On the verge of <Emphasis Type="Italic">Umdeutung</Emphasis> in Minnesota: Van Vleck and the correspondence principle. Part one

In October 1924, The Physical Review, a relatively minor journal at the time, published a remarkable two-part paper by John H. Van Vleck, working in virtual isolation at the University of Minnesota. Using Bohr’s correspondence principle and Einstein’s quantum theory of radiation along with advanced techniques from classical mechanics, Van Vleck showed that quantum formulae for emission, absorption, and dispersion of radiation merge with their classical counterparts in the limit of high quantum numbers. For modern readers Van Vleck’s paper is much easier to follow than the famous paper by Kramers and Heisenberg on dispersion theory, which covers similar terrain and is widely credited to have led directly to Heisenberg’s Umdeutung paper. This makes Van Vleck’s paper extremely valuable for the reconstruction of the genesis of matrix mechanics. It also makes it tempting to ask why Van Vleck did not take the next step and develop matrix mechanics himself. This paper was written as part of a joint project in the history of quantum physics of the Max Planck Institut für Wissenschaftsgeschichte and the Fritz-Haber-Institut in Berlin.     

The Response of Debris-Flow Events to Solar Proton Flares （Ⅰ）

By analyzing the observation data from Dongchuan Debris Flow Observation and Research Station and historical data from year 1965 to 1990 gotten from National Astronomical Ob-servatories/Yunnan Observatory,the responding of debris flow in Jiangjia Ravine to Solar Proton Flare is studied. The following conclusion can be drawn. Solar Proton Flare,as one of most im-portant astronomical factors,affects the activity of debris flow in Yunnan. Generally,from 1965 to1990,the more active Solar Pro-ton Flare is,the greater the probability of high frequency and large runoff of debris flow is. On the contrary,the less active Solar Pro-ton Flare is,the greater the probability of low frequency,small runoff,and low sediment transport of debris flow is.     

Bang bang control of unified chaotic system

The unified chaotic system contains the Lorenz system and the Chen system as two dual systems at the two extremes of its parameter spectrum. This paper presents the design of bang bang controller for unified system and multitude of numerical experiments under various control parameters. Numerical experiments meet the theoretic proof perfectly and convincingly demonstrated the controller can be effectively used for unified systems with uncertainty of the equilibrium points. The method enriches the applications of chaotic control. Foundation item: Supported by the National Natural Science Foundation of China(50209012) Biography: Deng Xiao-ming (1980-), male, Master candidate, research direction: chaos control.     

工程项目结构分解的优化及应用

工程项目结构分解及其编码是项目管理的基础工作。目前该方法的应用缺乏统一的标准和规范，影响其应用效果。针对这种情况，提出该方法的优化途径－－分解对象标准化，分解步骤统一化，分解规则规范化。进而指出该方法新的应用领域，特别是在项目管理信息集成方面，及对提高工程项目管理水平所起的作用。     

Ruin Probability with Variable Premium Rate and Disturbed by Diffusion in a Markovian Environment

We consider a risk model with a premium rate which varies with the level of free reserves. In this model, the occurrence of claims is described by a Cox process with Markov intensity process, and the influence of stochastic factors is considered by adding a diffusion process. The integro-differential equation for the ruin probability is derived by a infinitesimal method.     

Newton's Easy Quadratures ``Omitted for the Sake of Brevity'

In the 1687 Principia, Newton gave a solution to the direct problem (given the orbit and center of force, find the central force) for a conic-section with a focal center of force (answer: a reciprocal square force) and for a spiral orbit with a polar center of force (answer: a reciprocal cube force). He did not, however, give solutions for the two corresponding inverse problems (given the force and center of force, find the orbit). He gave a cryptic solution to the inverse problem of a reciprocal cube force, but offered no solution for the reciprocal square force. Some take this omission as an indication that Newton could not solve the reciprocal square, for, they ask, why else would he not select this important problem? Others claim that ``it is child's play' for him, as evidenced by his 1671 catalogue of quadratures (tables of integrals). The answer to that question is obscured for all who attempt to work through Newton's published solution of the reciprocal cube force because it is done in the synthetic geometric style of the 1687 Principia rather than in the analytic algebraic style that Newton employed until 1671. In response to a request from David Gregory in 1694, however, Newton produced an analytic version of the body of the proof, but one which still had a geometric conclusion. Newton's charge is to find both ``the orbit' and ``the time in orbit.' In the determination of the dependence of the time on orbital position, t(r), Newton evaluated an integral of the form ∫dx/x <sup>n</sup> to calculate a finite algebraic equation for the area swept out as a function of the radius, but he did not write out the analytic expression for time t = t(r), even though he knew that the time t is proportional to that area. In the determination of the orbit, θ (r), Newton obtained an integral of the form ∫dx/√(1−x<sup>2</sup>) for the area that is proportional to the angle θ, an integral he had shown in his 1669 On Analysis by Infinite Equations to be equal to the arcsin(x). Since the solution must therefore contain a transcendental function, he knew that a finite algebraic solution for θ=θ(r) did not exist for ``the orbit' as it had for ``the time in orbit.' In contrast to these two solutions for the inverse cube force, however, it is not possible in the inverse square solution to generate a finite algebraic expression for either ``the orbit' or ``the time in orbit.' In fact, in Lemma 28, Newton offers a demonstration that the area of an ellipse cannot be given by a finite equation. I claim that the limitation of Lemma 28 forces Newton to reject the inverse square force as an example and to choose instead the reciprocal cube force as his example in Proposition 41. (Received August 14, 2002) Published online March 26, 2003 Communicated by G. Smith     

Molecular dynamics study on the structure I helium hydrate

A 368- water molecule structure I gas hydrate, encased by the number of helium (He) molecules ranging from two to twenty-two, are calculated by molecular dynamical simulations. The potential TIP4P (transferable intermolecular potentical with four sites) is used for water interactions and Lennard-Jones for He-He and He-water interactions. He molecules do not affect the water lattice and can stabilize the hydrate when their concentration is small. A trough signature of He encased is found at 80～90 meV in the phonon density of states. He molecules prefer to be more off-center in 51262 cages. Heavier isotope He are energetically favorable to be filled in cages.     

不对称D—A反应区域选择性及其理论解析

本文以教学研究为基础,系统研究不对称D—A反应区域选译性规律,并运用前线分子轨道理论,采用图解量子化学方法予以理论解析。     

白兰瓜子叶和幼叶的组织培养

白兰瓜子叶和幼叶作为外植体直接诱导再生芽。讨论了不同种类和不同水平激素的作用、子叶上不同位置组织的差异、子叶与幼叶诱导频率的不同等。试验结果表明:生长素类激素和较高浓度的细胞分裂素激素类使子叶产生白色疏松的愈伤组织,MS+BA0.5ppm+Kt0.5ppm为诱导再生芽的最适培养基;子叶上不同部位组织的诱导率呈显著差异,近生长点端→远生长点端,诱导率由24.4％急剧下降至0％:幼叶的诱导率为27.4％,明显高于子叶9.7％的诱导率;不定芽的生根需极低浓度的Kt(0.01—0.05ppm)或不附加任何激素。     

LOGISTICS SCHEDULING： ANALYSIS OFTWO-STAGE PROBLEMS

This paper studies the coordination effects between stages for scheduling problems where decision-making is a two-stage process. Two stages are considered as one system. The system can be a supply chain that links two stages, one stage representing a manufacturer; and the other, a distributor It also can represent a single manufacturer, while each stage represents a different department responsible for a part of operations. A problem that jointly considers both stages in order to achieve ideal overall system performance is defined as a system problem. In practice, at times, it might not be feasible for the two stages to make coordinated decisions due to (i) the lack of channels that allow decision makers at the two stages to cooperate, and/or (ii) the optimal solution to the system problem is too difficult (or costly) to achieve.Two practical approaches are applied to solve a variant of two-stage logistic scheduling problems. The Forward Approach is defined as a solution procedure by which the first sta