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     

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.     

Technical Notes ：STUDIES ON THE VALUE OF SECONDARY MARKET TO THE SUPPLY CHAIN

This paper investigates the impact of a secondary market, where retailers can buy and sell excessinventories, on the supply chain. We develop a two-period model with a single manufacturer and tworetailers. At the beginning of the first period the retailers order and receive products from themanufacturer, but at the beginning of the second period, they can trade surplus products betweenthemselves in the secondary market. We investigate the impact of the correlated dependence ofretailers' demand on both the quantity effect and the allocation effect under the secondary market.Lastly,we study potential strategies for the manufacturer to increase sales with the existence of thesecondary market.     

FROM MANUFACTURING SCHEDULING TO SUPPLY CHAIN COORDINATION：THE CONTROL OF COMPLEXITY AND UNCERTAINTY

With time-based competition and rapid technology advancements, effective manufacturingscheduling and supply chain coordination are critical to quickly respond to changing marketconditions. These problems, however, are difficult in view of inherent complexity and variousuncertainties involved. Based on a series of results by the authors, decomposition and coordination byusing Lagrangian relaxation is identified in this paper as an effective way to control complexity anduncertainty.A manufacturing scheduling problem is first formulated within the job shop context withuncertain order arrivals, processing times, due dates, and part priorities as a separable optimizationproblem. A solution methodology that combines Lagrangian relaxation, stochastic dynamicprogramming, and heuristics is developed. Method improvements to effectively solve large problemsare also highlighted. To extend manufacturing scheduling within a factory to coordinate autonomicmembers across chains of suppliers, a decentralized supply chai     

固相红细胞凝集素（E—PHA）的制备及其应用

用江苏莱豆(Phaseolus vulgaris)E-PHA制备固相吸附剂。交联率87.7%。交联E-PHA量为0.59mg/cm~3胶,与肝癌血清γ-GT天冬酰胺连接的低聚糖的亲和反应,类似于进口同类产品。     

α—珠蛋白基因的PCR检测

用多对引物的复合ＰＣＲ技术，分别扩增α－珠蛋白基因族中α１和α２基因片段；参照β－珠蛋白基因ＰＣＲ扩增产物量，判断α１和α２基因是否正常，是否为缺失的纯合子或杂合子，对α－地中海贫血症先征者家系基因型进行ＰＣＲ分型诊断。     

用于兵器的微机控制的电液随动系统

本文介绍16位微机(TWS-0600)控制兵器的高精度电液随动系统的原理与结构,着重讨论了控制器的设计和实现,而控制器的设计,采取了双模控制与分离PID的方法,利用微机逻辑判断功能根据系统误差角大小适时地变更控制器的结构.实践表明这种设计方法对有大惯性负载的兵器随动系统实现高精度、快速、平稳跟踪等技术要求具有工程实际意义,而且,系统有较好的控制效果.     

岩基静荷试验方法及其适用条件分析

根据反力系统的不同 ,介绍了几种岩基载荷试验方法———堆载平台法、锚杆反力梁法、锚桩反力梁法、护壁反力法、斜壁支撑法等 ,并对其适用条件从经济、安全等方面进行了分析