Algebraic orbifold conformal field theories

We formulate the unitary rational orbifold conformal field theories in the algebraic quantum field theory framework. Under general conditions, we show that the orbifold of a given unitary rational conformal field theories generates a unitary modular category. Many new unitary modular categories are obtained. We also show that the irreducible representations of orbifolds of rank one lattice vertex operator algebras give rise to unitary modular categories and determine the corresponding modular matrices, which has been conjectured for some time.Comment: 24 pages, Amste

Counting integral points in certain homogeneous spaces

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Electrospinning of poly(ethylene-co-vinyl alcohol) nanofibres encapsulated with Ag nanoparticles for skin wound healing

Copyright © 2011 Chao Xu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.Skin wound healing is an urgent problem in clinics and military activities. Although significant advances have been made in its treatment, there are several challenges associated with traditional methods, for example, limited donor skin tissue for transplantation and inflammation during long-term healing time. To address these challenges, in this study we present a method to fabricate Poly(ethylene-co-vinyl alcohol) (EVOH) nanofibres encapsulated with Ag nanoparticle using electrospinning technique. The fibres were fabricated with controlled diameters (59nm-3m) by regulating three main parameters, that is, EVOH solution concentration, the electric voltage, and the distance between the injection needle tip (high-voltage point) and the fibre collector. Ag was added to the nanofibres to offer long-term anti-inflammation effect by slow release of Ag nanoparticles through gradual degradation of EVOH nanofibre. The method developed here could lead to new dressing materials for treatment of skin wounds. © 2011 Chao Xu et al.The work was partially supported by the National Natural Science Foundation of China (nos. 10825210, 10872157, and 31050110125) and the National 111 Project of China (no. B06024)

A new three-parameter correlation for gamma-ray bursts with a plateau phase in the afterglow

Gamma ray bursts (GRBs) have great advantages for their huge burst energies, luminosities and high redshifts in probing the Universe. A few interesting luminosity correlations of GRBs have been used to test cosmology models. Especially, for a subsample of long GRBs with known redshifts and a plateau phase in the afterglow, a correlation between the end time of the plateau phase (in the GRB rest frame) and the corresponding X-ray luminosity has been found. In this paper, we re-analyze the subsample and found that a significantly tighter correlation exists when we add a third parameter, i.e. the isotropic $\gamma$-ray energy release, into the consideration. Additionally, both long and intermediate duration GRBs are consistent with the same three-parameter correlation equation. It is argued that the new three-parameter correlation is consistent with the hypothesis that the subsample of GRBs with a plateau phase in the afterglow be associated with the birth of rapidly rotating magnetars, and that the plateau be due to the continuous energy-injection from the magnetar. It is suggested that the newly born millisecond magnetars associated with GRBs might provide a good standard candle in the Universe.Comment: 11 pages, 3 figures, 1 table; A&A, in pres

Ultra High Energy Cosmic Rays: Strangelets? -- Extra dimensions, TeV-scale black holes and strange matter

The conjecture that ultra high energy cosmic rays (UHECRs) are actually strangelets is discussed. Besides the reason that strangelets can do as cosmic rays beyond the GZK-cutoff, another argument to support the conjecture is addressed in this letter via the study of formation of TeV-scale microscopic black holes when UHECRs bombarding bare strange stars. It is proposed that the exotic quark surface of a bare strange star could be an effective astro-laboratory in the investigations of the extra dimensions and of the detection of ultra-high energy neutrino fluxes. The flux of neutrinos (and other point-like particles) with energy >2.3 x 10^{20} eV could be expected to be smaller than 10^{-26} cm^{-2}$ s^{-1} if there are two extra spatial dimensions.Comment: accepted by Chin. Phys. Lett., or at http://vega.bac.pku.edu.cn/~rxxu/publications/index_P.ht

Analytical smoothing effect of solution for the boussinesq equations

In this paper, we study the analytical smoothing effect of Cauchy problem for the incompressible Boussinesq equations. Precisely, we use the Fourier method to prove that the Sobolev H 1-solution to the incompressible Boussinesq equations in periodic domain is analytic for any positive time. So the incompressible Boussinesq equation admet exactly same smoothing effect properties of incompressible Navier-Stokes equations

Construction of optimal multi-level supersaturated designs

A supersaturated design is a design whose run size is not large enough for estimating all the main effects. The goodness of multi-level supersaturated designs can be judged by the generalized minimum aberration criterion proposed by Xu and Wu [Ann. Statist. 29 (2001) 1066--1077]. A new lower bound is derived and general construction methods are proposed for multi-level supersaturated designs. Inspired by the Addelman--Kempthorne construction of orthogonal arrays, several classes of optimal multi-level supersaturated designs are given in explicit form: Columns are labeled with linear or quadratic polynomials and rows are points over a finite field. Additive characters are used to study the properties of resulting designs. Some small optimal supersaturated designs of 3, 4 and 5 levels are listed with their properties.Comment: Published at http://dx.doi.org/10.1214/009053605000000688 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org