五阶各向同性Descartes张量

研究了五阶各向同性张量的存在性及其一般表示问题,得出了三阶各向同性Descartes张量的一般表达式。     

Ricci张量对称函数的预定问题

本文考虑Ricci张量的对称函数σ2(Ricg)的预定问题.假设(M,g)是闭的Einstein流形,我们得到了只要流形(M,g)不具有σ2(Ric)奇性,则对于变号的函数f∈C∞(M),存在度量g*,使得σ2(Ricg*) = f.然后,作为推论,得到了具有负数量曲率的闭Einstein流形上的预定曲率的结果.     

半对称度量循环联络的某些特征及曲率张量表示

The projective transformation of the special semi-symmetric metric recurrent connection is studied in this paper. First of all, an invariant under this transformation is granted; Secondly, by inducing of the invariant and making use of the properties that the corresponding covariant derivative keeps being fixed under the distinctness connection, the curvature tensor expression of the Riemannian manifold is posed at the same time.     

QDB-张量和SQDB-张量

在文中,我们提出了四类新的结构张量: QDB(QDB0)-张量和SQDB(SQDB0)-张量,并证明了对称偶数阶的QDB-张量和SQDB-张量的正定性,对称偶数阶的QDB0-张量和SQDB0-张量的半正定性.     

H-张量判定的新迭代准则及其应用

H-张量在科学和工程实际中具有重要应用,但在实际中要判定H-张量是比较困难的.通过构造不同的正对角阵,结合不等式的放缩技巧,给出了H-张量判定的几个新迭代准则.作为应用,给出了判定偶数阶实对称张量正定性的条件,相应的数值例子说明了结果的有效性.     

高阶各向同性张量的搜求方法

基于单位张量是唯一带有根本性意义的二阶各向同性张量的结论,系统推演搜求高阶各向同性张量的具体方法.     

H-张量的判定及其应用

H-张量在科学和工程实际中具有重要应用,但在实际中要判定H-张量是比较困难的.通过构造不同的正对角阵,结合不等式的放缩技巧,给出了一些比较实用的新条件.作为应用,给出判定偶数阶实对称张量正定性的条件,相应数值例子说明了结果的有效性.     

局部共形对称黎曼流形上的保圆曲率张量长度的整体刚性定理

本文我们研究了局部共形对称闭黎曼流形, 建立了一个关于保圆曲率矢量长度的整体刚度定理.     

一类非对称各向同性张量函数导数的不变表示

将Dui和Chen于2004年提出的求解对称各向同性张量函数导数的方法推广到一类满足可交换条件的非对称各向同性张量函数情况,此类函数比以往研究的更具一般性．在有3个不同特征根时,由可交换性引进张量函数相对应的标量函数,进而求得此类非对称各向同性张量函数及其导数的不变表示形式．在2或3重特征根时,利用求极限的办法给出此类张量函数及其导数的表示形式．     

论单位张量是唯一的二阶各向同性张量

在所有二阶张量中,只有单位张量(度规张量),是各向同性的;二阶各向同性张量一定是球张量,反之亦然;偏张量为零的二阶张量一定是各向同性的。     

用张量导数法求横观各向同性弹性材料的弹性张量的一般形式

用对张量函数求导的方法导出了横观各向同性材料和各向同性材料的弹性张量的一般形式与应力-应变关系式.从推导过程可更清楚地看出为什么横观各向同性材料和各向同性材料分别有五个和两个独立的弹性常数,即材料有几个独立的弹性常数是由其应变能函数的形式所决定的.     

Isotropic affine hypersurfaces of dimension 5

We study affine hypersurfaces M   which have isotropic difference tensor. Note that any surface always has isotropic difference tensor. Therefore, we may assume that n>2$n>2$. Such hypersurfaces have previously been studied by the first author and M. Djoric in [1] under the additional assumption that M is an affine hypersphere. Here we study the general case. As for affine spheres, we first show that isotropic affine hypersurfaces which are not congruent to quadrics are necessarily 5, 8, 14 or 26 dimensional. From this, we also obtain a complete classification in dimension 5.     

Isotropic affine spheres

In this paper, we study affine spheres which are isotropic and we obtain a complete classification. In particular, we show that all such affine spheres are hyperbolic affine spheres, isometric with SL(3 , R ) / SO(3), SL(3 , C ) / SU(3), SU*(6) / Sp(3) or E6 (-26) /F4 .     

Isotropic bodies and Bourgain''''s problem

Let K (?) Rn be a convex body of volume 1 whose barycenter is at the origin, LK be the isotropic constant of K. Finding the least upper bound of LK , being called Bourgain's problem, is a well known open problem in the local theory of Banach space. The best estimate known today is LK < cn1/4 log n, recently shown by Bourgain, for an arbitrary convex body in any finite dimension. Utilizing the method of spherical section function, it is proven that if K is a convex body with volume 1 and r1Bn2 (?) K (?) r2Bn2,(r1≥1/2, r2≤(?)/2), then (?) ≤(?) and find the conditions with equality. Further, the geometric characteristic of isotropic bodies is shown.     

Tensor logarithmic norm and its applications

Matrix logarithmic norm is an important quantity, which characterize the stability of linear dynamical systems. We propose the logarithmic norms for tensors and tensor pairs, and extend some classical results from the matrix case. Moreover, the explicit forms of several tensor logarithmic norms and semi‐norms are also derived. Employing the tensor logarithmic norms, we bound the real parts of all the eigenvalues of a complex tensor and study the stability of a class of nonlinear dynamical systems. Copyright © 2016 John Wiley & Sons, Ltd.     

Free Vibrations of Transversely Isotropic Hollow Cylinders

An asymptotic process for evaluating the frequencies of free axisymmetric vibrations of transversely isotropic hollow cylinders is proposed. This process is developed in detail for a cylinder with hinge-supported ends and free lateral surfaces. The approaches which make it possible to construct algorithms for identifying their natural frequencies within the given interval are tested on model problems. The results from the Kirchhoff-Love and Ambartsumyan theories are compared with those from the 3D elasticity theory. In the first term of an asymptotic expansion, two frequencies coinciding with those obtained using the applied shell theory are found and a countable set of frequencies absent in this theory is determined.