Isotropic Kähler structures on Engel 4-manifolds

Examples of isotropic Kähler manifolds (i.e., J²=0) which are neither complex nor symplectic, and therefore not indefinite Kähler, are constructed.     

The Selberg zeta function and a new Kähler metric on the moduli space of punctured Riemann surfaces

A local index theorem for families of -operators on Riemann surfaces with functures is proved. A new Kähler metric on the moduli space of punctured surfaces is described in terms of the Eisenstein-Maass series.     

Inequalities for the Casorati Curvature of Totally Real Spacelike Submanifolds in Statistical Manifolds of Type Para-Kähler Space Forms

The purpose of this article is to establish some inequalities concerning the normalized δ-Casorati curvatures (extrinsic invariants) and the scalar curvature (intrinsic invariant) of totally real spacelike submanifolds in statistical manifolds of the type para-Kähler space form. Moreover, this study is focused on the equality cases in these inequalities. Some examples are also provided.     

用于光催化领域的TiO_2与一维光量子阱复合结构的设计与优化

利用传输矩阵法设计并优化了用于光催化领域的TiO_2与一维光量子阱的复合结构,并分析了ZnS/SiO_2多层膜量子阱结构的透射特性.通过调节一系列的结构参数,在TiO_2光吸收波段(329.23 nm～482.71 nm)得到一个较宽的高反射率带隙,并且在吸收边附近(380 nm左右)得到了一个反射率高于93%的慢光子效应区.通过增加光线与TiO_2的作用时间和路径来提高光催化效率.     

Substituent effects on the reduction of 2–alkylcyclohexanones by LiAlH4: an investigation of conformational equilibria and transition states

Transition state (TS) structures for the reduction of 2‐Me and 2‐i‐Pr‐cyclohexanone by LiAlH₄ were optimized by density functional theory (B3LYP/6‐31G(d,p)). Four TS structures corresponding to axial and equatorial attacks by LiAlH₄ were located for each ketone conformer. Electronic potential maps were used to investigate the substituent electronic effect on the TS stabilization. The uneven carbonyl orbital distribution in the LUMO (π*) was also analyzed. Reduction stereoselectivity was shown to depend on both the ketone conformational ratio and on the reaction TS. Copyright © 2010 John Wiley & Sons, Ltd.     

Causal signal transmission by quantum fields. VI: The Lorentz condition and Maxwell’s equations for fluctuations of the electromagnetic field

The general structure of electromagnetic interactions in the so-called response representation of quantum electrodynamics (QED) is analysed. A formal solution to the general quantum problem of the electromagnetic field interacting with matter is found. Independently, a formal solution to the corresponding problem in classical stochastic electrodynamics (CSED) is constructed. CSED and QED differ only in the replacement of stochastic averages of c-number fields and currents by time-normal averages of the corresponding Heisenberg operators. All relations of QED connecting quantum field to quantum current lack Planck’s constant, and thus coincide with their counterparts in CSED. In Feynman’s terms, one encounters complete disentanglement of the potential and current operators in response picture.     

p‐toluenesulfonic acid‐catalyzed synthesis of polysubstituted quinolines via Friedländer reaction under ball‐milling conditions at room temperature and theoretical study on the mechanism using a density functional theory method

The synthesis of polysubstituted quinolines was accomplished through Friedländer annulation between 2‐aminoaryl ketones and different active methylene compounds at room temperature using ball‐milling technique in the presence of p‐toluenesulfonic acid. The mechanism of the reaction investigated by density functional theory‐based modeling is also reported. This study aims at giving insight into the mechanism of the Friedländer reaction in the presence of acid catalysts. Copyright © 2014 John Wiley & Sons, Ltd.     

Transmission characteristics including the coupling effect between normal and lateral degrees of freedom in step-barrier structures with a longitudinal magnetic field

In this paper we study the tunneling transport phenomena in a step-barrier structure under the influence of a longitudinal magnetic field, where the magneto-coupling effect is taken into account between the longitudinal motion component and the transverse Landau orbits of an electron. We also present numerical results of single square-barrier and asymmetrical double-barrier heterostructures for comparison. The results show that the coupling effect can play important role during the electronic tunneling process. It not only causes a significant shift of resonant peaks toward the low-energy region, but also enhances the transmission probability.     

Investigation of the role of oxygen in NO reduction by C2H4 on the surface of stepped Pt(3 3 2)

The influence of pre-dosed oxygen on NO–C₂H₄ interactions on the surface of stepped Pt(3 3 2) has been investigated using Fourier transform infrared reflection–absorption spectroscopy (FTIR-RAS) and thermal desorption spectroscopy (TDS). The presence of oxygen significantly suppresses the adsorption of NO on the steps of Pt(3 3 2), leading to a very specific adsorption state for NO molecules when oxygen–NO co-adlayers are annealed to 350 K (assigned as atop NO on step edges). An oxygen-exchange reaction also takes place between these two kinds of adsorbed molecules, but there appears to be no other chemical reaction, which can result in the formation of higher-valence NOx.

C₂H₄ molecules which are post-dosed at 250 K to adlayers consisting of ¹⁸O and NO do not have strong interactions with either the NO or the ¹⁸O atoms. In particular, interactions which may result in the formation of new surface species that are intermediates for N₂ production appear to be absent. However, C₂H₄ is oxidized to C¹⁸O₂ by ¹⁸O atoms at higher annealing temperature. This reaction scavenges surface ¹⁸O atoms quickly, and the adsorption of NO molecules on step sites is therefore quickly restored. As a consequence, NO dissociation on steps proceeds very effectively, giving rise to N₂ desorption which closely resembles that following only NO exposure on a clean Pt(3 3 2), both in peak intensity and desorption temperature. It is concluded that the presence of ¹⁸O₂ in the selective catalytic reduction (SCR) of NO with C₂H₄ on the surface of Pt(3 3 2) does not play a role of activating reactants.     

Control of the pulse width in a diode-pumped passively Q-switched Nd:YVO<Subscript>4</Subscript>/KTP green laser with GaAs saturable absorber

By varying the positions of the saturable absorber in the laser axis and the pump beam waist in the gain medium, respectively, we have theoretically and experimentally studied the control of the pulse width in a diode-pumped passively Q-switched Nd:YVO₄/KTP green laser with GaAs saturable absorber. A rate equation model is introduced, in which the intracavity photon density is assumed to be Gaussian spatial distribution, the longitudinal variation of the intracavity photon density and the pump beam spatial distribution are also considered. The experimental results are consistent with the numerical calculations of the rate equations.     

Studies of the crystal field energy levels and g factors for Ce in LiYF4 crystal

The five observed crystal field energy levels and EPR g factors g_//and g_⊥ for Ce³⁺-doped LiYF₄ crystal are calculated together from a complete diagonalization (of energy matrix) method. In the method, the contributions to g factors of ground Kramers doublet from all the rest doublets within the ground and excited manifolds ²F_5/2 and ²F_7/2 are included. The calculated results show reasonable agreement with the experimental values. The calculations suggest that the crystal field parameter B₂₀ > 0 in LiYF₄: Ce³⁺ crystal. The opinion of the parameter B₂₀ < 0 in the previous paper is not correct. Since this opinion is based on the calculation of g factors using a very simple method where only the contributions to g factors from the doublets within the ground manifold ²F_5/2 are considered, it is suggested that this simple method is not effective in the calculation of g factors for 4f¹ ions in crystals.     

Special solutions of the Fokker-Planck transport equation for arbitrary band structures; Mobility and diffusivity in a uniform field of force

A Fokker-Planck equation can be derived from a transition-type transport equation if the transition rates are nearly local in momentum space compared with the inhomogeneity length of the distribution. It is a second-order differential equation, whose coefficients depend on the band structureE(k), the viscosity tensor (k), and the temperatureT. Classical solutions of the Fokker-Planck equation deal with the parabolic band structure of free Brownian particles in a field of force. Mobility and diffusivity are then independent of the applied field. Here the explicit solution for the stationary state and the time-integrated conditional probability will be given in one dimension. This suffices to determine mobility and diffusivity. Assuming = 1, these quantities become independent of the field and the band structure, if the latter is nonperiodic, though the distribution still depends on it. This property even holds in three dimensions fork-independent viscosity tensors. Field-dependent mobility and diffusivity are obtained for ak-dependent viscosity or = 1 and periodic band structures. The latter is demonstrated for the caseE-cosk, which is also related to the noise problem in Josephson junctions.     

Cu1-xHxZr2(PO4)3中Cu2+的EPR谱和局域结构研究

本文采用Cu²⁺斜方对称电子顺磁共振（EPR）参量的高阶微扰公式计算了晶体Cu_1-xH_xZr₂（PO₄）₃中Cu²⁺的EPR参量（g因子和超精细结构常数A因子）．计算结果表明,晶体Cu_1-xH_xZr₂（PO₄）₃中[CuO₆]^10-基团的Cu-O键长分别为R_||≈0.241 nm,R_⊥≈0.215 nm,平面键角τ≈80.1°;由于对称性降低,中心金属离子基态²A_1g（θ）和²A_1g（ε）有一定程度混合,混合系数α≈0.995．所得EPR谱图的理论计算值与实验数据符合得很好．     

Al quadrupole interaction in zeolites loaded with probe molecules—a quantum-chemical study of trends in electric field gradients and chemical bonds in clusters

The electric field gradient (EFG) has been calculated in zeolite clusters at the aluminium site surrounded by four SiO₄ tetrahedra. Density functional theory (DFT) with the 6-31G^{* *} basis set has been employed. Formation of a Brønsted acid site by protonation of one oxygen atom of the A1O₄ tetrahedron perturbs the coordination of aluminium, i.e., the corresponding Al-O bond is considerably weaker than in the unprotonated case. This leads to a large EFG, and the calculated quadrupole coupling constant (QCC) for ²⁷Al is 18.2 MHz. Different probe molecules were adsorbed on the Brønsted site. The hydrogen bond formed between the acid proton and the probe molecule weakens the zeolitic O---H bond. For conservation of the overall bond order of the oxygen atom, its bonds to the neighboring tetrahedral atoms (Si, Al) become stronger. As a consequence, the perturbation of the AlO₄ tetrahedron and the EFG at the aluminium position decrease depending on the strength of the hydrogen bond. Perturbation of an oxygen atom of the AlO₄ tetrahedron by accepting a hydrogen bond from the base molecule also affects the corresponding AlO---O bond order. A linear correlation is found between the calculated QCC constants for ²⁷Al and the AlO---O bond orders of the oxygen atoms which are perturbed by protonation or by hydrogen bonds. A geometrical shear strain parameter and a simple electrostatic point charge model are less successful at predicting the trends in EFG which clearly shows the importance of the chemical bonds. Published by Elsevier Science B.V.     

MgmBn(m=1,2;n=1—4)团簇结构与性质的密度泛函理论研究

用密度泛函理论(DFT)的杂化密度泛函B3LYP方法在6-31G基组水平上对Mg_mB_n(m=1,2;n=1-4)团簇各种可能的构型进行几何结构优化，预测了各团簇的最稳定结构.并对最稳定结构的振动特性、电离势、成键特性、极化率和超极化率等性质进行了理论研究.结果表明，团簇的最稳定结构大多是平面结构，团簇的稳定结构中通常是几个呈负电性的B原子形成一个负电中心，而其他B原子和Mg原子通常处在端位，且显正电性；团簇中通常是B-B键和B-Mg键共存，极少出现Mg-Mg键， 关键词： mB_n(m=1')" href="#">Mg_mB_n(m=1 n=1-4)团簇 密度泛函理论 结构与性质     

Thermal reaction of electron deficient 4‐oxo‐4H‐pyrazole 1,2‐dioxide with cycloheptatriene: the first examples of the formation of an endo‐[4π + 6π]‐cycloadduct and an intramolecular 1,3‐dipolar reaction leading to a heterocage

The reaction of 3,5‐bis(methoxycarbonyl)‐4‐oxo‐4H‐pyrazole 1,2‐dioxide (1a) with 1,3,5‐cycloheptatriene (2b) gave a mixture of the novel endo‐[4 + 6]‐cycloadduct (4ab), anti‐exo‐[4 + 2]‐cycloadduct (5ab), and the heterocage (6ab) derived from the intramolecular 1,3‐dipolar cycloaddition reaction of the syn‐endo‐[4 + 2]‐cycloadduct. Analogous endo‐[4 + 6] selectivity in 1,3‐dipolar cycloadditions has not been reported previously. The X‐ray analysis indicates that 6ab has a very long N_sp3–N_sp3 bond distance of 1.617(4) Å. The cycloaddition behaviour is discussed on the basis of transition‐state structures optimized at the B3LYP/6‐31G(d) level of theory, from which predictions of the peri‐, regio‐, and stereoselectivities agreed well with the experimental results. Copyright © 2012 John Wiley & Sons, Ltd.     

Investigations of the spin-Hamiltonian parameters and defect structures for Gd ions in YMO4 (M=V, P, As) crystals

A 56×56 energy matrix containing the ground multiplet ⁸S_7/2 and the excited multiplets ⁶L_7/2 (where L=P, D, F, G, H, I) for 4f⁷ ion Gd³⁺ at a tetragonal crystal field and under an external magnetic field is constructed. By diagonalizing the energy matrix, the spin-Hamiltonian parameters (g factors g_‖, g_⊥ and zero-field splittings b₂⁰, b₄⁰, b₄⁴, b₆⁰, b₆⁴) for Gd³⁺ ion at the tetragonal Y³⁺ site of YMO₄ (M=V, P, As) crystals are calculated. The calculated results are in reasonable agreement with the experimental values. The defect structures of Gd³⁺ centers in YMO₄ crystals are estimated from the calculation. The results are discussed.