扰动Chebyshev结点上的Hermite－Fejer插值

本文发现当Ｃｈｅｂｙｓｈｅｖ结点产生某些扰动时，只要扰动量不超过，则基于扰动后的Ｃｈｅｂｙｓｈｅｖ结点的Ｈｅｒｍｉｔｅ－Ｆｅｊｅｒ插值过程仍然保持对［－１，１］上任意连续函数的一致收敛性，此外，文中还给出了这种收敛性的收敛速度估计。     

On Initial-boundary-value Problems for a Class of Systems of Quasi-linear Evolution Equations

In this paper the initial-boundary-value problems for pseudo-hyperbolic system of quasi-linear equations: {(-1)^Mu_{tt} + A(x, t, U, V)u_x^{2M}_{tt} = B(x, t, U, V)u_x^{2M}_{t} + C(x, t, U, V)u_x^{2M} + f(x, t, U, V) u_x^k(0,t) = ψ_{0k}(t), \quad u_x^k(l,t) = ψ_{lk}(t), \quad k = 0,1,…,M - 1 -u(x,0) = φ_0(x), \quad u_t(x,0) = φ_1(x) is studied, where U = (u_1, u_x,…,u_x^{2M - 1}) V = (u_t, u_{xt},…,u_x^{2M - 1_t}), A, B, C are m × m matrices, u, f, ψ_{0k}, ψ_{1k}, ψ_0, ψ_1 are m-dimensional vector functions. The existence and uniqueness of the generalized solution (in H² (0, T; H^{2M} (0, 1))) of the problems are proved.     

变分方法与反向上下解

本文在非线性方程的下解不小于上解这一条件（即反向上下解条件）下研究了其解的存在性．我们证明了，如果非线性算子方程有变分结构，有一对反向上下解，对应的算子映某个锥入锥并且满足一定的辅助条件，那么这一方程在锥中至少有两个解．另外，本文还研究了反向上下解条件下非线性椭圆边值问题正解的存在性．     

一类高阶线性微分方程解的增长性

研究了Aj（z）是整函数且σ（Aj）〈1,αj∈c＼{0}（j=0,1,…,k-1）,若存在某个αs（s≠0）,使argα,≠argαj（j≠s）,αi/αj=cij（i,j≠s,cij〉0）时,方程f^（k）＋…＋As（z）e^αx^zf^（s）＋…＋A0（z）e^α0^zf=0解的级及超级问题。     

基于偏序关系的Rough集模型及其应用

在标准Rough集理论的指导下,利用偏序关系性质构造了不同分类,并以此为基础探讨了上、下近似集,从而构建了基于偏序关系的Rough集模型。新模型将Rough集理论的应用范围由等价关系扩展到偏序关系。为了更好地增强模型的实用性和灵括性,一方面从程度、精度、概率等角度出发分别对其进行了扩展,另一方面引入依赖度使其适用于研究各种非严格的偏序关系。给出了实例分析,并结合现实生活中的现象阐述了模型的应用价值。     

考虑地表反射类型的气溶胶散射偏振特性

采用逐次阶散射法求解矢量辐射传输方程来研究气溶胶在不同地表反射模型下的散射偏振特性.首先,选取单一地表反射模型和耦合地表反射模型两种地表反射模型.然后,根据地表反射模型计算得到相应的地表反射率,进而采用逐次阶散射法对矢量辐射传输方程进行求解,得到散射光的Stokes矢量.最后,由Stokes矢量计算得出散射光的偏振度.仿真结果表明,两种地表反射模型下气溶胶单次散射的散射辐射强度和线偏振度均相等;耦合地表反射模型的总散射辐射强度和线偏振度总是大于单一地表反射模型;单一地表反射模型的气溶胶单次散射相对总散射的贡献总是大于耦合地表反射模型.研究结果对气溶胶光学特性的反演具有一定意义.     

Tunable magnetism through edge functionalization in zigzag green phosphorene nanoribbons

Ab initio density-functional theory calculations with spin polarization are performed to explore magnetic properties in zigzag green phosphorene nanoribbons (ZGPNRs) with no passivation or edge-saturated by H, OH and O chemical species. It is found that antiferromagnetic order at intra-edges is the most energetically favorable for the pristine and oxygen passivated ribbons, while H- or OH-saturated ZGPNRs show nonmagnetic order. It indicates that edge states arising from the unsaturated bonds are vital for the formation of the magnetic moment in the ZGPNRs. The magnitude of the edge magnetism in the pristine and O-saturated ZGPNRs is comparable to that in zigzag black phosphorene nanoribbons. Electronic band structures, spin densities and spd-orbital projected density of states for the studied pristine and O-passivated ZGPNRs are further analyzed to study their electronic properties. The magnetic and electronic properties discovered in the ZGPNRs may suggest potential applications in future spintronics and electronics.     

A note on testing for constant hazard against a change-point alternative

Summary The problem of testing for constant hazard against a change-point alternative is considered. It is shown that this problem is related to another one in quality control. Based on this relationship, a test is proposed. The main advantages of this test are its computational simplicity and the ready availability of small and large sample distribution theory.     

CuZnAl记忆合金有序转变的固体电子论分析

应用固体经验电子理论,并联系 G.Inden 的有序转变温度与原子间作用能的关系式,计算了 CuZnAl 记忆合金的 A_2到 B_2,B_2到 DO_3两种有序转变温度随合金元素变化的规律。计算得出的变化趋势与实验结果符合得相当好,表明所采用的理论模型可以说明 CuZnAl 合金的记忆性能和用来指导探索新的记忆合金。     

Neutron scattering by anharmonic crystals and the effect of sublattice displacements

A theory has been given for the scattering of neutrons by anharmonic crystals, for which terms of the typeV ⁽³⁾ (k _1j1; —k _1j1;o _j) which contribute to the sublattice displacements are not neglected. Using the standard perturbation theory in the interaction picture or Green’s function method, an expression has been derived for the differential scattering cross-section which brings in the shift and the width of the phonons in one-phonon energy exchange processes. It is shown that the sublattice displacements will modify the phase factor arising from the scattering by any atom in the unit cell, and the Debye-Waller factor also gets altered both by the sublattice displacements as well as by higher order terms arising from anharmonicity. It is shown that the differential scattering cross-section contains a term linearly depending on the third order anharmonicity coefficientV ⁽³⁾ (k _1j1;k _2j2;k _3j3) and neutron scattering by crystals should provide a useful method for evaluating the third order anharmonicity coefficients.