Oja神经网络模型的有限逸时性

O ja连续型全反馈神经网络模型可以有效计算实对称矩阵的主特征向量,该网络的动态行为由描述其模型的微分方程所决定,详细研究了O ja动力系统的稳定性问题.对于非正定实对称矩阵最大特征根为零,且至少有一特征根为负的情形,证明了从单位球外出发的解并不一定必然导致有限逸时,完善了O ja模型计算实对称矩阵主特征向量的收敛性结果,数值实验结果进一步验证了理论分析的正确性.     

销售商出售看跌期权的供应链优化研究

在由一个供应商和一个销售商组成的单期两级供应链中,处于主导地位的销售商以其卖场所具有的销售能力参与供应链合作,并从销售的每一个产品中获取既定收益。同时,销售商还向供应商出售建立在产品销售量保障基础上的看跌期权,以激励供应商参与供应链合作。论文对上述情形的销售商出售看跌期权的供应链合作问题进行了研究,通过建模与优化分析,证明了在销售商提供看跌期权的供应链合作中,供应商存在唯一的最优生产批量和看跌期权采购量,以及销售商存在最优的从每一单位产品销售中获取的既定收益。论文还揭示了销售商提供看跌期权,虽然无法实现供应链协调,但可以实现供应链参与企业所获得的收益与其所承担的风险相匹配。最后,论文论证了在销售商出售看跌期权机制下,供应链存在收益损失较小的理想合作区域。     

非奇异H-矩阵的判定

利用矩阵足码集的一个k-级划分,得出了非奇异H-矩阵的几个新的判定条件,改进和推广了一些相关结果,并用数值例子说明了结论的有效性.     

Some properties of two subclasses of k-fold symmetric functions associated with Srivastava-Attiya operator

In the present paper, by using the Srivastava-Attiya operator, we define two new subclasses of k-fold symmetric analytic functions. Some interesting properties of these subclasses such as integral representations, extreme points, close convex hulls and subordinations are obtained, which generalize and refine some previous results.     

Convergence of GAOR method for doubly diagonally dominant matrices

In this paper, we obtain bounds for the spectral radius of the matrix l_ω,r which is the iterative matrix of the generalized accelerated overrelaxation (GAOR) iterative method. Moreover, we present one convergence theorem of the GAOR method. Finally, we present two numerical examples.     

Isokinetic correlation analysis of the series of electrophilic substitution reactions of o -substituted phenylmercurials

Isokinetic relationships of the series of electrophilic substitution reactions ofo-substituted phenylmercurials are studied, and the results show, for the first time, that isokinetic correlation analysis can reveal the dominant factor in the system of the reactions. The analysis of S_E2 ofo-substituted phenylmercuric chlorides indicates that the steric effect ofo-substituents is the predominant factor when I₂ is used as electrophilic agent, however, the electronic effect ofo-substituents would become the predominant factor when HCl is used as the electrophilic agent. In S_E1 ofo-substituted phenylmercuric chlorides, the results of the analysis display that the predominant factor is the field effects ofo-substituents. The determination of predominant factors in those reactions would provide further scientific basis for those reaction mechanisms.     

Bi-block positive semidefiniteness of bi-block symmetric tensors

The positive definiteness of elasticity tensors plays an important role in the elasticity theory.In this paper,we consider the bi-block symmetric tensors,which contain elasticity tensors as a subclass.First,we define the bi-block M-eigenvalue of a bi-block symmetric tensor,and show that a bi-block symmetric tensor is bi-block positive(semi)definite if and only if its smallest bi-block M-eigenvalue is(nonnegative)positive.Then,we discuss the distribution of bi-block M-eigenvalues,by which we get a sufficient condition for judging bi-block positive(semi)definiteness of the bi-block symmetric tensor involved.Particularly,we show that several classes of bi-block symmetric tensors are bi-block positive definite or bi-block positive semidefinite,including bi-block(strictly)diagonally dominant symmetric tensors and bi-block symmetric(B)B0-tensors.These give easily checkable sufficient conditions for judging bi-block positive(semi)definiteness of a bi-block symmetric tensor.As a byproduct,we also obtain two easily checkable sufficient conditions for the strong ellipticity of elasticity tensors.     

ℋ-tensors and nonsingular ℋ-tensors

The H-matrices are an important class in the matrix theory, and have many applications. Recently, this concept has been extended to higher order ?-tensors. In this paper, we establish important properties of diagonally dominant tensors and ?-tensors. Distributions of eigenvalues of nonsingular symmetric ?-tensors are given. An ?₊-tensor is semi-positive, which enlarges the area of semi-positive tensor from ?-tensor to ?₊-tensor. The spectral radius of Jacobi tensor of a nonsingular (resp. singular) ?-tensor is less than (resp. equal to) one. In particular, we show that a quasi-diagonally dominant tensor is a nonsingular ?-tensor if and only if all of its principal sub-tensors are nonsingular ?-tensors. An irreducible tensor Ais an ?-tensor if and only if it is quasi-diagonally dominant.     

On Factorizations of Smooth Nonnegative Matrix-Values Functions and on Smooth Functions with Values in Polyhedra

We discuss the possibility to represent smooth nonnegative matrix-valued functions as finite linear combinations of fixed matrices with positive real-valued coefficients whose square roots are Lipschitz continuous. This issue is reduced to a similar problem for smooth functions with values in a polyhedron. The work was partially supported by NSF Grant DMS-0653121.     

Rounding Errors in Solving Block Hessenberg Systems

A rounding error analysis is presented for a divide-and-conquer algorithm to solve linear systems with block Hessenberg matrices. Conditions are derived under which the algorithm computes a stable solution. The algorithm is shown to be stable for block diagonally dominant matrices and for M-matrices.