四阶和一般偶数阶奇异边值问题正解的存在性

在本文中得到了四阶和一般偶数阶非线性方程奇异边值问题正解的存在性。从而推广了［１］［２］中的结果。     

Q_k(x)与F_k(x)的渐近公式

设ｎ，ｋ为自然数，Ｇ（ｎ）阶群中的同构类数，Ｆｋ（ｘ）与Ｑｋ（ｘ）分别表示不超过ｘ的自然数中使Ｇ（ｎ）＝ｋ的自然数、无平方因子自然数的个数．本文的目的是用Ｂｒｕｎ筛法证明Ｑｋ（ｘ）的条件渐近公式并对Ｆｋ（ｘ）的渐近性质做出了推测．     

Study of photoreaction in dichromated gelatin by laser photoacoustic technique

 An experimental method to study the photochemical reaction in solid-state dichromated gelatin during exposure is proposed, in which two laser sources with different wavelengths are used to induce photoreaction and to excite photoacoustic signal, respectively. This method is to obtain the real-time characteristics during the formation of the photoreaction product. The curve is fitted using the Rosencwaig-Gersho (R-G) theory and chemical kinetics. The reaction order and the rate of reaction may be obtained by fitting the parameters. The results show that photochemical reaction in dichromated gelatin conforms to the mechanism suggested by Watanable-Westheimer, and the photosensitivity of the samples, prepared under different conditions, is dependent on the initial concentration of photoactive ions. Received: 18 April 1995/Revised version: 3 May 1996     

一个内生人口生育率可解的C-K模型

得到一个具有可解内生人口出生率的Ｃａｓｓ－Ｋｏｏｐｍａｎｓ经济增长模型．给出此模型在不同劳动和资本的结合方式下存在唯一最优增长轨道和稳态解的条件．最后讨论存在多重最优增长轨道和多重稳态解的可能性态和文中主要结果的经济意义．     

Electronic structures of Fe in La1−x Ba x FeO3−y (0≤x≤0.70)

Mössbauer spectra of La_1–x Ba _x FeO_3–y recorded at room temperature for various values of x show a six-line and/or a single-line subspectrum. The six-line subspectrum with IS=0.41 mm/s and H=52 T results from an orthorhombic perovskite containing only Fe³⁺ ions. The single-line subspectrum at 0.17 mm/s from a cubic perovskite can be assigned to neither Fe³⁺ nor Fe⁴⁺ but to an intermediate valence state, which may be due to electron hopping between the Fe³⁺ and Fe⁴⁺ ions on the identical octahedral sites. The temperature dependence of electron hopping in the compound La_0.40Ba_0.60FeO_3–y is presented.     

一种非连续纳米氧化层自旋阀的显微结构研究

利用高分辨电子显微学方法(HREM)研究了纳米氧化层镜面反射自旋阀多层结构Ta(35nm)Ni80Fe20(2nm)Ir17Mn83(6nm)Co90Fe10(15nm)NOL1Co90Fe10(2nm)Cu(22nm)Co90Fe10(15nm)NOL2Ta(3nm).该自旋阀的巨磁电阻(GMR)效应高达15%,较无此镜面反射纳米氧化层(NOL)的自旋阀提高近1倍,同时交换偏置场亦有所增强.高分辨显微结构分析表明,介于钉扎层与被钉扎层之间的氧化层(NOL1)并未完全氧化,即除氧化过程生成的CoFe氧化物 关键词： 自旋阀 纳米氧化层 高分辨电子显微学 巨磁电阻效应     

A note on the efficiency of the conjugate gradient method for a class of time‐dependent problems

We discuss the efficiency of the conjugate gradient (CG) method for solving a sequence of linear systems; Auⁿ⁺¹ = uⁿ, where A is assumed to be sparse, symmetric, and positive definite. We show that under certain conditions the Krylov subspace, which is generated when solving the first linear system Au¹ = u⁰, contains the solutions {uⁿ} for subsequent time steps. The solutions of these equations can therefore be computed by a straightforward projection of the right‐hand side onto the already computed Krylov subspace. Our theoretical considerations are illustrated by numerical experiments that compare this method with the order‐optimal scheme obtained by applying the multigrid method as a preconditioner for the CG‐method at each time step. Copyright © 2007 John Wiley & Sons, Ltd.