Abstract:Boolean functions with large algebraic immunity can resist algebraic attacks to a certain degree, but may not resist fast algebraic attacks. In order to study general resistance of Boolean functions against fast algebraic attacks, the concept of e-fast algebraic immunity ( e-FAI) for n-variable Boolean functions is introduced, where e is a positive integer and 1=<e<n/2p. f is called an n-variable Boolean function with e-FAI if deg(fg)>=n-e holds for any nonzero n-variable Boolean function g with deg(g)=<e. A Boolean function have the optimal resistance against fast algebraic attacks if it has e-FAI for every e(1=<e<n/2p) . The relation between algebraic immunity and e-FAI is discussed and the sufficient and necessary condition of e-FAI is obtained. A class of Boolean functions with 1-FAI is constructed and an algorithm for deciding e-FAI is described. When deciding the optimal resistance against fast algebraic attacks of Boolean functions, this algorithm has better computation complexity compared with the algorithm given by Armknecht et al.

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	1. On Resistance of Boolean Functions to Fast Algebraic Attacks
	Du Yusong ,Pei Dingyi
	Mathematics 24 November 2010
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	Abstract:Boolean functions with large algebraic immunity can resist algebraic attacks to a certain degree, but may not resist fast algebraic attacks. In order to study general resistance of Boolean functions against fast algebraic attacks, the concept of e-fast algebraic immunity ( e-FAI) for n-variable Boolean functions is introduced, where e is a positive integer and 1=<e<n/2p. f is called an n-variable Boolean function with e-FAI if deg(fg)>=n-e holds for any nonzero n-variable Boolean function g with deg(g)=<e. A Boolean function have the optimal resistance against fast algebraic attacks if it has e-FAI for every e(1=<e<n/2p) . The relation between algebraic immunity and e-FAI is discussed and the sufficient and necessary condition of e-FAI is obtained. A class of Boolean functions with 1-FAI is constructed and an algorithm for deciding e-FAI is described. When deciding the optimal resistance against fast algebraic attacks of Boolean functions, this algorithm has better computation complexity compared with the algorithm given by Armknecht et al.
	TO cite this article:Du Yusong ,Pei Dingyi . On Resistance of Boolean Functions to Fast Algebraic Attacks[OL].[24 November 2010] http://en.paper.edu.cn/en_releasepaper/content/4392966


	2. Regularity of Keldys-Fichera Boundary Value Problem for Degenerate Elliptic Equations
	Limei Li,Tian Ma
	Mathematics 08 January 2010
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	Abstract:In this paper, we discuss the W1;p-solutions and the interior regularity of weak solutions for the Keldys-Fichera boundary value problem using the acute angle principle and the reversed H╫lder inequality, the generalized poinc碼re inequalities.
	TO cite this article:Limei Li,Tian Ma. Regularity of Keldys-Fichera Boundary Value Problem for Degenerate Elliptic Equations[OL].[ 8 January 2010] http://en.paper.edu.cn/en_releasepaper/content/38705

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	3. Symbolic Computation for Parametrized Wavelets in SAGE
	Wang Le
	Mathematics 17 December 2009
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	Abstract:In this paper, author mainly discusses parametrizing filter coefficients for wavelets in the open-source computer algebra system SAGE. We first recall the general ideas of wavelets construction and then we discuss how to solve wavelet design problems by using symbolic methods, in particular Groebner bases, for compactly supported orthonormal wavelets. Second, We make a brief review of the ideas of Regensburger and Scherzer for parametrizing compactly supported orthonormal wavelets by discrete moments and introduce the parametrization procedures for orthonormal wavelets with the corresponding functions defined in SAGE and analyze the solutions by using different reduction order during the symbolic computation. Complete solutions and analysis for parametrized filter coefficients of length eight in the orthonormal case are presented.
	TO cite this article:Wang Le. Symbolic Computation for Parametrized Wavelets in SAGE[OL].[17 December 2009] http://en.paper.edu.cn/en_releasepaper/content/37659


	4. Relative perturbation bounds for weighted polar decomposition
	Hanyu Li,Hu yang
	Mathematics 07 August 2009
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	Abstract:In this paper, we obtain the relative perturbation bounds for weighted unitary polar factor of the weighted polar decomposition in the weighted unitarily invariant norm, weighted spectral norm, and weighted Frobenius norm, respectively. As the special cases, we also derive the new bounds for subunitary and unitary polar factors of (generalized) polar decomposition. These special bounds improve the recent corresponding results to some extent.
	TO cite this article:Hanyu Li,Hu yang. Relative perturbation bounds for weighted polar decomposition[J].


	5. Relative perturbation bounds for generalized nonnegative and positive polar factors
	Hanyu Li,Hu Yang,Hua Shao
	Mathematics 07 August 2009
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	Abstract:The changes in the generalized nonnegative and positive polar factors of weighted polar decomposition are studied under the additive perturbation. Some relative perturbation bounds are obtained. In particular, the corresponding perturbation bounds for nonnegative and positive polar factors are also presented. These new bounds are different from previous ones in measure of perturbation.
	TO cite this article:Hanyu Li,Hu Yang,Hua Shao. Relative perturbation bounds for generalized nonnegative and positive polar factors[J].


	6. 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


	7. H∞ CONTROLLER DESIGN FOR NETWORKED CONTROL
	Wang Jihua
	Mathematics 26 May 2009
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	Abstract:A novel discrete time model is proposed for networked control system (NCS) which converts the uncertainty of time-delay into the uncertainty of the parameter matrix. Based on Lyapunov stability theory and LMI approach, we provide a sufficient condition to the asymptotical stability of NCS without disturbance and design a state feedback controller which stabilizes the system. For the NCS with disturbance, we point out a sufficient condition ensuring the system meeting prescribed H∞ performance gamma and a state feedback controller ensuring the system meeting optimal performance index. Numerical examples are given to illustrate the effectiveness of our results via TrueTime toolbox.
	TO cite this article:Wang Jihua. H∞ CONTROLLER DESIGN FOR NETWORKED CONTROL[OL].[26 May 2009] http://en.paper.edu.cn/en_releasepaper/content/32552


	8. Robust State Estimation for Neural Networks with Discontinuous Activations
	xiaoyang liu,jinde cao
	Mathematics 24 April 2009
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	Abstract:Discontinuous dynamical systems, especially neural networks with discontinuous activation functions, arise in a number of applications and have received considerable research attention in recent years. In this paper, the robust state estimation problem is investigated for uncertain neural networks with discontinuous activations and time-varying delay, where the neuron-dependent nonlinear disturbance on the network outputs are only assumed to satisfy the local Lipschitz condition. Based on the theory of differential inclusions and nonsmooth analysis, several criteria are presented to guarantee the existence of the desired robust state estimator for the discontinuous neural networks. It is shown that the design of the state estimator for such networks can be achieved by solving two linear matrix inequalities (LMIs), which are dependent on the size of the time derivative of the time-varying delay. Finally, numerical examples are given to illustrate the theoretical results.
	TO cite this article:xiaoyang liu,jinde cao. Robust State Estimation for Neural Networks with Discontinuous Activations[OL].[24 April 2009] http://en.paper.edu.cn/en_releasepaper/content/31699


	9. The Energy Consumption Model for Cell phones and Landlines
	Sien Deng,Yang Yang,Zhuanna Guo
	Mathematics 22 April 2009
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	Abstract:Nowadays, more and more people are likely to choose cell phone as their communicating tool rather than land phone, how will it affect the energy cost? We choose the US as an example to model the using condition of cells and lands in a perspective of energy. For the next 50 years, a prediction is finally given about the change of the energy consumption due to the cell phone revolution in the current US. The conclusion is that the tendency of the total energy consumption per year is decreasing mainly because of the decrease in cell phone manufacturing costs.
	TO cite this article:Sien Deng,Yang Yang,Zhuanna Guo. The Energy Consumption Model for Cell phones and Landlines[OL].[22 April 2009] http://en.paper.edu.cn/en_releasepaper/content/31608


	10. Mathematical Theory in Sudoku Puzzle
	Guo Changyu ,Wang Zhiqing ,Guo Huimin
	Mathematics 12 March 2009
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	Abstract:Solving a Sudoku is an NP problem. How to solve a Sudoku puzzle effectively is already a complex problem. To generate a validated Sudoku puzzle of desirable difficulty level is more complex. In this paper, an effective generating algorithm and a simple but efficient difficulty level are proposed. Firstly some common Logical Techniques and Brute Force Search Technique are introduced to solve a Sudoku puzzle. After that, demonstrate an generic generating algorithm, which uses a difficulty level based Analytic Hierarchy Process (AHP). This difficulty level is very reasonable by considering various factors. Some intelligent techniques and sub-processes are used to guarantee this generating algorithm efficient and correct. And the method to generate symmetrical Sudoku Puzzles is put forward just follow it. At last , some useful conclusion is obtained.
	TO cite this article:Guo Changyu ,Wang Zhiqing ,Guo Huimin . Mathematical Theory in Sudoku Puzzle[OL].[12 March 2009] http://en.paper.edu.cn/en_releasepaper/content/30187

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