Bayes分析中多源验前信息融合的ML-II方法

在Bayes小子样理论中,验前分布的获取和表示是一个关键问题.针对工程实践中遇到的验前信息的多源性,给出了一种基于第二类极大似然估计原理(M L-II)的多源异总体验前分布的融合方法,并通过仿真实例证明了该方法的有效性.     

Bi，Sb及稀土元素对AZ91镁合金高温性能影响机理研究

利用大角重位点阵概念建立了AZ91镁合金基体(α相)和镁［0001］对称倾斜晶界原子结构模型,应用实空间的连分数方法计算了体系的结构能,环境敏感镶嵌能以及相互作用能.结果发现,在镁合金基体中,Al和稀土形成团簇时比较稳定,Al,Bi或Sb与稀土形成团簇时不稳定.Bi或Sb和稀土元素同时存在于AZ91镁合金中时,一方面Bi或Sb将可与RE结合形成RE₂Bi(RE₂Sb)或RE-Bi(RE-Sb)化合物弥散分布于晶界,另一方面镁合金基体中会形成Al_{11关键词： 电子理论 晶界偏聚 合金元素 高温性能}     

Pair interaction of bilayer-coated nanoscopic particles

The pair interaction between bilayer membrane-coated nanosized particles has been explored by using the self-consistent field (SCF) theory. The bilayer membranes are composed of amphiphilic polymers. For different system parameters, the pair-interaction free energies are obtained. Particular emphasis is placed on the analysis of a sequence of structural transformations of bilayers on spherical particles, which occur during their approaching processes. For different head fractions of amphiphiles, the asymmetrical morphologies between bilayers on two particles and the inverted micellar intermediates have been found in the membrane fusion pathway. These results can benefit the fabrication of vesicles as encapsulation vectors for drug and gene delivery.     

Simulation study on terahertz vibrational absorption in liquid crystal compounds

The terahertz (THz) spectrum absorptions of nematic liquid crystal (LC) material, i.e. N-(p-methoxybenzylidene)-p-butylaniline (MBBA), and its relevant compounds are simulated in this paper by using the density functional theory (DFT) method. A strong absorptive frequency is located at 3.65 THz for the MBBA, which is in agreement with experimental data found in the literature. The result suggests that the DFT method is effective for dealing with the anisotropic nematic LC compounds.     

Complete Solutions and Extremality Criteria to Polynomial Optimization Problems

This paper presents a set of complete solutions to a class of polynomial optimization problems. By using the so-called sequential canonical dual transformation developed in the author’s recent book [Gao, D.Y. (2000), Duality Principles in Nonconvex Systems: Theory, Method and Applications, Kluwer Academic Publishers, Dordrecht/Boston/London, xviii + 454 pp], the nonconvex polynomials in can be converted into an one-dimensional canonical dual optimization problem, which can be solved completely. Therefore, a set of complete solutions to the original problem is obtained. Both global minimizer and local extrema of certain special polynomials can be indentified by Gao-Strang’s gap function and triality theory. For general nonconvex polynomial minimization problems, a sufficient condition is proposed to identify global minimizer. Applications are illustrated by several examples.     

钙钛矿结构材料Sr8CaRe3Cu4O24压力效应的研究

 基于密度泛函理论,运用局域轨道密度近似+哈伯德相互作用和平均场方法,研究了新型钙钛矿结构材料Sr₈CaRe₃Cu₄O₂₄在不同压强下的机械、电磁性质,并探讨该材料的居里温度T_C随压强变化的规律。计算结果表明：T_C随着压强的增加而升高,费米面附近能隙逐渐减小。最后通过海森伯模型对此作出了较为合理的解释。     

Au和3d过渡金属元素混合团簇结构、电子结构和磁性的研究

采用基于密度泛函理论的第一性原理方法系统研究了Au与3d过渡元素构成的混合小团簇的结构、稳定性、电子结构及磁性,得到了Au与3d过渡元素构成的混合小团簇的稳定结构.计算结果表明,Au与3d元素可形成大量的低能异构体,特别是有些异构体在结构上极相近,这不同于共价或离子键类型的团簇.与纯过渡金属团簇类似,这类团簇也表现出复杂的磁性.过渡金属元素的磁矩相比体材料而言既有增强的、也有减弱的,与轨道的交换劈裂密切相关.对于基态构型,AuCr₂,Au₂Cr_{2关键词： 密度泛函理论 第一性原理方法 团簇 电子结构}     

耦合相对转动非线性动力系统的稳定性与近似解

研究了一类含三次非线性耦合项的相对转动非线性动力系统的动力学行为. 建立了具有非线性弹性力、广义摩阻力耦合项的系统动力学方程. 运用多尺度法求解谐波激励下耦合非自治系统的近似解,通过讨论系统的主共振和内共振特性,分析了耦合项对系统响应的影响. 应用奇异性理论研究了主振稳态响应分岔方程的稳定性,得到了系统的转迁集和分岔曲线的拓扑结构. 关键词： 相对转动 非线性耦合动力系统 奇异性理论 稳定性     

Admissible Galois Structures and Coverings in Regular Mal’cev Categories

Given a regular Gumm category such that any regular epimorphism is effective for descent, we prove that any Birkhoff subcategory in gives rise to an admissible Galois structure. This result allows one to consider some new applications of the categorical Galois theory in the context of topological algebras. Given a regular Mal’cev category , we first characterize the coverings of the Galois structure induced by the subcategory of the abelian objects in . Then we consider as a subcategory of the category of the equivalence relations in , and we characterize the coverings of the corresponding Galois structure . By composing the Galois structures and we obtain the Galois structure induced by as a subcategory of . We give the characterization of the -coverings in terms of the coverings of and .     

General Theory of Acoustic Wave Propagation in Liquids and Gases

We study the propagation of small-amplitude acoustic waves in liquids and gases and use the hydrodynamic equations to obtain an exact dispersion equation. This equation in dimensionless variables contains only two material constants p and q. We solve the dispersion equation, obtaining an exact solution that holds for all values of the parameters and all frequencies up to hypersonic, and thus analytically establish exactly how the speed of sound c, the wave vector k, and the damping factor x depend on the frequency ω and the dimensionless material constants p and q. Studying the behavior of the solution in the sonic and ultrasonic frequency bands for ω < 10⁷ sec^-1 results in an expression for the damping factor, which differs from the Kirchhoff formula. The speed of sound c and the wave vector k are shown to have finite nonzero values for all hypersonic frequencies. At the same time, there exists a certain maximum frequency value, ω_max ≈ 10¹¹-10¹² sec^-1, at which the damping factor x is zero. This frequency determines the boundary of the applicability domain for the hydrodynamic equations. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 146, No. 2, pp. 340–352, February, 2006.