On the CR transversality of holomorphic maps into hyperquadrics

Let $M_\ell$ be a smooth Levi-nondegenerate hypersurface of signature $\ell$ in $\mathbf C^n$ with $n\ge 3$, and write $H_\ell^N$ for the standard hyperquadric of the same signature in $\mathbf C^N$ with $N-n< \frac{n-1}{2}$. Let $F$ be a holomorphic map sending $M_\ell$ into $H_\ell^N$. Assume $F$ does not send a neighborhood of $M_\ell$ in $\mathbf C^n$ into $H_\ell^N$. We show that $F$ is necessarily CR transversal to $M_\ell$ at any point. Equivalently, we show that $F$ is a local CR embedding from $M_\ell$ into $H_\ell^N$.Comment: To appear in Abel Symposia, dedicated to Professor Yum-Tong Siu on the occasion of his 70th birthda

Delay-dependent exponential stability of neutral stochastic delay systems

This paper studies stability of neutral stochastic delay systems by linear matrix inequality (LMI) approach. Delay dependent criterion for exponential stability is presented and numerical examples are conducted to verify the effectiveness of the proposed method

Robust Detection of Moving Human Target in Foliage-Penetration Environment Based on Hough Transform

Attention has been focused on the robust moving human target detection in foliage-penetration environment, which presents a formidable task in a radar system because foliage is a rich scattering environment with complex multipath propagation and time-varying clutter. Generally, multiple-bounce returns and clutter are additionally superposed to direct-scatter echoes. They obscure true target echo and lead to poor visual quality time-range image, making target detection particular difficult. Consequently, an innovative approach is proposed to suppress clutter and mitigate multipath effects. In particular, a clutter suppression technique based on range alignment is firstly applied to suppress the time-varying clutter and the instable antenna coupling. Then entropy weighted coherent integration (EWCI) algorithm is adopted to mitigate the multipath effects. In consequence, the proposed method effectively reduces the clutter and ghosting artifacts considerably. Based on the high visual quality image, the target trajectory is detected robustly and the radial velocity is estimated accurately with the Hough transform (HT). Real data used in the experimental results are provided to verify the proposed method