张量对称类上诱导线性算子的数值半径

设V是一个n维线性空间,V_x~m(G)为V上的张量对称类.A为V的线性算子T的矩阵,K(A)为V_x~m(G)上的诱导线性算子K(T)的矩阵.本文从K(A)的数值半径Υ(K(A))和可分数值半径Υ_x(K(A))定义出发,研究了Υ(K(A))、Υ_x(K(A))与范数||A||_p(1≤p≤2)、广义矩阵函数d_x~G(A)的关系,得到了它们之间的两个不等式.     

Unified approach to photo-and electro-production of mesons with arbitrary spins

A new approach to identify the independent amplitudes along with their partial wave multipole expansions, for photo-and electro-production is suggested, which is generally applicable to mesons with arbitrary spin-parity. These amplitudes facilitate direct identification of different resonance contributions.      

高频单线圈双调谐NMR单晶探头的研制

本文报道了一种测角单晶NMR探头。该探头采用单线圃双调谐电路,工作频率在90MHz-110 MHz连续可调,可进行交叉极化大功率去耦实验。文中提出了一种简单而有效的测角装置,可使单晶绕三个互相垂直轴转动实现单晶的NMR测量。作为典型的应用例子,本文利用该探头实现了单晶DGO(2NH₂CH₂COOH·H₂C₂O₄)屏蔽张量的测量。     

Separation of screw-sensed particles in a homogeneous shear field

The Stokes motions of three-dimensional screw-sensed slender particles in a homogeneous shear field are investigated, including the effects of buoyancy. Conclusions are drawn about the possibility of achieving a separation of mixtures of right- and left-handed particles. The linearity of the Stokes equations allows complex flows to be solved by adding the effects of the several terms which describe the flow in which the particle is immersed. The homogeneous shear flow considered here consists of three such terms; solutions for a series of 12 unit motions are sufficient to determine the hydrodynamic resistance tensors. The forces and torques experienced by screw-sensed particles are calculated from these 51 resistance tensors, using slender-filament theory. The results allow an estimate of the range of buoyancy parameters for which gravitational sedimentation can be neglected. The fundamental component of the particle motion is a rotation, at approximately the same angular velocity as that of the fluid. Superimposed on this are variations, of large period, in the particle orientation. A phase plane analysis is used to find the terminal orientations. Very long calculation times are required for the phase portrait. An approximate method based on azimuthally-averaged equations is developed to avoid the requirements for long time integration.     

On the successive supersymmetric rank‐1 decomposition of higher‐order supersymmetric tensors

In this paper, a successive supersymmetric rank‐1 decomposition of a real higher‐order supersymmetric tensor is considered. To obtain such a decomposition, we design a greedy method based on iteratively computing the best supersymmetric rank‐1 approximation of the residual tensors. We further show that a supersymmetric canonical decomposition could be obtained when the method is applied to an orthogonally diagonalizable supersymmetric tensor, and in particular, when the order is 2, this method generates the eigenvalue decomposition for symmetric matrices. Details of the algorithm designed and the numerical results are reported in this paper. Copyright © 2007 John Wiley & Sons, Ltd.     

Permutation representations in molecular symmetry

The reducible representations of the point groups are generally studied because of their relevance to molecular orbital and vibration theory. Triple correlations within the polyhedra are described by group-theoretical invariants that are related to the permutation representations and termed polyhedral isoscalar factors. These invariants are applied in theorems on matrix elements referring to the symmetry-adapted bases at different centres. Further invariants or geometrical weight factors inter-relate different types of reduced matrix elements of irreducible tensors (generalization of the Wigner-Eckart theorem to the polycentric case). As a demonstration a complete tabulation is given for the point group C ₄.     

Crystal structure and single crystal EPR of (NH_4)_2(15-crown-5)_3[Cu(mnt)_2] and (NH_4)_2(benzo-15-crown-5)_4[Cu(mnt)_2]·0.5H_2O

The X-ray crystal structures of (NH4)2(15-crown-5)3[Cu(mnt)2] (1) and (NH4)2(benzo-15-crown-5)4- [Cu(mnt)2]·0.5H2O (2) were determined. Two single crystals are composed of distinct structures of ammonium-crown ether supramolecular cation and [Cu(mnt)2]2? anion. The triple-decker dication in complex 1 and a sandwich dimmer in complex 2 were observed. X-Band EPR studies on the single crystals of both complex 1 and complex 2 have been carried out at room temperature, which revealed that complex 2 showed a perfect hyperfine structure of Cu whereas that of complex 1 could not be observed. The principal values and direction cosines of the principal axes of the g and A tensors were computed by a least-squares fitting procedure. The spin density of Cu(II) was estimated according to the principal values of the A tensors and compared well with the results calculated based on DFT method.     

A fast algorithm for the spectral radii of weakly reducible nonnegative tensors

In this paper, we propose a fast algorithm for computing the spectral radii of symmetric nonnegative tensors. In particular, by this proposed algorithm, we are able to obtain the spectral radii of weakly reducible symmetric nonnegative tensors without requiring the partition of the tensors. As we know, it is very costly to determine the partition for large‐sized weakly reducible tensors. Numerical results are reported to show that the proposed algorithm is efficient and also able to compute the spectral radii of large‐sized tensors. As an application, we present an algorithm for testing the positive definiteness of Z‐tensors. By this algorithm, it is guaranteed to determine the positive definiteness for any Z‐tensor.