Quasi-Whittaker modules for the Schr\"odinger algebra

In this paper, we construct a new class of modules for the Schr\"{o}dinger algebra \mS, called quasi-Whittaker module. Different from \cite{[ZC]}, the quasi-Whittaker module is not induced by the Borel subalgebra of the Schr\"{o}dinger algebra related with the triangular decomposition, but its Heisenberg subalgebra \mH. We prove that, for a simple \mS-module $V$, $V$ is a quasi-Whittaker module if and only if $V$ is a locally finite \mH-module; Furthermore, we classify the simple quasi-Whittaker modules by the elements with the action similar to the center elements in U(\mS) and their quasi-Whittaker vectors. Finally, we characterize arbitrary quasi-Whittaker modules.Comment: 17 page

A Robust Estimator of Image Thumbnail and Video Histogram Representation

For browsing and retrieval system, images are represented by thumbnails and video shots are represented by content representations. In order to achieve better visual quality and retrieval performance, the representation estimator is expected to be accurate and robust. From the statistical perspective, representation extraction can be treated as central value estimation. In this paper, we propose an adaptive alpha-trimmed average estimator based on Gaussian distribution hypothesis test (AATA-GDHT). For a set of values, this estimator extracts the representation by trimming extreme values and then averaging the rest. The criterion to distinguish between extreme values and useful data is derived from Gaussian distribution hypothesis test on the basis of global statics. Experimental results from standard images and videos show that our proposed scheme outperforms traditional methods.For the browsing and retrieval system, images are represented by thumbnails and video shots are represented by histogram representations. In order to achieve better visual quality and retrieval performance, the representation estimator is expected to be accurate and robust. From the statistical perspective, representation extraction can be treated as central value estimation. In this paper, we propose an adaptive alpha-trimmed average estimator based on the Gaussian distribution hypothesis test. For a set of values, this estimator extracts the representation by trimming extreme values and then averaging the rest. The criterion adopted to distinguish between extreme values and useful data is derived from the Gaussian distribution hypothesis test on the basis of global statics. Experimental results from standard images and videos show that our proposed scheme outperforms traditional methods