Positive ground state solutions for Schrödinger–Poisson system with critical nonlocal term in ℝ3

This paper is dedicated to studying the following Schrödinger–Poisson system $$\left\{\begin{array}{ll}-\mathrm{\Delta }u+V(x)u-K(x)\varphi |u{|}^{3}u=a(x)f(u),& x\in {ℝ}^3,\\ -\mathrm{\Delta }\varphi =K(x)|u{|}^5,& x\in {ℝ}^3.\end{array}\right.$$ Under some different assumptions on functions V(x), K(x), a(x) and f(u), by using the variational approach, we establish the existence of positive ground state solutions.     

Ni(111)表面一氧化碳和氢共吸附的密度泛函理论研究

本文用密度泛函理论(DFT)的总能计算研究了一氧化碳和氢原子在Ni(111)表面上p(2×2)共吸附系统的原子结构和电子态，结果表明CO和H原子分别被吸附于两个对角p(1×1)元胞的hcp和fcc位置.以氢分子和CO分子作为能量参考点，总吸附能为2.81 eV，相应的共吸附表面功函数φ为6.28 eV.计算得到的C—O，C—Ni和H—Ni的键长分别是1.19?, 1.96?和 1.71?，并且CO分子以C原子处于hcp的谷位与金属衬底原子结合.衬底Ni(111)的最外两层的晶面间距在吸附后的相对变化分别是 关键词： Fisher-Tropsch反应 催化作用 Ni(111) p(2×2)/(CO+H) 共吸附     

关于四元数矩阵乘积迹的不等式

设 H~(m×n)为 m×n 四元数矩阵的集合,σ_1(A)≥…≥σ_n(A)为 A∈H~(mxn)的奇异值。本文证明了:1)设 A∈H~(mxm),B∈H~(mxm),r=min(m,m),则|tr(4B)|≤c r σ_i(A)σ_i(B).2)设 A_i∈H~(mxm),i=1,2,…,n,(A_1A_2…A_n)k为 A_1A_2…A_n 的任一个 k 阶主子阵,则|tr(A_1.A_2…A_n)_k|≤sun form i=1 to k σ_i(A_1)…σ_i(A_n).我们还得到四元数矩阵迹的其它一些不等式。这些结果推广和改进了文[1],[2]中的结果,进一步解决了 Bellman 猜想。     

Anti-BZ-Structure in Effect Algebras

The definitions of sharply approximating effect algebras, anti-BZ-effect algebras, central approximating effect algebras, and S-anti-BZ-effect algebras are given, the relationships between sharply approximating effect algebras and anti-BZ-effect algebras, between central approximating effect algebras and anti-BZ-effect algebras are established, and the set of anti-BZ-sharp elements in S-anti-BZ-effect algebras is proved to be an orthomodular lattice.     

Vasiek利率模型下住房抵押贷款保证险的鞅定价

利用期权定价理论和鞅方法 ,分析了 Vasic∨ ek利率模型下住房抵押贷款保证险的定价问题 ,得到了全额担保和部分担保两类住房抵押贷款保证险的无套利定价公式 ,其中房价服从一般的扩散过程 .     

Synthesis,characterization, and curing kinetics of novel ladder‐like polysilsesquioxanes containing side‐chain maleimide groups

Two ladder‐like polysilsesquioxanes (LPS) containing side‐chain maleimide groups have been synthesized successfully by reacting N‐(4‐hydroxyphenyl)maleimide (HPM) with LPS containing 100 mol % of chloropropyl groups (Ladder A ) and 50 mol % of each methyl and chloropropyl group (Ladder B ). HPM was synthesized by reacting maleic anhydride with 4‐aminophenol, and the resulting amic acid was imidized using p‐toluenesulfonic acid as a catalyst (Scheme 1 ). The LPSs were characterized by Fourier transform infrared (FTIR), ¹H nuclear magnetic resonance (NMR), proton‐decoupled ¹³C NMR, ²⁹Si NMR, wide‐angle X‐ray diffraction (WAXD), differential scanning calorimetry (DSC), and thermogravimetric analysis (TGA). Characterization indicated that these polymers had ordered ladder‐like structures with possible defects. These polymers were soluble in common solvents at ambient temperature, which suggested that they were not crosslinked. Both the polymers and the HPM were cured, and their kinetics were followed by dynamic DSC. The Ozawa and Kissinger methods were used to calculate activation energies for curing. Curing increased the temperature at which both 5% weight loss and maximum rate of weight loss were observed. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 4036–4046, 2004     

具有奇异值分解性质的代数

设F为一个域,R为一个带有对合的F-代数,如果R上每一个矩阵都有奇异值分解(简称SVD),则称R为一个有SVD性质的F-代数.本文指出:R为一个有SVD性质的F-代数的充要条件是:R同构于R~+,或R~+上二次扩域,或R~+上四元数体((-1,-1)/R~+),其中R~+为R的对称元集合,并且R~+为一个Galois序闭域.     

三种群食物链交错扩散模型的整体

本文应用能量估计方法和Gagliardo-Nirenberg型不等式证明了一类强耦合反应扩散系统整体解的存在性和一致有界性，该系统是带自扩散和交错扩散项的三种群Lotka-Volterra食物链模型．通过构造Lyapunov函数给出了该模型正平衡点全局渐近稳定的充分条件．     

二维正方各向异性碲圆柱光子晶体完全禁带中缺陷模的FDTD计算分析和设计

用FDTD方法计算了二维正方晶胞各向异性碲圆柱光子晶体的点缺陷模.为了得到TE,TM模式在完全禁带中具有相同共振频率的缺陷模,对中心点缺陷半径Rd以及中心附近对称位置的点缺陷半径Rn做了一系列微调.计算表明,TM模对于Rn的变化不敏感,而TE模随着Rn的改变出现了明显的规则的移动趋势.通过计算分析,发现对应于f=0.4的背景(R=0.3568a),当Rd=0.55a,Rn=0.26a时在完全禁带中TE和TM的缺陷模具有相同的共振频率ω0=0.2466ωe(其中ωe=2πca,a为晶格常数) 关键词： 时域有限差分法 光子晶体 缺陷模 各向异性     

Surface profile measurement of low-frequency vibrating objects using temporal analysis of fringe pattern

A simple and accurate algorithm (phase scanning method) is proposed for 3D surface contouring and dynamic response determination of a vibrating object. A sinusoidal fringe pattern is projected onto a low-frequency vibrating object by a programmable liquid crystal display projector. The fringe patterns are captured by a high-speed CCD camera with a telecentric gauging lens. Phase values are evaluated point by point using phase scanning method. From the phase values of each point on the object, the contour of the specimen at different instants of vibration can be retrieved. In this paper, a small vibrating coin is used to demonstrate the validity of the method and the experimental results are compared with test results on a stationary coin using four-step phase shifting and fast Fourier transform methods. The technique is especially useful in applications where the vibrating object has a complicated shape.