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.     

Linearization effect in multifractal analysis: Insights from the Random Energy Model

The analysis of the linearization effect in multifractal analysis, and hence of the estimation of moments for multifractal processes, is revisited borrowing concepts from the statistical physics of disordered systems, notably from the analysis of the so-called Random Energy Model. Considering a standard multifractal process (compound Poisson motion), chosen as a simple representative example, we show the following: (i) the existence of a critical order q^∗ beyond which moments, though finite, cannot be estimated through empirical averages, irrespective of the sample size of the observation; (ii) multifractal exponents necessarily behave linearly in q, for q>q^∗. Tailoring the analysis conducted for the Random Energy Model to that of Compound Poisson motion, we provide explicative and quantitative predictions for the values of q^∗ and for the slope controlling the linear behavior of the multifractal exponents. These quantities are shown to be related only to the definition of the multifractal process and not to depend on the sample size of the observation. Monte Carlo simulations, conducted over a large number of large sample size realizations of compound Poisson motion, comfort and extend these analyses.     

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H矩阵与M-矩阵的等价条件

本文引进了局部对角占优矩阵的概念，得到了非奇Ｈ矩阵与Ｍ－矩阵的等价条件与判定准则，改进了文［１］的主要结果．     

A new criterion for the H-matrix property

For many applications, it is very useful to know whether a matrix is an H-matrix or not. Recently, some iterative tests have been proposed for distinguishing H-matrix. In this paper, we propose a new method for being able to distinguish only a scalar times column vector. Numerical evidence for the effectiveness of the proposed algorithm is presented.     

某类多叶解析函数的性质

设A(p)(p是指数，p≥1）表示在单位圆盘E内形如f(z)=z^p ap 1z^p 1…的解析函数族。本文引进了新的函数子类Hσ（p,α），找出了Hσ（p,α）闭凸包的极值点并给出精确的系数估计，还讨论了Hσ（p,α）其它一些有趣的性质。     

非奇H矩阵的简捷判据

本文给出了非奇Ｈ矩阵的充分条件及充分必要条件，改进了文（１）的相应结果。     

Schur functors on QF-3 standardly stratified algebras

Let A be a QF-3 standardly stratified algebra and f be a Schur functor corresponding to some projective-injective faithful A-module, denoted by Ae. The main result of this paper is to prove that, if the dominant dimension of A is sufficiently large, then ] induces a full embedding from ￡（△） to eAe-mod which preserves Ext-groups up to certain degrees, where ￡（△） denotes the full subcategory of A-mod whose objects are filtered by standard A-modules. We check this criterion on some typical examples, quantized Schur algebras Sq（n,r） with n≥r and finite-dimensional algebras associated with the Bernstein-Gelfand-Gelfand category O of semisimple complex Lie algebras.     

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.