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Xu A.,Zhejiang Wanli University
Electronic Journal of Combinatorics | Year: 2014

In this paper, by means of the q-Rice formula we obtain a general q-identity which is a unified generalization of three kinds of identities. Some known results are special cases of ours. Meanwhile, some identities on q-generalized harmonic numbers are also derived.

Xu Y.-F.,Zhejiang Wanli University
Communications in Theoretical Physics | Year: 2012

For the (2+1)-Dimensional HNLS equation, what are the dynamical behavior of its traveling wave solutions and how do they depend on the parameters of the systems? This paper will answer these questions by using the methods of dynamical systems. Ten exact explicit parametric representations of the traveling wave solutions are given. © 2012 Chinese Physical Society and IOP Publishing Ltd.

Fang Z.,Zhejiang Wanli University | Wang X.,Fudan University | Yuan X.,Chinese University of Hong Kong
IEEE Transactions on Signal Processing | Year: 2013

In this paper, we develop a unified framework for beamforming designs in non-regenerative multiuser two-way relaying (TWR). The core of our framework is the solution to the max-min signal-to-interference-plus-noise-ratio (SINR) problem for multiuser TWR. We solve this problem using a Dinkelbach-type algorithm with near-optimal performance and superlinear convergence. We show that, using the max-min SINR solution as a corner stone, the beamforming designs under various important criteria, such as weighted sum-rate maximization, weighted sum mean-square-error (MSE) minimization, and average bit-error-rate (BER) or symbol-error-rate (SER) minimization, etc, can be reformulated into a monotonic program. A polyblock outer approximation algorithm is then used to find the desired solutions with guaranteed convergence and optimal performance (provided that the core max-min SINR solver is optimal). Furthermore, the proposed unified approach can provide important insights for tackling the optimal beamforming designs in other emerging network models and settings. For instances, we extend the proposed framework to address the beamforming design in collaborative TWR and multi-pair MIMO TWR. Extensive numerical results are presented to demonstrate the merits of the proposed beamforming solutions. © 1991-2012 IEEE.

Zeng S.,Zhejiang GongShang University | Zeng S.,Zhejiang Wanli University | Su W.,Zhejiang GongShang University
Knowledge-Based Systems | Year: 2011

The ordered weighted distance [27,49] is a new decision-making technique, having been proved useful for the treatment of input data in the form of exact numbers. In this paper, we consider the situation with intuitionistic fuzzy information and develop an intuitionistic fuzzy ordered weighted distance (IFOWD) operator. The IFOWD operator is very suitable to deal with the situations where the input data are represented in intuitionistic fuzzy information and includes a wide range of distance measures and aggregation operators. We study some of its main properties and different families of IFOWD operators. Finally, we develop an application of the new approach in a group decision-making under intuitionistic fuzzy environment and illustrate it with a numerical example. © 2011 Elsevier B.V. All rights reserved.

Chen L.,National University of Singapore | Xu A.,Zhejiang Wanli University | Zhu H.,National University of Singapore
Physical Review A - Atomic, Molecular, and Optical Physics | Year: 2010

We provide methods for computing the geometric measure of entanglement for two families of pure states with both experimental and theoretical interests: symmetric multiqubit states with non-negative amplitudes in the Dicke basis and symmetric three-qubit states. In addition, we study the geometric measure of pure three-qubit states systematically in virtue of a canonical form of their two-qubit reduced states and derive analytical formulas for a three-parameter family of three-qubit states. Based on this result, we further show that the W state is the maximally entangled three-qubit state with respect to the geometric measure. © 2010 The American Physical Society.

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