Sequential estimation of a parameter of an exponential distribution

We consider the problem of minimum risk point estimation for the parameter =a+b of the exponential distribution with unknown location parameter and scale parameter when the loss function is squared error plus linear cost. In this paper, we propose a sequential estimator of and show that the associated risk is asymptotically one cost less than that given by Ghosh and Mukhopadhyay (1989,South African Statist. J.,23, 251–268).     

Bayesian sequential reliability for Weibull and related distributions

Assume that the probability density function for the lifetime of a newly designed product has the form: [H(t)/Q()] exp{–H(t)/Q()}. The Exponential(), Rayleigh, WeibullW(, ) and Pareto pdf's are special cases.Q() will be assumed to have an inverse Gamma prior. Assume thatm independent products are to be tested with replacement. A Bayesian Sequential Reliability Demonstration Testing plan is used to eigher accept the product and start formal production, or reject the product for reengineering. The test criterion is the intersection of two goals, a minimal goal to begin production and a mature product goal. The exact values of various risks and the distribution of total number of failures are evaluated. Based on a result about a Poisson process, the expected stopping time for the exponential failure time is also found. Included in these risks and expected stopping times are frequentist versions, thereof, so that the results also provide frequentist answers for a class of interesting stopping rules.This research was supported by NSF grants DMS-8703620 and DMS-8923071, and forms part of the Ph.D. Thesis of the first author, the development of which was supported in part by a David Ross grant at Purdue University. The authors thank the editors and a referee for insightful comments and suggestions.     

The six-membered annulation reaction involving sequential palladium-catalyzed allylic alkylation and Michael addition: scope and limitations

The palladium-catalyzed condensation of a variety of active methylene compounds with methyl 6-acetoxymethyl-hepta-2,6-dienoate was investigated. The six-membered adducts resulting from a η³ palladium complex alkylation-Michael addition sequence were obtained with moderate to good yields. In some cases, further evolution of the primary adduct was observed. The process has been expanded to access nitrogen heterocycles by using sodium p-toluenesulfonamide as the nucleophilic partner.     

Synthesis of a model cyclic triblock terpolymer of styrene,isoprene, and methyl methacrylate

The synthesis of a model cyclic triblock terpolymer [cyclic(S‐b‐I‐b‐MMA] of styrene (S), isoprene (I), and methyl methacrylate (MMA) was achieved by the end‐to‐end intramolecular amidation reaction of the corresponding linear α,ω‐amino acid precursor [S‐b‐I‐b‐MMA] under high‐dilution conditions. The linear precursor was synthesized by the sequential anionic polymerization of S, I, and MMA with 2,2,5,5‐tetramethyl‐1‐(3‐lithiopropyl)‐1‐aza‐2,5‐disilacyclopentane as an initiator and amine generator and 4‐bromo‐1,1,1‐trimethoxybutane as a terminator and carboxylic acid generator. The separation of the unreacted linear polymer from the cyclic terpolymer was facilitated by the transformation of the unreacted species into high molecular weight polymers by the evaporation of the reaction solvent and the continuation of the reaction under high‐concentration conditions. The intermediate materials and the final cyclic terpolymer, characterized by size exclusion chromatography, vapor pressure osmometry, thin‐layer chromatography, IR and NMR spectroscopy, exhibited high molecular weight and compositional homogeneity. Dilute‐solution viscosity measurements were used as an additional proof of the cyclic structure. © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 40: 1476–1483, 2002     

综合创新型实验:乙胺嘧啶合成的设计与教学实践

乙胺嘧啶(商品名:达拉匹林)是一种抗寄生虫药物,改进了合成方法,并设计转化为创新型综合教学实验。从对氯苯乙腈出发,使用丙酸乙酯为酰化试剂,在叔丁醇钾作用下得到烯醇前体。在三甲基氧鎓四氟硼酸盐(Me3O·BF4,Meerwein盐)和碱作用下进行选择性甲基化反应得到烯醇甲醚后,与胍在碱性条件下环化得到最终产物达拉匹林,并通过红外光谱、核磁共振对其结构进行表征。改进后的实验方法具有重现性好、毒性低、操作方便、实验微型化等优点。实验过程中不仅提升了学生的实验技能和科研思维,更提高了学生的创新能力和绿色环保意识。     

STUDY ON POLYSULFONE-POLYESTER BLOCK COPOLYMERS

Synthesis and characterization of a series of Polysulfone (PSF)-Polyester (PEs) block copolymers were studied.The degree of randomness (B) of these block eopolymers was calculated from the intensities of their proton signals in ~1H NMR spectra and lies in the region of 0相似文献   

色谱分析发展简史及其给我们的启示

简要回顾了色谱分析技术的发展史，厘清了某些中文文献中的不妥表述。通过分析色谱发展过程中的几个重要突破，总结了在科学技术创新方面给我们的启示：（1）基础研究始终是色谱技术进步的源泉；（2）社会发展的需求是各种色谱方法创新的驱动力；（3）学科交叉是色谱分析技术创新的重要途径；（4）不懈坚持和勇于探索是科学技术创新的必要条件。最后对色谱发展的前景作了展望。     

Random and cooperative sequential adsorption on infinite ladders and strips

We analyze various processes where particles are added irreversibly and sequentially at the sites of infinite ladders or broader strips (i.e., on terraces) of adsorption sites. For sufficiently narrow strips or ladders, exact solution in closed form is possible for a variety of processes. Often this is most naturally achieved by mapping the process onto an equivalent one-dimensional process typically involvingcompetitive adsorption. We demonstrate this procedure for sequential adsorption with nearest-neighbor exclusion on a 2× square ladder. For other select processes on strips slightly too broad for exact solution, almost exact analysis is possible exploiting an empty-site shielding property. In this way, we determine a jamming coverage of 0.91556671 for random sequential adsorption of dimers on a 2× square ladder. For broader strips, we note that the complexity of these problems quickly approaches that for × lattices.     

Numerical solution of minimax problems of optimal control,part 1

This paper contains general transformation techniques useful to convert minimax problems of optimal control into the Mayer-Bolza problem of the calculus of variations [Problem (P)]. We consider two types of minimax problems: minimax problems of Type (Q), in which the minimax function depends on the state and does not depend on the control; and minimax problems of Type (R), in which the minimax function depends on both the state and the control. Both Problem (Q) and Problem (R) can be reduced to Problem (P).For Problem (Q), we exploit the analogy with a bounded-state problem in combination with a transformation of the Jacobson type. This requires the proper augmentation of the state vectorx(t), the control vectoru(t), and the parameter vector , as well as the proper augmentation of the constraining relations. As a result of the transformation, the unknown minimax value of the performance index becomes a component of the parameter vector being optimized.For Problem (R), we exploit the analogy with a bounded-control problem in combination with a transformation of the Valentine type. This requires the proper augmentation of the control vectoru(t) and the parameter vector , as well as the proper augmentation of the constraining relations. As a result of the transformation, the unknown minimax value of the performance index becomes a component of the parameter vector being optimized.In a subsequent paper (Part 2), the transformation techniques presented here are employed in conjunction with the sequential gradient-restoration algorithm for solving optimal control problems on a digital computer; both the single-subarc approach and the multiple-subarc approach are discussed.This research was supported by the National Science Foundation, Grant No. ENG-79-18667, and by Wright-Patterson Air Force Base, Contract No. F33615-80-C3000. This paper is a condensation of the investigations reported in Refs. 1–7. The authors are indebted to E. M. Coker and E. M. Sims for analytical and computational assistance.     

“保守系统平衡位置微振动”案例教学的探讨与实践

以“保守系统平衡位置微振动”为例,论述在理论力学中如何适当地整合知识点使之成为一个案例,使学生从具体的案例出发经过思考、分析、讨论,得到可能的解决方案,并进行评价、提炼理论.实践证明,把案例教学引入理论力学教学中,通过多个阶段的实践过程锻炼,有助于学生形成“主体性”和“实践性”的习惯,从而改善课堂教学关系,提高学生的独立学习和实践创新能力.