This paper studies two kinds of nonlinear transformations, namely the higher-dimensional Arnold transformation and the higher-dimensional Fibonacci Q-transformation and discusses the scrambling action of the two trans...This paper studies two kinds of nonlinear transformations, namely the higher-dimensional Arnold transformation and the higher-dimensional Fibonacci Q-transformation and discusses the scrambling action of the two transformations focusing on the phase space of the digital images. A sufficient and necessary condition that a matrix transformation of digital image has periodicity is given. The results show that the two transformations have potential application in the storage and transportation of image information for the purpose of information security.展开更多
Structural probabilistic analysis quantifies the effect of input random variables, such as material proper- ties, geometrical parameters and loading conditions, on the structural responses. The point estimate method (...Structural probabilistic analysis quantifies the effect of input random variables, such as material proper- ties, geometrical parameters and loading conditions, on the structural responses. The point estimate method (PEM) is a direct and easy-used way to perform the structural probabilistic analysis in practice. In this paper, a novel and efficient point estimate method is proposed for computing the first four statistical moments of structural response which is a function of input random variables. The method adopts Nataf transformation to replace Rosenblatt transformation in conventional point estimate method. Because of the nature of engineering problems and limited statistical data, the joint probability density function (PDF) of all input random variables is hard to acquire, but it must be known in Rosenblatt transformation. A more common case is that the marginal PDF of each random variable and the correlation matrix are available, which just satisfy the service condition of Nataf transformation. Hence the Nataf transformation based point estimate method is particularly suitable for engineering applications. The comparison between the proposed method and the conventional point estimate method shows that (1) they are equivalent when all random variables are mutually independent; (2) if the marginal PDFs and the correlation matrix are known, the conventional PEM cannot be applicable, but the proposed method can give a rational approximation. Finally, the procedure is demonstrated in detail through a simple illustration.展开更多
文摘This paper studies two kinds of nonlinear transformations, namely the higher-dimensional Arnold transformation and the higher-dimensional Fibonacci Q-transformation and discusses the scrambling action of the two transformations focusing on the phase space of the digital images. A sufficient and necessary condition that a matrix transformation of digital image has periodicity is given. The results show that the two transformations have potential application in the storage and transportation of image information for the purpose of information security.
基金the National Natural Science Foundation of China (Grant No. 10572117)Program for New Century Excellent Talents in University (Grant No. NCET-05-0868)+1 种基金Aviation Science Foundation (Grant No. 2007ZA53012)Hi-Tech Research and Development Program of China (Grant No. 2007AA04Z401)
文摘Structural probabilistic analysis quantifies the effect of input random variables, such as material proper- ties, geometrical parameters and loading conditions, on the structural responses. The point estimate method (PEM) is a direct and easy-used way to perform the structural probabilistic analysis in practice. In this paper, a novel and efficient point estimate method is proposed for computing the first four statistical moments of structural response which is a function of input random variables. The method adopts Nataf transformation to replace Rosenblatt transformation in conventional point estimate method. Because of the nature of engineering problems and limited statistical data, the joint probability density function (PDF) of all input random variables is hard to acquire, but it must be known in Rosenblatt transformation. A more common case is that the marginal PDF of each random variable and the correlation matrix are available, which just satisfy the service condition of Nataf transformation. Hence the Nataf transformation based point estimate method is particularly suitable for engineering applications. The comparison between the proposed method and the conventional point estimate method shows that (1) they are equivalent when all random variables are mutually independent; (2) if the marginal PDFs and the correlation matrix are known, the conventional PEM cannot be applicable, but the proposed method can give a rational approximation. Finally, the procedure is demonstrated in detail through a simple illustration.
