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.     

连铸小方坯的组织与性能研究

The hot cracking of the continuous casting bullit is connected with its macrostructure and mechanical property burnt. The macrostructure and the mechanical property of 0. 13 wt- %C continuous casting bullit was investigated. The results are as follows: 1) the classical representation of the casting bullit shows three distinct zones, a peripherial region of small equiaxed grains, a columnar zone, and a central equiaxed zone. The rapid increase of the under cooling layer thickness is the criterion of the transformation from the columnar zone to central equiaxed zone; 2) The hardness decreases with the reducing of the solidification speed; 3) The tensile strength decreases gradually from the peripherial equiaxed maximum principal strain zone to central equiaxed zone ,and increases with the drop of the temperature.     

一种用于自动标引系统的主题词自动切分方法

该文着重介绍一种知识指导下的主题词自动切分方法，该方法能灵活处理自然主题词、大幅度跳跃及关联词的切分问题，其字面切分精度达９９．３３％，综合切分精度达９８．９１％。     

先秦黄钟律管考——利用现代声学公式推测先秦黄钟律管管径的尝试

《吕氏春秋》记载的黄钟律管长度为三寸九分，而汉代后，古人普遍采纳黄钟九寸。为了研究先秦黄钟律管真实长度，对文献进行系统地考证，发现《吕氏春秋》记载的三寸九分黄钟律管应为清黄钟律管，发音当是九寸管的高八度。文献研究亦表明了先秦古人听声定律的事实，即三寸九分律管和九寸律管都为听声定律产物。由此，根据声学公式，结合文献考证，计算了黄钟律管的管径，结论为：先秦律管应是竹管，管径范围约是0．71寸。同时，考证了黄钟律管八寸十分一说和八寸七分一说，认为这两种说法都不可靠。     

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     

语文教育必须重视人的精神建设

长期以来，语文教育观念和教育目标的定位有失偏颇，造成语文教育的负面影响。要改变这种状况，必须从人的精神建设的高度来定位语文教育的观念和目标。语言即精神。语文教育最根本的任务就是要培植学生的精神，塑造学生完美的人格。     

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