Arene C?H Amination at Nickel in Terphenyl–Diphosphine Complexes with Labile Metal–Arene Interactions

The meta‐terphenyl diphosphine, m‐P₂, 1 , was utilized to support Ni centers in the oxidation states 0, I, and II. A series of complexes bearing different substituents or ligands at Ni was prepared to investigate the dependence of metal–arene interactions on oxidation state and substitution at the metal center. Complex (m‐P₂)Ni ( 2 ) shows strong Ni⁰–arene interactions involving the central arene ring of the terphenyl ligand both in solution and the solid state. These interactions are significantly less pronounced in Ni⁰ complexes bearing L‐type ligands ( 2‐L : L=CH₃CN, CO, Ph₂CN₂), Ni^IX complexes ( 3‐X : X=Cl, BF₄, N₃, N₃B(C₆F₅)₃), and [(m‐P₂)Ni^IICl₂] ( 4 ). Complex 2 reacts with substrates, such as diphenyldiazoalkane, sulfur ylides (Ph₂S?CH₂), organoazides (RN₃: R=para‐C₆H₄OMe, para‐C₆H₄CF₃, 1‐adamantyl), and N₂O with the locus of observed reactivity dependent on the nature of the substrate. These reactions led to isolation of an η¹‐diphenyldiazoalkane adduct ( 2‐Ph₂CN₂ ), methylidene insertion into a Ni? P bond followed by rearrangement of a nickel‐bound phosphorus ylide ( 5 ) to a benzylphosphine ( 6) , Staudinger oxidation of the phosphine arms, and metal‐mediated nitrene insertion into an arene C? H bond of 1 , all derived from the same compound ( 2 ). Hydrogen‐atom abstraction from a Ni^I–amide ( 9 ) and the resulting nitrene transfer supports the viability of Ni–imide intermediates in the reaction of 1 with 1‐azido‐arenes.     

ZnO/CdS复合材料的合成与可见光催化性能

采用喷雾辅助气相沉积法在水热法合成的ZnO纳米线上沉积CdS纳米颗粒。采用X射线衍射仪（XRD）、激光拉曼仪（Raman）、扫描电镜（SEM）、透射电镜（TEM）、X射线光电子能谱分析谱（XPS）和紫外可见漫反射光谱等测试手段对复合光催化剂进行表征。结果表明,3~10 nm的CdS纳米粒子修饰在直径约为100 nm ZnO纳米线的表面。XPS和Raman表明复合材料中ZnO和CdS之间存在化学相互作用。可见光催化降解罗丹明B实验结果表明ZnO/CdS复合材料的催化性能优于单相CdS或ZnO,沉积时间为30 s合成的ZnO/CdS速率常数分别是CdS和ZnO的2.91和4.03倍,且具有较高的稳定性。ZnO/CdS复合材料光催化性能增强的可能原因为光吸收范围的拓展和光生载流子分离效率的提高。     

Nonlinear Schrödinger equation in a semi-strip: Evolution of the Weyl–Titchmarsh function and recovery of the initial condition and rectangular matrix solutions from the boundary conditions

Rectangular matrix solutions of the defocusing nonlinear Schrödinger equation (dNLS) are studied in quarter-plane and semi-strip. Evolution of the corresponding Weyl–Titchmarsh (Weyl) function is described in terms of the initial Weyl function and boundary conditions. In the next step, the initial Weyl function is recovered (for the quarter-plane case) from the long-time asymptotics of the wave function considered at the boundary. Thus, it is shown that the evolution of the Weyl function is uniquely defined by the boundary conditions. Moreover, a procedure to recover solutions of dNLS (uniquely defined by the boundary conditions) is given. In a somewhat different way, the same boundary value problem is also dealt with in a semi-strip (for the case of a quasi-analytic initial condition).     

Fine singularity analysis of solutions to the Laplace equation

We present here a fine singularity analysis of solutions to the Laplace equation in special polygonal domains in the plane. We assume piecewise constant Neumann data on one component of the boundary. Our motivation is to study the so‐called Berg effect, which is explained in the introduction. Copyright © 2014 John Wiley & Sons, Ltd.     

END样本最近邻密度估计的强相合速度

本文研究了扩展负相依(END)样本最近邻密度估计的强相合性问题.利用END序列的Bernstein型不等式和截尾的方法,获得了END样本最近邻密度估计的强相合速度,推广了NA样本和ND样本最近邻密度估计的相应结果.     

Synchronization of multiple bursting neurons ring coupled via impulsive variables

Synchronization behavior of bursting neurons is investigated in a neuronal network ring impulsively coupled, in which each neuron exhibits chaotic bursting behavior. Based on the Lyapunov stability theory and impulsive control theory, sufficient conditions for synchronization of the multiple systems coupled with impulsive variables can be obtained. The neurons become synchronous via suitable impulsive strength and resetting period. Furthermore, the result is obtained that synchronization among neurons is weakened with the increasing of the reset period and the number of neurons. Finally, numerical simulations are provided to show the effectiveness of the theoretical results.© 2014 Wiley Periodicals, Inc. Complexity 21: 29–37, 2015     

On a problem of Hornik

In 1991,Hornik proved that the collection of single hidden layer feedforward neural networks(SLFNs)with continuous,bounded,and non-constant activation functionσis dense in C(K)where K is a compact set in R~s(see Neural Networks,4(2),251-257(1991)).Meanwhile,he pointed out"Whether or not the continuity assumption can entirely be dropped is still an open quite challenging problem".This paper replies in the affirmative to the problem and proves that for bounded and continuous almost everywhere(a.e.)activation functionσon R,the collection of SLFNs is dense in C(K)if and only ifσis un-constant a.e..