Refraction of light in media

The roles of the magnetic field and electric field of the light are investigated when the light is refracted in the medium. The model of the electron cloud conductor is presented. Electron cloud in a molecule is treated as a conductor and the Faraday’s Law is applied to this conductor that is in the alternating magnetic field of the light. dB _M/dt of the light gives rise to an alternating induced current on the electron cloud conductor, and the light exchanges energy, i.e. the refractive energy, with the electron cloud conductor. Formulas of refractive index, which is the ratio of light speed in vacuum to that in the medium, are derived with this model. These formulas are tested with several mediums and Langevin’s diamagnetic susceptibility of helium gas, and the results are in good agreement with the measured data. The anisotropy and the nonlinearity of the refractive index are explained with the theory described in this work. Supported by Beijing Science and Technology New Star Program (Grant No. 952870400), the Beijing Municipal Commission of Education and the Excellent Young Teachers Program of Ministry of Education of China     

Practical stopping criteria for validating safety-critical software by estimating impartial reliability

In this research, we investigate stopping rules for software testing and propose two stopping rules from the aspect of software reliability testing based on the impartial reliability model. The impartial reliability difference (IRD-MP) rule considers the difference between the impartial transition-probability reliabilities estimated for both software developer and consumers at their predetermined prior information levels. The empirical–impartial reliability difference (EIRD-MP) rule suggests stopping a software test when the computed empirical transition reliability is tending to its estimated impartial transition reliability. To insure the high-standard requirement for safety-critical software, both rules take the maximum probability (MP) of untested paths into account.     

火工品可靠性试验数据的综合分析方法

升降法试验数据和固定刺激量下的成败型试验数据,是两种最常见的火工品可靠性试验数据．我们应用Markov链,研究了升降法试验数据下,感度分布参数的极大似然估计的特性．在此基础上,应用Bootstrap方法和Bayes方法,给出了综合分析两种试验数据的方法．最后,将该方法应用于520底火的可靠性鉴定,得出了有益的结论．     

Converged properties of clean metal surfaces by all-electron first-principles calculations

All-electron full-potential linearized augmented plane-wave calculations of the surface energy, work function, and interlayer spacings of close-packed metal surfaces are presented, in particular, for the free-electron-like metal surfaces, Mg(0 0 0 1) and Al(1 1 1), and for the transition metal surfaces, Ti(0 0 0 1), Cu(1 1 1), Pd(1 1 1), and Pt(1 1 1). We investigate the convergence of the surface energy as a function of the number of layers in the slab, using the Cu(1 1 1) surface as an example. The results show that the surface energy, as obtained using total energies of the slab and bulk from separate calculations, converges well with respect to the number of layers in the slab. Obviously, it is necessary that bulk and surface calculations are performed with the same high accuracy. Furthermore, we discuss the performance of the local-density and generalized gradient approximations for the exchange-correlation functional in describing the various surface properties.     

Cyclic cohomology and algebra extensions

We construct a spectral sequence to study cyclic cohomology for an extension A = R/I of algebras. When R is a free algebra we describe the cyclic cohomology of A in terms of traces defined on R or powers of I. Explicit cyclic cocycles representing the cyclic cohomology class belonging to the trace are constructed as analogues of Chern character and Chern-Simons forms.Dedicated to Alexander Grothendieck     

多约束下的串、并联混合系统可靠度与冗余度的优化判定模型及算法

本文给出了单目标多约束下串、并联混合系统中 ,由选取重要单元 (重要度最大的单元 )的方法 ,来提高系统可靠度的有效优化判定模型及算法 ,用同样思想给出了串、并联系统中冗余度的优化判定模型及算法     

Generalized indices of operators inB(H)

A generalized dimension is further developed. Here subtraction and addition of two generalized dimensions are defined, so that the operations: ∞ ± n = ∞, ∞ + ∞ = ∞, which used to play an inflexible role, are refined and moreover, ∞ - ∞, which used to be meaningless, is done in sense. Then generalized index for semi-Fred-holm operators is developed to wholeB(H), i.e. all of bounded linear operators in Hilbert spaceH. Theorem 2.2 is proved with an example, which is in contradiction to a known proposition for semi-Fredholm operators in form, practically a refined result of the known proposition. Then, it is proved thatB(H) is the union of countably many disjoint arewise connected sets over all the generalized dimensions ofB(H). Project supported by the National Natural Science Foundation of China     

Corrections of proofs for Hansen and Mélot's two theorems

The Randi? index R(G) of a (chemical) graph G is also called connectivity index. Hansen and Mélot [Variable neighborhood search for extremal graphs 6: analyzing bounds for the connectivity index, J. Chem. Inf. Comput. Sci. 43 (2003) 1-14] in their paper, characterized the chemical trees of given order and number of pendent vertices which have the minimum and maximum Randi? index, respectively. In this note, we point out the mistakes in the proofs of their results Theorems 8 and 10, while we still believe that the two theorems are true, and then we give their corrected proofs.     

动态模糊随机信息处理的数学方法

本文系统地概述了我们近年来提出的动态模糊随机信息处理的数学方法,内容包括模糊随机变量、模糊随机过程和模糊随机微分方程的基本解法等方面的基本概念、基本定义和某些重要的定理,以及动态系统的模糊随机响应与可靠性分析的方法等。这些方法是为我们研究工程实际问题的需要逐步发展起来的,对于处理某些类型的问题简便实用。     

3-乙氧基-6-取代苯氧基哒嗪除草活性的相关性研究

在分子拓扑理论的基础上,构建了新的结构信息价连接性指数mχY和取代基染色指数I,并用它们研究了3 乙氧基 6 取代苯氧基哒嗪的除草活性pI50与其结构之间的定量关系,给出了相关方程,相关性良好,复相关系数分别为R1=0.9807、R2=0.9926、R3=0.9881,并预测了几个化合物的pI50值,预测值pI50(cal.)与测定值pI50(exp.)相当吻合.新方法计算方便、结果可靠.