Spontaneous Stepwise Self‐Assembly of a Polyoxometalate–Organic Hybrid into Catalytically Active One‐Dimensional Anisotropic Structures

An inorganic–organic hybrid surfactant with a hexavanadate cluster as the polar head group was designed and observed to assemble into micelle structures, which further spontaneously coagulate into a 1D anisotropic structure in aqueous solutions. Such a hierarchical self‐assembly process is driven by the cooperation of varied noncovalent interactions, including hydrophobic, electrostatic, and hydrogen‐bonding interactions. The hydrophobic interaction drives the quick formation of the micelle structure; electrostatic interactions involving counterions leads to the further coagulation of the micelles into larger assemblies. This process is similar to the crystallization process, but the specific counterions and the directional hydrogen bonding lead to the 1D growth of the final assemblies. Since most of the hexavanadates are exposed to the surface, the 1D assembly with nanoscale thickness is a highly efficient heterogeneous catalyst for the oxidation of organic sulfides with appreciable recyclability.     

多酸在电催化析氢反应中的应用研究进展

电催化水裂解是一种可持续用于生产可再生氢能源的技术。然而,开发高效稳定、低成本的析氢电催化剂仍是一项具有挑战性的任务。多金属氧酸盐(多酸)是一种离散的金属氧簇合物,通常由氧配体和高价的钒(V)、钼(VI)、钨(VI)金属构成。由于多酸含有丰富的氧化还原活性金属中心,因此,近几年来,多酸在水裂解应用研究方面备受关注。本综述将聚焦于多酸在电催化水裂解析氢的应用研究进展。本文还突出强调了电催化析氢目前面临的主要问题,以及对多酸基催化剂及作为催化剂前体在电催化析氢方面的应用及发展前景做了展望。     

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.     

Path integral and effective Hamiltonian in loop quantum cosmology

We study the path integral formulation of Friedmann universe filled with a massless scalar field in loop quantum cosmology. All the isotropic models of $k=0,+1,-1$ are considered. To construct the path integrals in the timeless framework, a multiple group-averaging approach is proposed. Meanwhile, since the transition amplitude in the deparameterized framework can be expressed in terms of group-averaging, the path integrals can be formulated for both deparameterized and timeless frameworks. Their relation is clarified. It turns out that the effective Hamiltonian derived from the path integral in deparameterized framework is equivalent to the effective Hamiltonian constraint derived from the path integral in timeless framework, since they lead to same equations of motion. Moreover, the effective Hamiltonian constraints of above models derived in canonical theory are confirmed by the path integral formulation.     

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.