An asymptotic property of gap series

Takahashi [15] gave a concrete upper bound estimate of the law of the iterated logarithm for ∑ f(n _k x). We extend this result and prove the best possibility of this bound. This revised version was published online in August 2006 with corrections to the Cover Date.     

一维光子晶体带隙随偏振光入射角的演变

用特征矩阵方法得到了一维光子晶体的反射率计算公式,并以λ/4波片堆结构为例对不同入射角度下p偏振光和s偏振光的反射率进行了计算,分析了两种不同偏振光入射情况下光子带隙随入射角演化的特点.     

Spontaneous emission spectrum of a four-level atom in a double-band photonic crystal

The spontaneous emission spectrum from a four-level atom in a double-band photonic crystal has been investigated.We use the model which assumes three atomic transitions. One of the transitions interacts with the free vacuum modes,and the other two transitions couple to the modes of the isotropic photonic band gap (PBG), the anisotropic PBG and another free vacuum. The effects of the fine structure of the lower levels on the spontaneous emission spectrum of an atom are investigated in detail in the three cases. New features of four (two) transparencies with two (one) spontaneous emission peaks, resulting from the fine structure of the lower levels of an atom, are predicted in the case of isotropic PBG modes.     

Gap Functions and Existence of Solutions to Set-Valued Vector Variational Inequalities

The variational inequality problem with set-valued mappings is very useful in economics and nonsmooth optimization. In this paper, we study the existence of solutions and the formulation of solution methods for vector variational inequalities (VVI) with set-valued mappings. We introduce gap functions and establish necessary and sufficient conditions for the existence of a solution of the VVI. It is shown that the optimization problem formulated by using gap functions can be transformed into a semi-infinite programming problem. We investigate also the existence of a solution for the generalized VVI with a set-valued mapping by virtue of the existence of a solution of the VVI with a single-valued function and a continuous selection theorem.     

Relationship between orbital energy gaps and excitation energies for long‐chain systems

The difference between the excitation energies and corresponding orbital energy gaps, the exciton binding energy, is investigated based on time‐dependent (TD) density functional theory (DFT) for long‐chain systems: all‐trans polyacetylenes and linear oligoacenes. The optimized geometries of these systems indicate that bond length alternations significantly depend on long‐range exchange interactions. In TDDFT formalism, the exciton binding energy comes from the two‐electron interactions between occupied and unoccupied orbitals through the Coulomb‐exchange‐correlation integral kernels. TDDFT calculations show that the exciton binding energy is significant when long‐range exchange interactions are involved. Spin‐flip (SF) TDDFT calculations are then carried out to clarify double‐excitation effects in these excitation energies. The calculated SF‐TDDFT results indicate that double‐excitation effects significantly contribute to the excitations of long‐chain systems. The discrepancies between the vertical ionization potential minus electron affinity (IP–EA) values and the HOMO–LUMO excitation energies are also evaluated for the infinitely long polyacetylene and oligoacene using the least‐square fits to estimate the exciton binding energy of infinitely long systems. It is found that long‐range exchange interactions are required to give the exciton binding energy of the infinitely long systems. Consequently, it is concluded that long‐range exchange interactions neglected in many DFT calculations play a crucial role in the exciton binding energies of long‐chain systems, while double‐excitation correlation effects are also significant to hold the energy balance of the excitations. © 2016 Wiley Periodicals, Inc.     

Fluoride-assisted synthesis of anatase TiO2 nanocrystals with tunable shape and band gap via a solvothermal approach

A simple solvothermal approach employing oleic acid has been developed to prepare anatase TiO₂ nanocrystals with different shapes, which were tuned from nanorods to nano-ellipsoids by increasing the amount of NaF from 0 to 0.5 mmol, and the optical band gap decreased from 3.47 eV to 3.29 eV accordingly. However, when the fluoride was changed to NH₄F, the resultant TiO₂ nanocrystals possessed an anatase phase but weremade up of smaller-sized nanocrystals and nanorods, and the band gap was increased to 3.53 eV. The X-ray photoelectron spectroscopy (XPS) results illustrated an increase of fluorine content with an increasing amount of NaF could account for the variation of the shape and optical band gap of TiO₂ nanocrystals. Moreover, the absence of fluorine content brought about less change of shape and increase of optical band gap of the product synthesized in the presence of NH₄F. This result may offer another way to alter the shape and band gap of metal oxide nanocrystals with the assistance of fluoride.     

PHM技术国内外发展情况综述

随着现代武器装备复杂化、综合化、智能化程度的不断提高,传统的故障诊断技术难以适应新的需求。为了满足信息化战争对武器装备作战效能和快捷、精准、持续保障的要求,20世纪90年代中期,PHM(故障预测与健康管理)技术应运而生。从发展概况、应用成效、PHM验证评价、典型案例分析以及发展规划5个方面总结了国外PHM技术发展的应用成效;并对国内PHM技术的基础理论、工程技术与应用方面的发展状况进行了总结;通过对比国内外PHM技术的发展应用现状,总结分析了目前国内PHM技术发展现状与国外先进水平之间的差距以及未来发展的借鉴启示。     

Fundamental absorption edge and normal dispersion of β-LiNaSO4 single crystal

Lithium sodium sulfate (LiNaSO₄)single crystal is synthesized and grown by the slow evaporation of supersaturated aqueous solution at constant temperature (303 K). Powder X-ray diffraction is measured at room temperature in order to identify the grown crystal. Transmittance and reflectance measurements are used to study the optical properties of this crystal at room temperature phase (β-LiNaSO₄). The type of transition is determined. The values of optical energy gap, phonon energy and phonon equivalent temperature are calculated. Refractive index and extinction coefficient are calculated as functions of photon energy. The obtained optical data of β-LiNaSO₄ crystal are used to check the validity of both Wemple-DiDomenico and Cauchy-Sellimaier dispersion relations. Normal dispersion parameters of this crystal are calculated for the first time.     

Long cycles in graphs without hamiltonian paths

For a graph G, p(G) and c(G) denote the order of a longest path and a longest cycle of G, respectively. Bondy and Locke [J.A. Bondy, S.C. Locke, Relative length of paths and cycles in 3-connected graphs, Discrete Math. 33 (1981) 111-122] consider the gap between p(G) and c(G) in 3-connected graphs G. Starting with this result, there are many results appeared in this context, see [H. Enomoto, J. van den Heuvel, A. Kaneko, A. Saito, Relative length of long paths and cycles in graphs with large degree sums, J. Graph Theory 20 (1995) 213-225; M. Lu, H. Liu, F. Tian, Relative length of longest paths and cycles in graphs, Graphs Combin. 23 (2007) 433-443; K. Ozeki, M. Tsugaki, T. Yamashita, On relative length of longest paths and cycles, preprint; I. Schiermeyer, M. Tewes, Longest paths and longest cycles in graphs with large degree sums, Graphs Combin. 18 (2002) 633-643]. In this paper, we investigate graphs G with p(G)−c(G) at most 1 or at most 2, but with no hamiltonian paths. Let G be a 2-connected graph of order n, which has no hamiltonian paths. We show two results as follows: (i) if , then p(G)−c(G)≤1, and (ii) if σ₄(G)≥n+3, then p(G)−c(G)≤2.     

An almost sure scaling limit theorem for Dawson-Watanabe superprocesses

We establish a scaling limit theorem for a large class of Dawson-Watanabe superprocesses whose underlying spatial motions are symmetric Hunt processes, where the convergence is in the sense of convergence in probability. When the underling process is a symmetric diffusion with -coefficients or a symmetric Lévy process on Rd whose Lévy exponent Ψ(η) is bounded from below by cα|η| for some c>0 and α∈(0,2) when |η| is large, a stronger almost sure limit theorem is established for the superprocess. Our approach uses the principal eigenvalue and the ground state for some associated Schrödinger operator. The limit theorems are established under the assumption that an associated Schrödinger operator has a spectral gap.