In this paper, we propose a new nonlinear conjugate gradient method for large-scale unconstrain optimization which possesses the following properties:(i)the sufficient descent condition −g k dk ≥ 7 8 ‖gk‖ 2 holds without any line searches;(ii)With exact line search, this method reduces to a nonlinear version of the Liu-Storey conjugate gradient scheme.(iii)Under some assumption, global converge...

Code equivalence is a basic concept in coding theory. The well-known theorem by MacWilliams gives a sufficient condition for code equivalence. Recently the MacWilliams theorem has been generalized, by Fan, Liu and Puig, making use of the generalized Hamming weights (GHWs). In this paper, we will present a further generalization of the MacWilliams theorem. Our result extends both the MacWilliams...

A variational method is introduced to study the propagation of elastic waves in two-dimensional periodic systems. First, it has been applied to a binary system consisting of an array of high-density cylinders in an epoxy background, where the advantages of the method are pointing out in regard with the well-known plane-wave expansion formalism. Second, a comprehensive study is performed for the...

For simplicity, we focus on the bivariate case (X and Y are each one-dimensional variables). The extension to proof in multivariate case is straight forward. We first work on the mutual information, then show the similar arguments on the copula distances. To prove the theorem, we use Le Cam [1973]’s method to find the lower bound on the minimax risk of the estimating mutual information MI . To ...

For this paper, we consider the almost sure exponential stability of uncertain stochastic Hopfield neural networks based on subadditive measures. Firstly, deduce two corollaries, using Itô–Liu formula. Then, introduce concept for networks. Next, investigate networks, Lyapunov method, Liu inequality, lemma, and martingale inequality. In addition, prove sufficient conditions stability. Furthermor...

We define Liu morphisms and quasi-Liu between Berkovich analytic spaces. show that behave exactly as affine quasi-affine of schemes.

In this letter we analyse an amazing variational approach to chemical reactions. Our results clearly show that the variational expressions are unsuitable for the analysis of empirical data obtained from chemical reactions. Some time ago Liu and He [1] proposed the application of a variational approach to chemical reactions. Their method consisted of the transformation of the differential equati...