Hexatungstate subunit as building block in the hydrothermal synthesis of organic-inorganic hybrid materials: synthesis, structure and optical properties of Co2(bpy)6 (W6O19)2 (bpy=4,4′-bipyridine)

A hydrothermal reaction of WO₃, CoCl₂ and 4,4′-bipyridine, yields a novel organic-inorganic hybrid compound, Co₂(bpy)₆(W₆O₁₉)₂, at 170°C. X-ray single crystal structure determination reveals a two-dimensional covalent structure belonging to monoclinic crystal system, space group C2/c, with cell parameters a=19.971(4) Å, b=11.523(2) Å, c=16.138(3) Å, β=96.49(3)°, V=3690.0 Å³ and Z=2. The hexatungstate, [W₆O₁₉]²⁻, acts as a building block in bidentate fashion to bridge the Co(II) centers in the crystal structure. The title compound is found to have an optical energy gap of 2.2 eV from UV-Vis-NIR reflectance spectra.     

On constrained generalized inverses of matrices and their properties

A matrix G is called a generalized inverse (g-invserse) of matrix A if AGA = A and is denoted by G = A ⁻. Constrained g-inverses of A are defined through some matrix expressions like E(AE)⁻, (FA)⁻ F and E(FAE)⁻ F. In this paper, we derive a variety of properties of these constrained g-inverses by making use of the matrix rank method. As applications, we give some results on g-inverses of block matrices, and weighted least-squares estimators for the general linear model.     

A characterization of L p(ℝ) by local trigonometric bases with 1<p<∞

We show that the local trigonometric bases introduced by Malvar, Coifman and Meyer constitute bases, but not unconditional bases, for L^p(ℝ) with 1<p<∞, p≠2. In addition, we characterize the functions in L^p(ℝ) for 1<p<∞ in terms of their local trigonometric basis coefficients. Dedicated to Dr. Charles A. Micchelli for his 60th birthday Mathematics subject classification (2000) 42C15. Supported by Prof. Y. Xu under his grant in program of “One Hundred Distinguished Chinese Scientists” of the Chinese Academy of Sciences, the National Natural Science Foundation of China (No. 10371122), and the second author is supported by Tianyuan Fund for Mathematics (No. A0324648).     

DMAP-catalyzed esterification of pentaerythritol-derivatized POMs: a new route for the functionalization of polyoxometalates

We have demonstrated that a pentaerythritol-derivatized hexavanadate can be easily esterified with acid anhydrides using 4-(N,N-dimethylamino)pyridine (DMAP) as a catalyst, which provides a convenient method for the functionalization of polyoxometalates.     

Hermitian‐type generalized singular value decomposition with applications

For a pair of given Hermitian matrix A and rectangular matrix B with the same row number, we reformulate a well‐known simultaneous Hermitian‐type generalized singular value decomposition (HGSVD) with more precise structure and parameters and use it to derive some algebraic properties of the linear Hermitian matrix function A?BXB* and Hermitian solution of the matrix equation BXB* = A, and the canonical form of a partitioned Hermitian matrix and some optimization problems on its inertia and rank. Copyright © 2012 John Wiley & Sons, Ltd.     

行分块矩阵值域上正交投影的展开式

We give in this note some expansion formulas for the orthogonal projectors onto the range of the row block matrix [ A, B ], and use the expansion formulas to examine relations among the orthogonal projectors onto the ranges of A, B and [A, B]. In particular, we present some identifying conditions for a pair of orthogonal projectors of the same size to commute.     

The effects of indium segregation on the valence band structure and optical gain of GaInAs/GaAs quantum wells

The effects of indium segregation on the valence band structures and the optical gain in GaInAs/GaAs quantum wells are theoretically investigated using 4×4 Luttinger–Kohn Hamiltonian matrix. The method for the band structure calculation is based on the finite difference method, then the optical gain is calculated using the density matrix approach. For segregation coefficient R less than 0.7, indium segregation has little influence on optical gain, but for segregation coefficient R more than 0.7, it has a significant influence on optical gain, the gain spectra can be blue-shifted with the increase of segregation coefficient R, and the peak gains are decreased as segregation coefficient R increases, which is mainly due to the reduction of the carrier population inversion.