Gravitational Lensing Statistics as a Probe of Dark Energy

By using the comoving distance, we derive an analytic expression for the optical depth of gravitational lensing, which depends on the redshift to the source and the cosmological model characterized by the cosmic mass density parameter $\Omega_m$, the dark energy density parameter $\Omega_x$ and its equation of state $\omega_x = p_x/\rho_x$. It is shown that, the larger the dark energy density is and the more negative its pressure is, the higher the gravitational lensing probability is. This fact can provide an independent constraint for dark energy.Comment: 9 pages, 2 figure

Learning distance to subspace for the nearest subspace methods in high-dimensional data classification

The nearest subspace methods (NSM) are a category of classification methods widely applied to classify high-dimensional data. In this paper, we propose to improve the classification performance of NSM through learning tailored distance metrics from samples to class subspaces. The learned distance metric is termed as ‘learned distance to subspace’ (LD2S). Using LD2S in the classification rule of NSM can make the samples closer to their correct class subspaces while farther away from their wrong class subspaces. In this way, the classification task becomes easier and the classification performance of NSM can be improved. The superior classification performance of using LD2S for NSM is demonstrated on three real-world high-dimensional spectral datasets

Crystals for high-energy calorimetry in extreme environments

Crystals are used as a homogeneous calorimetric medium in many high-energy physics experiments. For some experiments, performance has to be ensured in very difficult operating conditions, like a high radiation environment, very large particle fluxes, high collision rates, placing constraints on response and readout time. An overview is presented of recent achievements in the field, with particular attention given to the performance of Lead Tungstate (PWO) crystals exposed to high particle fluxes.Comment: To be published in Proc. of the Meeting of the Division of Particles and Fields of the American Physical Society, DPF2004 (Riverside, USA, August 26th to 31st, 2004

Gravitational lensing statistical properties in general FRW cosmologies with dark energy component(s): analytic results

Various astronomical observations have been consistently making a strong case for the existence of a component of dark energy with negative pressure in the universe. It is now necessary to take the dark energy component(s) into account in gravitational lensing statistics and other cosmological tests. By using the comoving distance we derive analytic but simple expressions for the optical depth of multiple image, the expected value of image separation and the probability distribution of image separation caused by an assemble of singular isothermal spheres in general FRW cosmological models with dark energy component(s). We also present the kinematical and dynamical properties of these kinds of cosmological models and calculate the age of the universe and the distance measures, which are often used in classical cosmological tests. In some cases we are able to give formulae that are simpler than those found elsewhere in the literature, which could make the cosmological tests for dark energy component(s) more convenient.Comment: 14 pages, no figure, Latex fil

Integration of twisted Dirac brackets

The correspondence between Poisson structures and symplectic groupoids, analogous to the one of Lie algebras and Lie groups, plays an important role in Poisson geometry; it offers, in particular, a unifying framework for the study of hamiltonian and Poisson actions. In this paper, we extend this correspondence to the context of Dirac structures twisted by a closed 3-form. More generally, given a Lie groupoid $G$ over a manifold $M$, we show that multiplicative 2-forms on $G$ relatively closed with respect to a closed 3-form $\phi$ on $M$ correspond to maps from the Lie algebroid of $G$ into the cotangent bundle $T^*M$ of $M$, satisfying an algebraic condition and a differential condition with respect to the $\phi$-twisted Courant bracket. This correspondence describes, as a special case, the global objects associated to twisted Dirac structures. As applications, we relate our results to equivariant cohomology and foliation theory, and we give a new description of quasi-hamiltonian spaces and group-valued momentum maps.Comment: 42 pages. Minor changes, typos corrected. Revised version to appear in Duke Math.

Superconductivity in Ti-doped Iron-Arsenide Compound Sr4Cr0.8Ti1.2O6Fe2As2

Superconductivity was achieved in Ti-doped iron-arsenide compound Sr4Cr0.8Ti1.2O6Fe2As2 (abbreviated as Cr-FeAs-42622). The x-ray diffraction measurement shows that this material has a layered structure with the space group of \emph{P4/nmm}, and with the lattice constants a = b = 3.9003 A and c = 15.8376 A. Clear diamagnetic signals in ac susceptibility data and zero-resistance in resistivity data were detected at about 6 K, confirming the occurrence of bulk superconductivity. Meanwhile we observed a superconducting transition in the resistive data with the onset transition temperature at 29.2 K, which may be induced by the nonuniform distribution of the Cr/Ti content in the FeAs-42622 phase, or due to some other minority phase.Comment: 3 pages, 3 figure