On the Penrose inequality for general horizons

For asymptotically flat initial data of Einstein's equations satisfying an energy condition, we show that the Penrose inequality holds between the Arnowitt-Deser-Misner mass and the area of an outermost apparent horizon, if the data are suitably restricted. We prove this by generalizing Geroch's proof of monotonicity of the Hawking mass under a smooth inverse mean curvature flow, for data with non-negative Ricci scalar. Unlike Geroch we need not confine ourselves to minimal surfaces as horizons. Leaving smoothness issues aside, we also show that our restrictions on the data can be locally fulfilled by a suitable choice of the initial surface in a given spacetime.     

非结构网格上一种新型的高分辨率高精度无波动的有限元格式

在非结构网格上构造出无波动无自由参数耗散性有限元格式 ,即NND有限元格式 .通过若干个典型二维跨音速和超音速可压缩无粘定常流动的算例证明这确是一个高精度的 ,对激波具有高分辨率的无波动的新型有限元格式 .特别与网格自适应相结合 ,可得到十分满意的结果     

LETTER TO THE EDITOR: General Non-Rotating Perfect-Fluid Solution with an Abelian Spacelike C3 Including Only One Isometry

The general solution for non-rotating perfect-fluid spacetimes admitting one Killing vector and two conformal (non-isometric) Killing vectors spanning an abelian three-dimensional conformal algebra (C₃) acting on spacelike hypersurfaces is presented. It is of Petrov type D; some properties of the family such as matter contents are given. This family turns out to be an extension of a solution recently given in [9] using completely different methods. The family contains Friedman-Lemaître-Robertson-Walker particular cases and could be useful as a test for the different FLRW perturbation schemes. There are two very interesting limiting cases, one with a non-abelian G₂ and another with an abelian G₂ acting non-orthogonally transitively on spacelike surfaces and with the fluid velocity non-orthogonal to the group orbits. No examples are known to the authors in these classes.     

Renormalization of the inverse square potential

The quantum-mechanical D-dimensional inverse square potential is analyzed using field-theoretic renormalization techniques. A solution is presented for both the bound-state and scattering sectors of the theory using cutoff and dimensional regularization. In the renormalized version of the theory, there is a strong-coupling regime where quantum-mechanical breaking of scale symmetry takes place through dimensional transmutation, with the creation of a single bound state and of an energy-dependent s-wave scattering matrix element.     

Geometry of Normal Graphs in Euclidean Space and Applications to the Penrose Inequality in Minkowski

The Penrose inequality in Minkowski is a geometric inequality relating the total outer null expansion and the area of closed, connected and spacelike codimension-two surfaces \({{\bf \mathcal{S}}}\) in the Minkowski spacetime, subject to an additional convexity assumption. In a recent paper, Brendle and Wang A (Gibbons–Penrose inequality for surfaces in Schwarzschild Spacetime. arXiv:1303.1863, 2013) find a sufficient condition for the validity of this Penrose inequality in terms of the geometry of the orthogonal projection of \({{\bf \mathcal{S}}}\) onto a constant time hyperplane. In this work, we study the geometry of hypersurfaces in n-dimensional Euclidean space which are normal graphs over other surfaces and relate the intrinsic and extrinsic geometry of the graph with that of the base hypersurface. These results are used to rewrite Brendle and Wang’s condition explicitly in terms of the time height function of \({{\bf \mathcal{S}}}\) over a hyperplane and the geometry of the projection of \({{\bf \mathcal{S}}}\) along its past null cone onto this hyperplane. We also include, in Appendix, a self-contained summary of known and new results on the geometry of projections along the Killing direction of codimension two-spacelike surfaces in a strictly static spacetime.     

Single-wavelength-pump bi-directional hybrid fiber amplifier for bi-directional local area network application

This paper proposes a novel bi-directional hybrid fiber amplifier using a single-wavelength pump laser diode (LD) at 1495 nm. The hybrid amplifier is theoretically applied in a 50 km bi-directional local area network (LAN) with 26 ch × 10 Gb/s for bi-directional transmission. Thirteen C-band channels serve as downlink signals while the other 13 L-band channels are employed as uplink signals. Without loss of generality, four channels (two from each band) are experimentally analyzed. Erbium doped fiber (EDF) provides amplification for the C-band channels and Raman amplification amplifies the L-band channels. The pump efficiency is improved by employing a double-pass scheme for both the Erbium doped fiber amplifier (EDFA) and Raman fiber amplifier (RFA). The chromatic dispersion incurred by all the channels is precisely compensated for by inserting a fiber Bragg grating (FBG) array in appropriate locations along the dispersion compensating fiber (DCF) segments. Moreover, gain equalization of all the channels is achieved by adjusting the FBG reflectivity. Both the simulation results and experimental measurements confirm the proposed device feasibility and potential application in a bi-directional LAN.     

In vitro cytotoxic and antiviral activities of Ficus carica latex extracts

The latex of fig fruit (Ficus carica) is used in traditional medicine for the treatment of skin infections such as warts and also diseases of possible viral origin. Five extracts (methanolic, hexanic, ethyl acetate, hexane-ethyl acetate (v/v) and chloroformic) of this species were investigated in?vitro for their antiviral potential activity against herpes simplex type 1 (HSV-1), echovirus type 11 (ECV-11) and adenovirus (ADV). To evaluate the capacity of the extracts to inhibit the replication of viruses, the following assays were performed: adsorption and penetration, intracellular inhibition and virucidal activity. Observation of cytopathic effects was used to determine the antiviral action. The hexanic and hexane-ethyl acetate (v/v) extracts inhibited multiplication of viruses by tested techniques at concentrations of 78 μg mL(-1). These two extracts were possible candidates as herbal medicines for herpes virus, echovirus and adenovirus infectious diseases. All extracts had no cytotoxic effect on Vero cells at all tested concentrations.     

分子内结构环境对解离能的影响

为了理解化学键的这一结构效应, 本文对具有相同化学键而分子内结构环境不同的系列分子进行了计算研究, 讨论了化学键结构环境对解离能的影响.