Functional Central Limit Theorems for Triangular Arrays of Function-Indexed Processes under Uniformly Integrable Entropy Conditions

Functional central limit theorems for triangular arrays of rowwise independent stochastic processes are established by a method replacing tail probabilities by expectations throughout. The main tool is a maximal inequality based on a preliminary version proved by P. Gaenssler and Th. Schlumprecht. Its essential refinement used here is achieved by an additional inequality due to M. Ledoux and M. Talagrand. The entropy condition emerging in our theorems was introduced by K. S. Alexander, whose functional central limit theorem for so-calledmeasure-like processeswill be also regained. Applications concern, in particular, so-calledrandom measure processeswhich include function-indexed empirical processes and partial-sum processes (with random or fixed locations). In this context, we obtain generalizations of results due to K. S. Alexander, M. A. Arcones, P. Gaenssler, and K. Ziegler. Further examples include nonparametric regression and intensity estimation for spatial Poisson processes.     

光谱复杂的稀土基体中稀土杂质ICP光谱测定的一些问题

ICP激发光源以其独特的功能使ICP/AES技术在稀土分析中的应用日益广泛,在一定程度上取代了经典的直流电弧光谱法,但应指出,由于常规雾化器的低雾化效率(≤5％)和试样的高倍稀释,ICP/AES技术的实际检测能力的改善并不明显,本文用ICP光谱法测定了     

Interval estimation of the critical value in a general linear model

Summary This paper concerns interval estimation of the critical value θ which satisfies under the general linear model,Y _i =μ(x _i )+ε _i (i=1,2,···), where for and the functional forms off _j ^′ s are known. From an asymptotic expansion it is shown that, under reasonable conditions, the limiting distribution of is normal. Thus in the large-sample case a confidence interval for θ can be obtained. Such a result is useful when one is interested in carrying out a retrospective analysis rather than designing the experiment (as in the Kiefer-Wolfowitz procedure). In Section 3 a sequential procedure is considered for confidence intervals with fixed width 2d. It is shown that, for a given stopping variableN, is also asymptotically normal asd→0. Thus the coverage probability converges to 1−α (preassigned) asd→0. An example of application in estimating the phase parameter in circadian rhythms is given for the purpose of illustration. Research partially supported by the NSF Grant DMS-8502346.     

芯片式流通池顺序注射可更新表面反射光谱法用于酶反应检测

将芯片式流通池顺序注射可更新表面反射光谱法用于酶反应检测。HRP催化H2O2氧化BPR底物的反应用于对H2O2的检测。此反应体系与葡萄糖氧化酶联用，用于对血清中葡萄糖的检测。     

A multisyringe flow-through sequential extraction system for on-line monitoring of orthophosphate in soils and sediments

A fully automated flow-through microcolumn fractionation system with on-line post-extraction derivatization is proposed for monitoring of orthophosphate in solid samples of environmental relevance. The system integrates dynamic sequential extraction using 1.0 mol l⁻¹ NH₄Cl, 0.1 mol l⁻¹ NaOH and 0.5 mol l⁻¹ HCl as extractants according to the Hieltjes-Lijklema (HL) scheme for fractionation of phosphorus associated with different geological phases, and on-line processing of the extracts via the Molybdenum Blue (MB) reaction by exploiting multisyringe flow injection as the interface between the solid containing microcolumn and the flow-through detector. The proposed flow assembly, capitalizing on the features of the multicommutation concept, implies several advantages as compared to fractionation analysis in the batch mode in terms of saving of extractants and MB reagents, shortening of the operational times from days to hours, highly temporal resolution of the leaching process and the capability for immediate decision for stopping or proceeding with the ongoing extraction. Very importantly, accurate determination of the various orthophosphate pools is ensured by minimization of the hydrolysis of extracted organic phosphorus and condensed inorganic phosphates within the time frame of the assay. The potential of the novel system for accommodation of the harmonized protocol from the Standards, Measurement and Testing (SMT) Program of the Commission of the European Communities for inorganic phosphorus fractionation was also addressed. Under the optimized conditions, the lowest detectable concentration at the 3σ level was ≤0.02 mg P l⁻¹ for both the HL and SMT schemes regardless of the extracting media. The repeatability of the MB assay was better than 2.5% and the dynamic linear range extended up to 7.0 mg P l⁻¹ in NH₄Cl and NaOH media and 15 mg P l⁻¹ whenever HCl is utilized as extractant for both the HL and SMT protocols.     

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     

Evaluating the mobility of toxic metals in untreated industrial wastewater sludge using a BCR sequential extraction procedure and a leaching test

The distribution and speciation of toxic metals in industrial wastewater sludge (IWS) was investigated. In this work, the modified BCR three-stage sequential extraction procedure was applied to the fractionation of Cr Pb Ni, and Cd in untreated industrial wastewater sludge from industrial sites in Hyderabad (Pakistan). The extracts were analyzed using electrothermal atomic absorption spectrometry. The procedure was evaluated using a certified reference material for soil mixed with sewage sludge BCR 483. The results from the partitioning study indicate that more easily mobilized forms (acid exchangeable) of Cd were dominant. The oxidizable fraction was dominant for all four toxic metals. Metal recovery was good, with <4% difference between the total metal recovered through the extractant steps and the total metal determined after microwave digestion. Lixiviation tests (DIN 38414-S4) were used to evaluate the leaching of toxic species from IWS, and it was observed that levels of leachable toxic metals were low compared to the amount of metal extracted in the exchangeable fraction of the BCR protocol.