The method originally proposed by Yu et al. [Opt. Lett. 23, 409 (1998)] for evaluating the zero-order Hankel transform is generalized to high-order Hankel transforms. Since the method preserves the discrete form of the Parseval theorem, it is particularly suitable for field propagation. A general algorithm for propagating an input field through axially symmetric systems using the generalized me...

—Pointwise-supported generalised wavelets are introduced, based on Dirac, doublet and further derivatives of (t). A generalised biorthogonal analysis leads to standard Taylor series and new Dual-Taylor series that may be interpreted as Laurent Schwartz distributions. A Parseval-like identity is also derived for Taylor series, showing that Taylor series support an energy theorem. New representa...

A better parser combination approach is proposed in this paper to combine the n-best outputs of individual parsers for higher performance. Under the constituent weighting and reparsing framework, we propose a constrained constituent recombination method to address the ”flat tree” problem of traditional constituent recombination. The better combination parser generated four runs ranked the top N...

Gabor system plays an important role in signal processing, image processing and other applications because of their redundancy properties. In this paper, symmetric or antisymmetric Gabor frames in two dimensions about any symmetric points are constructed from Gabor frames given. In special, symmetric or antisymmetric Parseval Gabor frames with better properties are obtained. Some thoughts of ex...

This paper presents our work for participation in the 2009 CIPS-Parseval shared task on Chinese syntactic tree parsing, for which we adopt a general PCFG parsing procedure with a conditional random fields (CRF) tagger for head constituent recognition. Our experiments show that an acceptable tagging result is obtained on the basis of a standard PCFG parsing output and a further evaluation on oth...

The problem of representation and analysis of functions defined on manifolds (signals, images, and data in general) is ubiquities in many fields ranging from statistics and cosmology to neuroscience and biology. It is very common to consider input signals as points in a high-dimensional measurement space, however, meaningful structures lay on a manifold embedded in this space. In the last decad...

Frames have turned out to be an essential tool for many applications such as, for example, data transmission, due to their robustness not only against noise but also against losses and due to their freedom in design [4, 6]. Their main advantage lies in the fact that a frame can be designed to be redundant while still providing a reconstruction formula. Since the frame operator Sg = ∑n i=1 〈g, f...

Abstract In this paper, we introduce the two-sided fractional quaternion Fourier transform (FrQFT) and give some properties of it. The main results paper are divided into three parts. Firstly a definition FrQFT. Secondly based on QFT, study relationship between QFT FrQFT, differential FrQFT Parseval identity. Finally, an example to illustrate application its inverse in solving partial equations.