摘要：
In this paper, employing Lyapunov functional and elementary inequality $(2ab\leq ra^2+\frac{1}{r}b^2,\ r>0)$(2ab\leq ra^2+\frac{1}{r}b^2,\ r>0), some sufficient conditions are derived for the existence and uniqueness of periodic solution of fuzzy bi-directional associative memory (BAM) networks with time-varying delays, we obtain some new and simple criteria to ensure global exponential stability of periodic solution. These criteria are important in the design and applications of fuzzy BAM neural networks.
作者机构：
[Qi, Liqun] Hong Kong Polytech Univ, Dept Appl Math, Kowloon, Hong Kong, Peoples R China.;[Wang, Fei] Hunan City Univ, Dept Math, Yiyang, Hunan, Peoples R China.;[Wang, Yiju] Qufu Normal Univ, Sch Operat Res & Management Sci, Rizhao 276800, Shandong, Peoples R China.
通讯机构：
[Qi, Liqun] H;Hong Kong Polytech Univ, Dept Appl Math, Kowloon, Hong Kong, Peoples R China.
摘要：
As a global polynomial optimization problem, the best rank-one approximation to higher order tensors has extensive engineering and statistical applications. Different from traditional optimization solution methods, in this paper, we propose some Z-eigenvalue methods for solving this problem. We first propose a direct Z-eigenvalue method for this problem when the dimension is two. In multidimensional case, by a conventional descent optimization method, we may find a local minimizer of this problem. Then, by using orthogonal transformations, we convert the underlying supersymmetric tensor to a pseudo-canonical form, which has the same E-eigenvalues and some zero entries. Based upon these, we propose a direct orthogonal transformation Z-eigenvalue method for this problem in the case of order three and dimension three. In the case of order three and higher dimension, we propose a heuristic orthogonal transformation Z-eigenvalue method by improving the local minimum with the lower-dimensional Z-eigenvalue methods, and a heuristic cross-hill Z-eigenvalue method by using the two-dimensional Z-eigenvalue method to find more local minimizers. Numerical experiments show that our methods are efficient and promising.
摘要：
For a graph G = (V, E), the modified Schultz index of G is defined as S*(G) = Σ{u, v}⊂V(G) (d(u)·d(v))dG(u, v) where d(u) (or d(v)) is the degree of the vertex u (or v) of G, and dG(u, v) is the distance between u and v. Explicit formulas for calculating the modified Schultz index of armchair polyhex nanotubes are provided in this paper.
摘要：
The modified Schultz index of a graph is defined as S*(G) = Σ{u, v}⊂V(G)(d(u)·d(v))dG(u, v) where d(u) (or d(v)) is the degree of the vertex u (or v), and dG(u, v) is the distance between u and v. Explicit formulas for calculating the modified Schultz index of Zig-zag polyhex nanotubes are provided in this paper.
摘要：
In this paper, we deal with a class of inequality problems for dynamic frictional contact between a piezoelectric body and a foundation. The model consists of a system of the hemivariational inequality of hyperbolic type for the displacement, the time dependent elliptic equation for the electric potential. The friction condition is described to be the Clarke subdifferential relations of nonmonotone and multivalued character in the tangential directions on the boundary. The existence of a weak solution to the model is proved by embedding the problem into a class of second-order evolution inclusions, and by applying a surjectivity result for multivalued operators.
