Specifying angular momentum and center of mass for vacuum initial data sets

We show that it is possible to perturb arbitrary vacuum asymptotically flat spacetimes to new ones having exactly the same energy and linear momentum, but with center of mass and angular momentum equal to any preassigned values measured with respect to a fixed affine frame at infinity. This is in contrast to the axisymmetric situation where a bound on the angular momentum by the mass has been shown to hold for black hole solutions. Our construction involves changing the solution at the linear level in a shell near infinity, and perturbing to impose the vacuum constraint equations. The procedure involves the perturbation correction of an approximate solution which is given explicitly.Comment: (v2) a minor change in the introduction and a remark added after Theorem 2.1; (v3) final version, appeared in Comm. Math. Phy

SafeWeb: A Middleware for Securing Ruby-Based Web Applications

Web applications in many domains such as healthcare and finance must process sensitive data, while complying with legal policies regarding the release of different classes of data to different parties. Currently, software bugs may lead to irreversible disclosure of confidential data in multi-tier web applications. An open challenge is how developers can guarantee these web applications only ever release sensitive data to authorised users without costly, recurring security audits. Our solution is to provide a trusted middleware that acts as a “safety net” to event-based enterprise web applications by preventing harmful data disclosure before it happens. We describe the design and implementation of SafeWeb, a Ruby-based middleware that associates data with security labels and transparently tracks their propagation at different granularities across a multi-tier web architecture with storage and complex event processing. For efficiency, maintainability and ease-of-use, SafeWeb exploits the dynamic features of the Ruby programming language to achieve label propagation and data flow enforcement. We evaluate SafeWeb by reporting our experience of implementing a web-based cancer treatment application and deploying it as part of the UK National Health Service (NHS)

Study of the Anti-Proliferative Activity of 5-Substituted 4,7-Dimethoxy-1,3-Benzodioxole Derivatives of SY-1 from Antrodia camphorata on Human COLO 205 Colon Cancer Cells

A set of 10 4,7-dimethoxy-1,3-benzodioxole derivatives based on a lead compound previously discovered by our group, SY-1, which was isolated from Antrodia camphorata, were evaluated for their in vitro inhibitory activity on human colorectal carcinoma cells (COLO 205). Structure-activity relationship studies of the 10 compounds indicated the importance of the chain length of the alkyl group at the 5-position, and the 2-propenyl substituent named “apiole” exhibited the most potent inhibitory activity. In the present study, we demonstrate that the SY-1 analogue “apiole” decreased the proliferation of COLO 205 cells, but not that of normal human colonic epithelial cells (FHC). The G0/G1 cell cycle arrest induced by apiole (75–225 μM) was associated with significantly increased levels of p53, p21 and p27 and decreased levels of cyclin D1. Concerning COLO 205 cell apoptosis, apiole (>150 μM) treatment significantly increased the levels of cleaved caspases 3, 8, 9 and bax/bcl-2 ratio and induced ladder formation in DNA fragmentation assay and sub-G1 peak in flow cytometry analysis. These findings suggest that apiole can suppress COLO 205 cell growth; however, the detailed mechanisms of these processes require further investigation

Critical Exponents of the Statistical Multifragmentation Model

For the statistical multifragmentation model the critical indices $\alpha^\prime, \beta, \gamma^\prime, \delta$ are calculated as functions of the Fisher parameter $\tau$. It is found that these indices have different values than in Fisher's droplet model. Some peculiarities of the scaling relations are discussed. The basic model predicts for the index $\tau$ a narrow range of values, $1.799< \tau < 1.846$, which is consistent with two experiments on nuclear multifragmentation.Comment: minor changes of the text, four references adde

Deformations of the hemisphere that increase scalar curvature

Consider a compact Riemannian manifold M of dimension n whose boundary \partial M is totally geodesic and is isometric to the standard sphere S^{n-1}. A natural conjecture of Min-Oo asserts that if the scalar curvature of M is at least n(n-1), then M is isometric to the hemisphere S_+^n equipped with its standard metric. This conjecture is inspired by the positive mass theorem in general relativity, and has been verified in many special cases. In this paper, we construct counterexamples to Min-Oo's conjecture in dimension n \geq 3.Comment: Revised version, to appear in Invent. Mat

A New Relativistic High Temperature Bose-Einstein Condensation

We discuss the properties of an ideal relativistic gas of events possessing Bose-Einstein statistics. We find that the mass spectrum of such a system is bounded by $\mu \leq m\leq 2M/\mu _K,$ where $\mu$ is the usual chemical potential, $M$ is an intrinsic dimensional scale parameter for the motion of an event in space-time, and $\mu _K$ is an additional mass potential of the ensemble. For the system including both particles and antiparticles, with nonzero chemical potential $\mu ,$ the mass spectrum is shown to be bounded by $|\mu |\leq m\leq 2M/\mu _K,$ and a special type of high-temperature Bose-Einstein condensation can occur. We study this Bose-Einstein condensation, and show that it corresponds to a phase transition from the sector of continuous relativistic mass distributions to a sector in which the boson mass distribution becomes sharp at a definite mass $M/\mu _K.$ This phenomenon provides a mechanism for the mass distribution of the particles to be sharp at some definite value.Comment: Latex, 22 page

Thermodynamic Description of the Relaxation of Two-Dimensional Euler Turbulence Using Tsallis Statistics

Euler turbulence has been experimentally observed to relax to a metaequilibrium state that does not maximize the Boltzmann entropy, but rather seems to minimize enstrophy. We show that a recent generalization of thermodynamics and statistics due to Tsallis is capable of explaining this phenomenon in a natural way. The maximization of the generalized entropy $S_{1/2}$ for this system leads to precisely the same profiles predicted by the Restricted Minimum Enstrophy theory of Huang and Driscoll. This makes possible the construction of a comprehensive thermodynamic description of Euler turbulence.Comment: 15 pages, RevTe

Static black holes with a negative cosmological constant: Deformed horizon and anti-de Sitter boundaries

Using perturbative techniques, we investigate the existence and properties of a new static solution for the Einstein equation with a negative cosmological constant, which we call the deformed black hole. We derive a solution for a static and axisymmetric perturbation of the Schwarzschild-anti-de Sitter black hole that is regular in the range from the horizon to spacelike infinity. The key result is that this perturbation simultaneously deforms the two boundary surfaces--i.e., both the horizon and spacelike two-surface at infinity. Then we discuss the Abbott-Deser mass and the Ashtekar-Magnon one for the deformed black hole, and according to the Ashtekar-Magnon definition, we construct the thermodynamic first law of the deformed black hole. The first law has a correction term which can be interpreted as the work term that is necessary for the deformation of the boundary surfaces. Because the work term is negative, the horizon area of the deformed black hole becomes larger than that of the Schwarzschild-anti-de Sitter black hole, if compared under the same mass, indicating that the quasistatic deformation of the Schwarzschild-anti-de Sitter black hole may be compatible with the thermodynamic second law (i.e., the area theorem).Comment: 31 pages, 5 figures, one reference added, to be published in PR

How does the substrate affect the Raman and excited state spectra of a carbon nanotube?

We study the optical properties of a single, semiconducting single-walled carbon nanotube (CNT) that is partially suspended across a trench and partially supported by a SiO2-substrate. By tuning the laser excitation energy across the E33 excitonic resonance of the suspended CNT segment, the scattering intensities of the principal Raman transitions, the radial breathing mode (RBM), the G-mode and the D-mode show strong resonance enhancement of up to three orders of magnitude. In the supported part of the CNT, despite a loss of Raman scattering intensity of up to two orders of magnitude, we recover the E33 excitonic resonance suffering a substrate-induced red shift of 50 meV. The peak intensity ratio between G-band and D-band is highly sensitive to the presence of the substrate and varies by one order of magnitude, demonstrating the much higher defect density in the supported CNT segments. By comparing the E33 resonance spectra measured by Raman excitation spectroscopy and photoluminescence (PL) excitation spectroscopy in the suspended CNT segment, we observe that the peak energy in the PL excitation spectrum is red-shifted by 40 meV. This shift is associated with the energy difference between the localized exciton dominating the PL excitation spectrum and the free exciton giving rise to the Raman excitation spectrum. High-resolution Raman spectra reveal substrate-induced symmetry breaking, as evidenced by the appearance of additional peaks in the strongly broadened Raman G band. Laser-induced line shifts of RBM and G band measured on the suspended CNT segment are both linear as a function of the laser excitation power. Stokes/anti-Stokes measurements, however, reveal an increase of the G phonon population while the RBM phonon population is rather independent of the laser excitation power.Comment: Revised manuscript, 20 pages, 8 figure

Tunable local polariton modes in semiconductors

We study the local states within the polariton bandgap that arise due to deep defect centers with strong electron-phonon coupling. Electron transitions involving deep levels may result in alteration of local elastic constants. In this case, substantial reversible transformations of the impurity polariton density of states occur, which include the appearance/disappearance of the polariton impurity band, its shift and/or the modification of its shape. These changes can be induced by thermo- and photo-excitation of the localized electron states or by trapping of injected charge carriers. We develop a simple model, which is applied to the $O_P$ center in $GaP$. Further possible experimental realizations of the effect are discussed.Comment: 7 pages, 3 figure