poor ones. We find no obvious difference between the luminosity distributions of LMXBs in GCs and in field, but the cumulative spectrum of the LMXBs in GCs tends to be softer than that of the LMXBs in field. We detected 3 X-ray sources that have isotropic luminosities larger than 1e39 erg/s. The one located in the joint Chandra-HST field is found to be associated with a GC. By studying the ACIS spectra we infer that the this may be a candidate black hole system with a mass of 15-135 M_sun. One of the other sources with a luminosity brighter than 1e39 ergs/s reveals temporal variations in brightness on timescales greater than an hour.Comment: Accepted for publication in Ap

Multiscale Simulation of Surface Defect Influence in Nanoindentation by a Quasi-Continuum Method

Microscopic properties of crystal aluminum thin film have been investigated using the quasi-continuum method in order to study the influence of surface defects in nanoindentation. Various distances between the surface pit defect and indenter and various sizes of the pit have been calculated. In this simulation, as the distance between the pit and indenter increases, the nanohardness increases in a wave that goes up in a period of three atoms, and it is found closely related to the crystal structure of periodic atom arrangement on {1 1 1} atomic close-packed planes of FCC metal; there is almost no influence on the nanohardness when the adjacent distance between the pit and indenter is more than 16 atomic spacing. We have modified the theoretical equation of the necessary load for elastic-to-plastic transition of Al film with the initial surface defect size. Furthermore, when the size coefficient of width (of height) equals about one unit (half unit), the yield load experiences an obvious drop. When it reaches about two units (one unit), the yield load is nearly close to that of the nanoindentation on a stepped surface. Additionally, compared to the width, the height of surface pit defect displays a greater influence on the yield load of thin film