几乎各向同性的高维空间分数阶扩散方程的分块快速正则Hermite分裂预处理方法

一类空间分数阶扩散方程经过有限差分离散后所得到的离散线性方程组的系数矩阵是两个对角矩阵与Toeplitz型矩阵的乘积之和.在本文中,对于几乎各向同性的二维或三维空间分数阶扩散方程的离散线性方程组,采用预处理Krylov子空间迭代方法,我们利用其系数矩阵的特殊结构和具体性质构造了一类分块快速正则Hermite分裂预处理子.通过理论分析,我们证明了所对应的预处理矩阵的特征值大部分都聚集于1的附近.数值实验也表明,这类分块快速正则Hermite分裂预处理子可以明显地加快广义极小残量(GMRES)方法和稳定化的双共轭梯度(BiCGSTAB)方法等Krylov子空间迭代方法的收敛速度.     

Convergence of splitting and Newton methods for complementarity problems: An application of some sensitivity results

This paper is concerned with two well-known families of iterative methods for solving the linear and nonlinear complementarity problems. For the linear complementarity problem, we consider the class of matrix splitting methods and establish, under a finiteness assumption on the number of solutions, a necessary and sufficient condition for the convergence of the sequence of iterates produced. A rate of convergence result for this class of methods is also derived under a stability assumption on the limit solution. For the nonlinear complementarity problem, we establish the convergence of the Newton method under the assumption of a pseudo-regular solution which generalizes Robinson's concept of a strongly regular solution. In both instances, the convergence proofs rely on a common sensitivity result of the linear complementarity problem under perturbation.This work was based on research supported by the National Science Foundation under grant ECS-8717968.     

PHOTOCATALYTIC HYDROGEN EVOLUTION FROM WATER SPLITTING UNDER VISIBLE LIGHT IRRADIATION ON NOVEL PHOTOCATALYST FULLENES-PVP-ZN0.999NI0.001S

Fullerenes (C60/C70) linked up to Ni-doped ZnS through the medium of an amphalic polymer polyvinyl pyrrolidone (PVP) to form a new kind of photocatalyst for hydrogen evolution from aqueous Na2S/Na2SO3 solution under visible light irradiation, the photocatalytic activities of this novel photocatalyst C60/C70-PVP-Zn0.999Ni0.001S are 3-5 fold higher compared with that of precurse catalyst Zn0.999Ni0.001S. This result could be attributed to Schottky barrier layer built between C60/C70 and Zn0.999Ni0.001S due to the electro-negativity of C60 and characteristic of being used as a multiple electron acceptor. C60 or C60/C70, its moiety, with its low energy first excited singlet state, is a good energy acceptor and in addition readily accepts multiple electrons, making it a potential electron accumulate as we know, which could protect the separation between electrons and holes against combination. This is an important reason for the marked increase of amount of H2 evolution during the photocatalytic process for the composite system C60/C70-PVP-Zn0.999Ni0.001S.     

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利用太阳能光解水制氢和降解有机污染物对解决能源和环境问题具有重要意义，而可见光响应催化剂的研制是实现太阳光高效利用的关键。本文从可见光响应光催化剂的设计思路出发，从电子能带结构、固溶体结构和微观复合结构三方面介绍了目前光催化剂的研究进展和发展方向。     

对一个大单轴磁各向异性镍(Ⅱ)配合物中的磁跃迁的直接观察

最近Ruamps和同事发现三角双锥构型的Ni（Ⅱ）配合物[Ni（Me₆tren）Cl]ClO₄（1，Me₆tren=tris（2-（dimethylamino）ethyl）amine）具有大的单轴磁各向异性（J.Am.Chem.Soc.，2013，135：3017-3026）。他们利用HF-EPR研究获得横向零场分裂（ZFS）参数E=1.56（5）cm^-1但未能确定轴向零场分裂参数D。在本工作中，我们利用0~17.5 T和5 K的变磁场远红外光谱（FIRMS）来检测自旋基态S=1中的M_S=±1和M_S=0态之间的磁跃迁。在FIRMS中直接观察到Zeeman分裂态之间的跃迁，得出轴向ZFS参数D=-110.7（3）cm^-1。我们对1的晶体结构进行了Hirshfeld表面分析，揭示了1分子中的阳离子与阴离子之间以及分子之间的相互作用。     

Band splitting in overloaded isocratic elution chromatography I. The experimental evidence

A series of samples of increasing volume (from 0.001 to 4.0 cm3), containing the same constant concentration (40 g/l) of two simple compounds, ethylbenzoate and 4-tert.-butylphenol were injected on a Kromasil-C18 column with methanol-water (62:38. v/v) as the mobile phase. Complex band profiles were observed when the volume of the sample became large enough and strong band interference took place. The analysis of the fractions collected during the elution of the mixed band demonstrates that, for samples larger than 2 cm3, the band of 4-tert.-butylphenol is split into two separate bands, one eluted before and the other eluted after the band of ethylbenzoate. Such a phenomenon has never been observed yet in RPLC, under isocratic elution conditions.     

CdS nanocrystallites sensitized ZnO nanorods with plasmon enhanced photoelectrochemical performance

A sandwiched structure of CdS/Ag/ZnO nanorod photoanode exhibits greatly enhanced photoelectrochemical activity for solar hydrogen generation, due to synergistic effect of CdS nanocrystallites and plasmonic Ag nanoparticles for the enhanced optical absorption and the promoted charge carrier separation.     

Potential energy surfaces and nonadiabatic transitions in the asymptotic regions of ICN photodissociation to study the interference effects in the F1 and F2 spin-rotation levels of the CN products

One of the most spectacular yet unsolved problems for the ICN -band photodissociation is the non-statistical spin-rotation F₁ = N + 1/2 and F₂ = N − 1/2 populations for each rotation level N of the CN fragment. The F₁/F₂ population difference function f(N) exhibits strong N and λ dependences with an oscillatory behavior. Such details were found to critically depend on the number of open-channel product states, namely, whether both I (²P_3/2) and I (²P_1/2) are energetically available or not as the dissociation partner. First, in the asymptotic region, the exchange and dipole-quadrupole inter-fragment interactions were studied in detail. Then, as the diabatic basis, we took the appropriate symmetry adapted products of the electronic and rotational wavefunctions for the F₁ and F₂ levels at the dissociation limits. We found that the adiabatic Hamiltonian exhibits Rosen–Zener–Demkov type nonadiabatic transitions reflecting the switch between the exchange interaction and the small but finite spin-rotation interaction within CN at the asymptotic region. This non-crossing type nonadiabatic transition occurs with the probability 1/2, that is, at the diabatic limit through a sudden switch of the quantization axis for CN spin S from the dissociation axis to the CN rotation axis N . We have derived semiclassical formulae for f(N) and the orientation parameters with a two-state model including the 3A′ and 4A′ electronic states, and with a four-state model including the 3A′ through 6A′ electronic states. These two kinds of interfering models explain general features of the F₁ and F₂ level populations observed by Zare's group and Hall's group, respectively. © 2018 Wiley Periodicals, Inc.     

Dependence of Spin-orbit Parameters in Al_xGa_(1-x)N/GaN Quantum Wells on the Al Composition of the Barrier

In this paper, we obtain considerable spin-orbit (SO) parameters in AlxGa1-xN/GaN quantum wells (QWs) with sheet carrier concentration Ns=120×1011/cm2 . With increasing Al content (x) of the barrier, the SO parameters increase as a whole, and the two major contributions are found to be the decrease of the expansion region of the envelope functions and the increase of the polarized electric field in the well. Compared with the Rashba parameters for the first two subbands, the intersubband SO parameter is a bit smaller and varies more slowly with x. The results indicate the SO parameters, especially the Rashba parameters can be engineered by the Al composition of the barrier, which may be helpful to the spin manipulation of III-nitride low-dimensional heterostructures.     

TiO_2/CuPc/NiFe-LDH photoanode for efficient photoelectrochemical water splitting

Photoelectrochemical(PEC) water splitting is a promising approach for renewable hydrogen production.However,the practical PEC solar-to-fuel conversion efficiency is still low owing to poor light absorption and rapid recombination of charge carriers in photoelectrode.In this work,we report a ternary photoanode with simultaneously enhancement of light absorption and water oxidation efficiency by introducing copper phthalocyanine(CuPc) and nickel iron-laye red double hydroxide(NiFe-LDH) on TiO_2(denoted as TiO_2/CuPc/NiFe-LDH).An experimental study reveals that CuPc loading on TiO_2 bring strong visible light absorption;NiFe-LDH as an oxygen evolution reaction catalyst efficiently accelerates the surface water oxidation reaction.This synergistic effect of CuPc and NiFe-LDH gives enhanced photocurrent density(2.10 mA/cm2 at 0.6 V vs.SCE) and excellent stability in the ternary TiO_2/CuPc/NiFeLDH photoanode.