作者机构：
[李天然] Department of Mathematics, Hunan City College, Yiyang, 413000, China;[陈传淼] Institute of Computation, Hunan Normal University, Changsha, 410081, China
作者机构：
[Zhang, ZZ] Hunan City Univ, Dept Math, Yiyang, Peoples R China.;Cent S Univ, Sch Math Sci, Changsha, Peoples R China.;Hunan Univ, Fac Math & Econometr, Changsha, Peoples R China.
通讯机构：
[Zhang, ZZ] H;Hunan City Univ, Dept Math, Yiyang, Peoples R China.
作者机构：
[邓汉元] Department of Mathematics, Mathematics/Computer Sciencs College, Hunan Normal University, Changsha 410081, China;[夏方礼] Department of Mathematics, Yiyang Teacher's College, Yiyang 413049, China;[夏建业] Department of Basic Sciences, Guangzhou Financial College, Guangzhou 510521, China
期刊：
Journal of Mathematical Analysis and Applications,2003年287(1):296-306 ISSN：0022-247X
通讯作者：
Song, YQ
作者机构：
Hunan City Univ, Dept Math & Calc, Yiyang 413000, Hunan, Peoples R China.;Nanjing Univ Sci & Tech, Sch Sci, Nanjing 210094, Peoples R China.;[Song, YQ] Hunan City Univ, Dept Math & Calc, Zhaoyang Rd 4, Yiyang 413000, Hunan, Peoples R China.
通讯机构：
[Song, YQ] H;Hunan City Univ, Dept Math & Calc, Zhaoyang Rd 4, Yiyang 413000, Hunan, Peoples R China.
关键词：
Bvh function;Heisenberg group;Decomposition of a radon measure;Chain rule;Compactness theorem;Perimeter;Spaces
摘要：
At first in the setting of the Heisenberg group we show the chain rule for a function u is an element of BVH (Omega) when composed with a Lipschitz function f : R --> R and prove that nu = f o u belongs to BV (H) (Omega) and D(H)nu much less than D(H)u. More precisely the following result is shown: D(H)nu = f' ((u) over tilde)del(H)uL(2n+1) + 2omega(2n-1)/omega(2n+1) (f(u(+)) - f(u(-)))nu(u)S(d)(Q-1) [J(u) + f' ((u) over tilde) D(H)(c)u. Secondly using the chain rule above we prove a compactness theorem for SBVH functions. (C) 2003 Elsevier Inc. All rights reserved. [References: 16]
摘要：
In this Letter, we study BAM (bidirectional associative memory) networks with variable coefficients. By some spectral theorems and a continuation theorem based on coincidence degree, we not only obtain some new sufficient conditions ensuring the existence, uniqueness, and global exponential stability of the periodic solution but also estimate the exponentially convergent rate. Our results are less restrictive than previously known criteria and can be applied to neural networks with a broad range of activation functions assuming neither differentiability nor strict monotonicity. Moreover, these conclusions are presented in terms of system parameters and can be easily verified for the globally Lipschitz and the spectral radius being less than 1. Therefore, our results should be useful in the design and applications of periodic oscillatory neural circuits for neural networks with delays. (C) 2003 Elsevier B.V. All rights reserved.
