On three conjectures by K. E. Shuler

Some fifteen years ago, Shuler formulated three conjectures relating to the large-time asymptotic properties of a nearest-neighbor random walk on ² that is allowed to make horizontal steps everywhere but vertical steps only on a random fraction of the columns. We give a proof of his conjectures for the situation where the column distribution is stationary and satisfies a certain mixing codition. We also prove a strong form of scaling to anisotropic Brownian motion as well as a local limit theorem. The main ingredient of the proofs is a large-deviation estimate for the number of visits to a random set made by a simple random walk on . We briefly discuss extensions to higher dimension and to other types of random walk.Dedicated to Prof. K. E. Shuler on the occasion of his 70th birthday, celebrated at a Symposium in his honor on July 13, 1992, at the University of California at San Diego, La Jolla, California.     

An existence result for linear partial differential equations with coefficients in an algebra of generalized functions

We prove the existence of solutions for essentially all linear partial differential equations with -coefficients in an algebra of generalized functions, defined in the paper. In particular, we show that H. Lewy's equation has solutions whenever its right-hand side is a classical -function.

     

The Boolean Prime Ideal Theorem Plus Countable Choice Do Not Imply Dependent Choice

Two Fraenkel-Mostowski models are constructed in which the Boolean Prime Ideal Theorem is true. In both models, AC for countable sets is true, but AC for sets of cardinality 2 and the 2m = m principle are both false. The Principle of Dependent Choices is true in the first model, but false in the second. Mathematics Subject Classification: 03E25, 03E35, 04A25.     

Optimal life strategies in organisms exposed to recurrent critical events

The optimal partition of energy between survival and reproduction is considered for a population subject to recurrent and potentially lethal critical events. The best strategy is found by maximizing fitness, a functional derived from the Lotka equation. The dynamics is governed by a second-order, age-varying, nonlinear system. The energy storage and the probability of survival are the state variables, while the amounts of energy placed into and withdrawn from the storage are the controls. The optimal life strategy is shown to be as follows: build up the storage at the very beginning of life, and then progressively deplete it to resist the critical events.This work was partially supported by MURST Project Ricerche sui Fondamenti della Conservazione della Natura. The authors would like to thank C. Ricci for suggesting the problem and C. Matessi for helpful discussion.     

关于铀同位素标准物质的几个问题

讨论了铀同位素标准物质(UIRM)研制中的一些技术问题,如IRM中同位素丰度的定值,IRM不确定度的影响因素等,并介绍了国内外UIRM研制情况。     

On some variational approximations in two-dimensional classical lattice systems

A new derivation is presented of some variational approximations for classical lattice systems that belong to the class of cluster-variation methods, among them the well-known Bethe-Peierls and Kramers-Wannier approximations. The limiting behavior of a hierarchical sequence of cluster-variation approximations, the so-calledC hierarchy, is discussed. It is shown that this hierarchy provides a monotonically decreasing sequence of upper boundsf _n on the free energy per lattice sitef and thatf _n f asn . Our results are based on extension theorems for states given on subsets of the lattice, which might be of some independent interest, and on an application of transfer matrix concepts to the variational characterization of translation-invariant equilibrium states.     

Reaction of ethyl bromoacetate with substituted naphthoate ions

Rate constants for the reaction of ethyl bromoacetate with three series of substituted naphthoate ions have been measured in an acetone-water mixture (90% v/v). Using σ _p values rate constants at 30^o correlate well with the Hammett equation yielding ρ=−0.54, −0.19 and −0.25 for (4,1−), (6,1−) and (6,2−) series, respectively. Comparison of these ρ values with those of the reaction of phenacyl bromide reveals the failure of the reactivity-selectivity principle RSP in these reactions. Failure of RSP has been explained in terms of isoselective temperature.     

Evaluation of measurement uncertainty for analytical procedures using a linear calibration function

In the EURACHEM/CITAC draft ”Quantifying uncertainty in analytical measurement” estimations of measurement uncertainty in analytical results for linear calibration are given. In this work these estimations are compared, i.e. the uncertainty deduced from repeated observations of the sample vs. the uncertainty deduced from the standard residual deviation of the regression. As a result of this study it is shown that an uncertainty estimation based on repeated observations can give more realistic values if the condition of variance homogeneity is not correctly fulfilled in the calibration range. The complete calculation of measurement uncertainty including assessment of trueness is represented by an example concerning the determination of zinc in sediment samples using ICP-atomic emission spectrometry. Received: 9 February 2002 Accepted: 17 April 2002     

可移动式微量氧分析仪检定装置研制

研制一种新型可移动式微量氧分析仪检定装置。该装置由标准气体、零点气、脱氧纯化器、减压阀、调节阀、4通阀、5通阀、不锈钢管路、流量控制系统、移动平台等组成。该装置气密性好,15 min内可将装置内氧气浓度由20.9%降至不大于0.1μmol/mol,对于0~10μmol/mol的微量氧分析仪检定结果的扩展不确定度为Urel=1.7%FS(k=2)。该装置满足气体标准物质的连续切换和在线检定的需要,检定时间短,结果准确可靠,可为在线式和非在线式微量氧分析仪的量值溯源提供有效保障。     

对在建标技术报告中正确贯彻《测量不确定度表示指南》的理解

针对计量人员在贯彻《测量不确定表示指南》,尤其是在撰写“建标技术报告”时遇到的一些体问题,进行了探讨。