Subwavelength grating coupler

A method, system or device for configuring an optical coupling device including obtaining characteristics of an optical signal and ambient conditions for storage in memory, utilizing a processor for identifying an optimum effective subwavelength area refractive index and a grating period for the input signal and ambient characteristics stored in memory, and utilizing the processor for identifying a preferred filling factor for a transverse polarization.Board of Regents, University of Texas Syste

Non-integrable stable approximation by Stein's method

We develop Stein's method for $\alpha$-stable approximation with $\alpha\in(0,1]$, continuing the recent line of research by Xu \cite{lihu} and Chen, Nourdin and Xu \cite{C-N-X} in the case $\alpha\in(1,2).$ The main results include an intrinsic upper bound for the error of the approximation in a variant of Wasserstein distance that involves the characterizing differential operators for stable distributions, and an application to the generalized central limit theorem. Due to the lack of first moment for the approximating sequence in the latter result, we appeal to an additional truncation procedure and investigate fine regularity properties of the solution to Stein's equation

Introduction and Suggestions on the Chinese Securities Credit Rating System from a Comparative Perspective

Credit rating is a burgeoning industry in China. However, ever since it was established by State Council in 1993, the development of the industry has faced various impediments. There are currently three major problems hindering its further development, as result of a lack of systematic statutory and judicial guidelines. These problems are: limited competition in the industry, rampant rating shopping and conflicts of interest, and limited remedy in a suit against false ratings. The rating industry in China has followed a different pattern. The statutory threshold requirement has proven too demanding for most rating agencies to comply with, barring many potential participants from the market. In addition, provisions prohibiting rating shopping and regulating conflicts of interest are narrowly drawn, targeting only direct conflicts of interest. While freedom of speech remains an invalid defense, judges\u27 reluctance to recognize substantial intangible harm combined with an insufficient judicial framework together make it hard for plaintiffs to prevail in lawsuits against false ratings

Multivariate stable approximation in Wasserstein distance by Stein's method

We investigate regularity properties of the solution to Stein's equation associated with multivariate integrable $\alpha$-stable distribution for a general class of spectral measures and Lipschitz test functions. The obtained estimates induce an upper bound in Wasserstein distance for the multivariate $\alpha$-stable approximation