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     

利用芒硝石膏炒制建筑石膏的研究

本文分析了芒硝石膏的性能,通过对国内外有关资料的分析和实验,得出了利用芒硝石膏完全可以炒制三级以上建筑石膏的结论     

实现汽车发动机可变气门相位的新方法

介绍一种用于双顶置凸轮轴式发动机的采用两级谐波传动的新型进气凸轮轴调相机构。它由输入刚轮（正时带轮）、柔轮、输出刚轮（与进气凸轮轴联接）、固定波发生器、动波发生器和步进电机等组成。用步进电机驱动动波发生器可改变输出、输入刚轮的相对位置，从而改变进气相位。该机构能在很大角度范围内，以小步长实现多级调相，轴向尺寸小，转动惯量小，控制驱动功率小。２００ｈ试验表明，该机构工作可靠，能够准确地根据控制信号进行凸轮轴的调相。     

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。     

MeV Pb离子在非晶Si中的射程离散──离子束混合和增强扩散的影响

１．０ＭｅＶ２０８Ｐｂ离子在非晶Ｓｉ中的投影射程ＲＰ和射程偏差ΔＲＰ作为注量和温度二者的函数用背散射法进行测定．注量的变化范围为５×１０１３～７×１０１４ｃｍ－２．注入是在室温和ｔ＝－１２０℃下完成的．由由实验所确定的投影射程，射程偏差与注量或温度无关，并且分别等于２９５和７２．２ｎｍ．与ＴＲＩＭ８６的计算结果相比较，发现ＲＰ的偏离为１８％，而ΔＲＰ的偏离为３６％．ＲＰ和ΔＲＰ二者与注量及温度的无关性，排除了所观察到的与ＴＲＩＭ的矛盾是由于注入期间辐射增强扩散或离子束混合效应而引起的解释。     

氧化物半导瓷中晶界势垒的起源

提出了一个关于氧化物半导瓷晶界势垒起源的新观点，认为晶界势垒起源于烧结过程中外界氧在晶界中的扩散，与材料的结构、化学缺陷、掺杂、外界气氛、烧结工艺、组成状态等有密切关系，并用此理论解释了许多实验现象。     

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     

STABILITY CRITERIA FOR A CLASS OF UNCERTAINSYSTEMS WITH TIME—DELAY

Some stability criteria are obtained for a class of uncertain systems with time-delay usingLyapunov functional and analytic techniques. It is easy to check the criteria by making use of theboundedness of the uncertainties.     

专家系统技术在注塑模故障诊断中的应用

论述了用人工智能技术对模具故障进行诊断和确定对策的原理和方法。对模具在工作中常遇到的与模具制造、工艺条件及塑料材料有关的问题及相应对策进行了归纳整理，组成了模具诊断与维修知识库。收集了常用工程塑料的各种有关成型工艺条件和主要性能，建立了塑料材料数据库。采用正向推理控制策略搜索知识库，并将推理结果与理论计算结果进行对比校验，最后确定出模具工作中出现故障的原因，并输出相应的解决办法和建议．