氧化铬外延薄膜的x射线研究

采用分子束外延技术(MBE)在MgO(001)基板上沉积了氧化铬薄膜，并利用x射线衍射 (XRD)和x射线反射谱(XRR)对薄膜的晶体结构进行了表征.θ—2θ扫描和倒易空间图(R SM)揭示出薄膜为单相c轴外延生长，晶体结构为体心正交，晶胞常数a，b，c分别为0.8940±0.0003，0.298±0.0002和0.3897±0.0002nm.扫描表明薄膜在面内具有90°孪晶，取向关系为a∥MgO〈110〉,c∥MgO(001).XRR谱测得薄膜的电子 密度为1350±20nm-3，与由晶胞体积 计算得 关键词： 一氧化铬薄膜 x射线衍射 倒易空间图 x射线反射谱     

Orientation relationship between α-Fe precipitate and α-Al2O3 matrix in iron-implanted sapphire

Fe ions were implanted into α-Al₂O₃ single crystals (sapphire) at room temperature and annealed in a reducing atmosphere. The orientation relationships (ORs) between α-Fe particles and sapphire matrix were investigated using transmission electron microscopy (TEM). All the α-Fe particles have the orientation relationship (OR) of (1 1 1)_α-Fe || (0 0 0 1)_sapphire and ${[1\overline{1}0]}_{\alpha \text{-Fe}}\left|\right|{[11\overline{2}0]}_{\text{sapphire}}$ with sapphire. This OR is predicted precisely by the coincidence of reciprocal lattice points (CRLP) method. The other OR of (1 1 0)_α-Fe || (0 0 0 1)_sapphire and ${[111]}_{\alpha \text{-Fe}}\left|\right|{[5\overline{1}\overline{4}0]}_{\text{sapphire}}$ reported before is confirmed by the same method to be one of the secondary preferred orientation relationships in the α-Fe/sapphire system.     

The Qiao--Liu Equation with Self-Consistent Sources and Its Solutions

The Qiao--Liu equation with self-consistent sources (QLESCS) and its Lax representation are derived. A reciprocal transformation for the QLESCS is given. By making use of the reciprocal transformation and the solutions of the mKdV equation with self-consistent sources (mKdVSCS), the solutions of the QLESCS are presented.     

On approximation by reciprocals of polynomials with positive coefficients in Orlicz spaces

This paper discusses the approximation by reciprocals of polynomials with positive coefficients in Orlicz spaces and proved that if f(x) ∈ LM*[0,1], changes its sign at most once in (0,1), then there exists x0 ∈ (0,1) and a polynomial Pn ∈ Πn(+) such that f (x) -Pn (x)x-x0 M ≤ Cω( f,n-1/2 )M, where Πn(+) indicates the set of all polynomials of degree n with positive coefficients.     

一对超标准互反关系及应用

The method of non-standard analysis(NSA) is used to construct a pair of hyperstandard reciprocal formulas involving certain non-standard difference operators with realnumber orders.Our main result consists of some extensions of earlier results appearing previously [5].An essential meaning of the paper is to indicate the fact that only the basic idea of NSA is applicable to the construction of a unified pattern that may have certain applications to both the analysis and the number theory.     

求解矩形夹层板在集中载荷下的稳定问题

在考虑了横向切应力和横向正应力对夹层板稳定影响的情况下,给出了矩形夹层板结构屈曲失稳的控制方程、基本解以及边界条件。应用功的互等定理求解了在均布载荷作用下的矩形夹层板的屈曲失稳问题。     

应用混合变量余能原理求解不同载荷作用下四边简支矩形板的弯曲

由功的互等定理导出了弯曲矩形板混合变量的总余能,应用混合变量余能原理求解四边简支矩形板弯曲问题,给出了四边简支矩形板的混合变量余能表达式,求解了不同载荷作用下四边简支矩形板的弯曲问题,并将计算的不同载荷作用下的挠度和弯矩值与ANSYS有限元的计算值比较,给出了一种求解四边简支矩形板的新方法。     

关于与广义Fibonacci,Lucas数有关的一些级数的注记

求出了一些与广义Fibonacci,Lucas数有关的一些倒数级数的值。     

A New Integrable Equation with Peakon Solutions

We consider a new partial differential equation recently obtained by Degasperis and Procesi using the method of asymptotic integrability; this equation has a form similar to the Camassa–Holm shallow water wave equation. We prove the exact integrability of the new equation by constructing its Lax pair and explain its relation to a negative flow in the Kaup–Kupershmidt hierarchy via a reciprocal transformation. The infinite sequence of conserved quantities is derived together with a proposed bi-Hamiltonian structure. The equation admits exact solutions as a superposition of multipeakons, and we describe the integrable finite-dimensional peakon dynamics and compare it with the analogous results for Camassa–Holm peakons.     

Student-like models for risky asset with dependence

We present a new construction of the Student and Student-like fractal activity time model for risky asset. The construction uses the diffusion processes and their superpositions and allows for specified exact Student or Student-like marginal distributions of the returns and for flexible and tractable dependence structure. The fractal activity time is asymptotically self-similar, which is a desired feature seen in practice.