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	1. $K(lowercase{m,n})$ Equations with Fifth Order Symmetries and Their Integrability
	Kai Tian
	Mathematics 09 May 2016
	Show/Hide Abstract \| Cite this paper︱Full-text: PDF (0 B)

	Abstract:For a third order equation involving two parameters, first introduced by Rosenau and Hyman, all cases admitting fifth order symmetries are identified. Bi-Hamiltonian structures of five less studied cases are established through their invertible links with some famous integrable equations. Therefore, all cases, having fifth order symmetries, of Rosenau and Hyman's equation are integrable in the bi-Hamiltonian sense. As an interesting observation, their Hamiltonian operators are linearly combinations of basic ingredients in the bi-Hamiltonian theory of Korteweg-de Vries and modified Korteweg-de Vries equations.
	TO cite this article:Kai Tian. $K(lowercase{m,n})$ Equations with Fifth Order Symmetries and Their Integrability[OL].[ 9 May 2016] http://en.paper.edu.cn/en_releasepaper/content/4688351


	2. A comparison of two conjugate direction methods, with applications to Markov chains
	WEN Chun,HUANG Tingzhu
	Mathematics 06 July 2013
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	Abstract:Motivated by the celebrated extending applications of the conjugateresidual method to nonsymmetric linear systems by Sogabe, Sugiharaand Zhang [An extension of the conjugate residual method tononsymmetric linear systems [J]. J. Comput. Appl. Math., 266:103-113, 2009],this paper describes two conjugate directionmethods, Bi-CR and Bi-CG, and attempts to extend their applicationsto compute the stationary probability distribution for anirreducible Markov chain. Numerical experiments show the feasibilityof the Bi-CR and Bi-CG methods to some extent, with applications toseveral practical Markov chain problems.
	TO cite this article:WEN Chun,HUANG Tingzhu. A comparison of two conjugate direction methods, with applications to Markov chains[OL].[ 6 July 2013] http://en.paper.edu.cn/en_releasepaper/content/4550973


	3. A Nonlocal Variational Inequality and Related Free Boundary arising from PricingRetirement Benefits
	BIAN Baojun,YUAN Quan
	Mathematics 06 January 2013
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	Abstract:This paper is concerned with a nonlocal parabolicvariational inequality which arises from the financial valuation of defined benefits retirement pension plan that allows early retirement.The paid benefits on retirement dependon the salary at that time.The underlying salary is assumed to follow a jump-diffusion process.We characterize the financial value of the retirementbenefits as the solution of anoptimal stopping time problem, which corresponds to a variationalinequality or a free boundary problem of an integro-differentialoperator of the parabolic type. The existence and uniqueness of the solutionto the variational inequality are proved and the properties for related free boundary are discussed.
	TO cite this article:BIAN Baojun,YUAN Quan. A Nonlocal Variational Inequality and Related Free Boundary arising from PricingRetirement Benefits[OL].[ 6 January 2013] http://en.paper.edu.cn/en_releasepaper/content/4511964


	4. Quasi-periodic solutions of the Lotka-Volterra Competition Systems with Quasi-periodic Perturbations
	Qihuai Liu,Dingbian Qian,Zhiguo Wang
	Mathematics 04 January 2011
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	Abstract:In this paper, we prove the existence of positive quasi-periodic solutions for the Lotka-Volterra competition systems with quasi-periodic coefficients by KAM technique. The result shows that, in most case, quasi-periodic solutions exist for sufficiently small quasi-periodic perturbations of the autonomous Lotka-Volterra systems. Moreover, these quasi-periodic solutions will tend to an equilibrium of the autonomous Lotka-Volterra.
	TO cite this article:Qihuai Liu,Dingbian Qian,Zhiguo Wang. Quasi-periodic solutions of the Lotka-Volterra Competition Systems with Quasi-periodic Perturbations[OL].[ 4 January 2011] http://en.paper.edu.cn/en_releasepaper/content/4403702


	5. Incremental Learning of Bidirectional Principal Components for Face Recognition
	Ren ChuanXian,Dai DaoQing
	Mathematics 25 June 2009
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	Abstract:Recently, bidirectional PCA(BDPCA) has been proven to be an e眂ient tool for pattern recognition and image analysis. Encouraging experimental results have been reported and discussed in the literature. However, BDPCA has to be performed in batch mode, it means that all the training data has to be ready before we calculate the projection matrices. If there are additional samples need to be incorporated into an existing system, it has to be retrained with the whole updated training set. Moreover, the scatter matrices of BDPCA are formulated as the sum of K(samples size) image covariance matrices, this leads to the incremental learning directly on the scatters impossible, thus it presents new challenge for on-line training. In fact, there are two major reasons for building incremental algorithms. The 痳st reason is that in some cases, when the number of training images is very large, the batch algorithm can not process the entire training set due to large computational or space requirements of the batch approach. The second reason is when the learning algorithm is supposed to operate in a dynamical settings, that all the training data is not given in advance, and new training samples may arrive at any time, and they have to be processed in an online manner. Through matricizations of 3th-order tensor, we successfully transfer the eigenvalue decomposition problem of scatters to the SVD of corresponding unfolded matrices, followed by complexity and memory analysis on the novel algorithm. A theoretical clue for selecting suitable dimensionality parameters without losing classi痗ation information is also presented in this paper. Experimental results on FERET and CMU PIE databases show that the IBDPCA algorithm gives a close approximation to the BDPCA method, but using less time.
	TO cite this article:Ren ChuanXian,Dai DaoQing. Incremental Learning of Bidirectional Principal Components for Face Recognition[J].Pattern Recognition ，2010，43(1):318 ~330

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