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

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

Robust variable selection in partially varying coefficient single-index model

By combining basis function approximations and smoothly clipped absolute deviation (SCAD) penalty, this paper proposes a robust variable selection procedure for a partially varying coefficient single-index model based on modal regression. The proposed procedure simultaneously selects significant variables in the parametric components and the nonparametric components. With appropriate selection of the tuning parameters, we establish the theoretical properties of our procedure, including consistency in variable selection and the oracle property in estimation. Furthermore, we also discuss the bandwidth selection and propose a modified expectation-maximization (EM)-type algorithm for the proposed estimation procedure. The finite sample properties of the proposed estimators are illustrated by some simulation examples.The research of Zhu is partially supported by National Natural Science Foundation of China (NNSFC) under Grants 71171075, 71221001 and 71031004. The research of Yu is supported by NNSFC under Grant 11261048

Tackling Challenges in Seebeck Coefficient Measurement of Ultra-High Resistance Samples with an AC Technique

Seebeck coefficient is a widely studied semiconductor property. Conventional Seebeck coefficient measurements are based on DC voltage measurement. Normally this is performed on samples with moderate resistances (e.g., below a few MΩ level). Certain semiconductors are intrinsic and highly resistive. Many examples can be found in optical and photovoltaic materials. The hybrid halide perovskites that have gained extensive attention recently are a good example. Despite great attention from the materials and physics communities, few successful studies exist of the Seebeck coefficient of these compounds, for example CH3NH3PbI3. An AC-technique-based Seebeck coefficient measurement is reported, which makes high-quality Seebeck voltage measurements on samples with resistances up to the 100 GΩ level. This is achieved through a specifically designed setup to enhance sample isolation and increase capacitive impedance. As a demonstration, Seebeck coefficient measurement of a CH3NH3PbI3 thin film is performed at dark, with sample resistance 150 GΩ, and found S = +550 µV K−1. The strategy reported could be applied to the studies of fundamental transport parameters of all intrinsic semiconductors that have not been feasible