A Number Theoretic Conjecture and the Existence of S–Cyclic Steiner Quadruple Systems

In their survey article on cyclic Steiner Quadruple Systems SQS(v) M. J. Grannel and T. S. Griggs advanced the conjecture (cf. [8, p. 412]) that their necessary condition for the existence of S-cyclic SQS(v) (cf. [7, p. 51]) is also sufficient. Some years prior to that E. Köhler [10] used a graph theoretical method to construct S-cyclic SQS(v). This method was extended in [17]-[20] and eventually used to reduce the conjecture of Grannel and Griggs to a number theoretic claim (cf. also [21], research problem 146). The main purpose of the present paper is to attack this claim. For the long intervals we have to distinguish four cases. The proof of cases I–III can be accomplished by a thorough study of how the multiples of a certain set belonging to the first column of a certain matrix (the elements of which are essentially the vertices of a graph corresponding to SQS(2p)) are distributed over the columns. The proof is by contradiction. Case IV is most difficult to treat and could only be dealt with by very deep lying means. We have to use an asymptotic formula on the number of lattice points (x,y) with xy 1 mod p (we speak of 1-points) in a rectangle and this formula shows that the 1-points are equidistributed. But even so our claim could not be proved for all intervals of admissible length. Intervals [a,b] with for some m and could not be covered. In the last section we discuss some conclusions which would follow from the non-existence of complete intervals.     

Composition operators on Hardy spaces on Lavrentiev domains

For any simply connected domain , we prove that a Littlewood type inequality is necessary for boundedness of composition operators on , , whenever the symbols are finitely-valent. Moreover, the corresponding ``little-oh' condition is also necessary for the compactness. Nevertheless, it is shown that such an inequality is not sufficient for characterizing bounded composition operators even induced by univalent symbols. Furthermore, such inequality is no longer necessary if we drop the extra assumption on the symbol of being finitely-valent. In particular, this solves a question posed by Shapiro and Smith (2003). Finally, we show a striking link between the geometry of the underlying domain and the symbol inducing the composition operator in , and in this sense, we relate both facts characterizing bounded and compact composition operators whenever is a Lavrentiev domain.

     

Colour quenching corrections on the measurement of 90Sr through Cerenkov counting

The determination of ⁹⁰Sr through the Cerenkov radiation emitted by its descendant ⁹⁰Y is a well-known method and firmly established in literature. Nevertheless, in order to obtain an accurate result based on a Cerenkov measurement, the experimental work must be extremely rigorous because the efficiency of Cerenkov counting is especially sensitive to the presence of colour. Any traces of colour in the sample produce a decrease in the number of photons detected in the photomultipliers and, therefore, this might cause a diminution in Cerenkov counting efficiency. It is essential not only to detect the effect of colour quenching in the sample but also to correct the decrease in counting efficiency. For this reason, colour quenching correction curves versus counting efficiency are usually done when measuring through Cerenkov counting. One of the most widely used techniques to evaluate colour quenching in these measurements is the channel ratio method, which consists of the measurement of the shift of the spectrum measuring the ratio of counts in two different windows. The selection of the windows for the application of the corrections might have an influence on the quality of the fitting parameters of the correction curves efficiency versus colour quenching degree and hence on the final ⁹⁰Sr result. This work is focused on the calculation of the counting efficiency decrease using the channel ratio method and on obtaining the best fitting correction curve. For this purpose, empirical curves obtained through artificial quenchers have been studied and the results have been tested in real samples. Additionally, given that the Packard Tri-Carb 3170 TR/SL liquid scintillation counter is a novel detector for use in Cerenkov counting, the previous calibration of the Tri-Carb 3170 TR/SL detector, necessary for the measurement of ⁹⁰Sr, is included.     

Nonparametric estimation for censored lifetimes suffering from unknown selection bias

In a population of individuals, where the random variable (r.v.) σ denotes the birth time and X the lifetime, we consider the case, where an individual can be observed only if its life-line (σ, X) = {(σ + y, y), 0 ≤ y ≤ X} intersects a given Borel set S in ℝ × ℝ₊. Denoting by σ _S and X _S the birth time and lifetime for the observed individuals, we point out that the distribution function (d.f.) F _S of the r.v. X _S suffers from a selection bias in the sense that F _S = ∝ w d F/μ _S, where w and μ _S depend only on the distribution of σ and on F, the d.f. of X. Assuming in addition that the r.v. X _S is randomly right-censored as soon as the individual is selected, we construct a productlimit estimator for the d.f. F _S and a nonparametric estimator ŵ for the weight function w. We prove a consistency result for ŵ and a weak convergence result for . We establish in addition an exponential bound for .      

合肥光源测量束团纵向精细结构的单光子计数系统设计

本文介绍了用单光子计数法测量束团纵向精细结构的原理.介绍了合肥同步辐射光源测量束团纵向精细结构的单光子计数系统的设计.由于单光子计数法具有高时间分辨率(2ps)和大的动态测量范围(10⁵)等优点,所以该系统不仅可以测量束团长度,而且可以精密测量单束团的纯净度.最后,分析了该系统的性能,并讨论了该系统在尾场和纵向阻抗的研究、束团伸长效应的研究以及影响单束团不纯净机理的研究中的应用.     

BCK-代数的几个计数定理

本文推广了文献中的有限BCK-代数子代数个数估计定理,给出了任意BCK-代数的子代数个数下界的一个估计。对于n阶BCK-代数和n阶半直接既约交换BCK-代数,本文分别给出了其子代数个数下界的较具体的表达公式。另处我们还讨论了互不同构的n阶BCK-代数的个数的下界值的估计问题。     

无机盐对非离子表面活性剂从水相到油相传质的影响研究

采用同位素示踪原子法研究了非离子表面活性剂在无机盐存在下从水相到油相传质的规律,发现无机盐强烈地影响非离子表面活性剂Ａｐ型和Ｓｐ型的传质行为,而且因无机盐性质的不同,表面活性剂结构的差异,传质行为亦会有很大的不同。中外,利用此技术研究解决了连续定量测定微量表活剂的问题,为系统研究表面传质问题开辟了一个新方法。     

Moment Solutions for the State Exiting Counting Processes of a Markov Renewal Process

Important performance measures for many Markov renewal processes are the counts of the exits from each state. We present solutions for the conditional first, second, and covariance moments of the state exiting counting processes for a Markov renewal process, and solutions for the unconditional equilibrium versions of the moments. We demonstrate the relationship between the conditional first moments for the state exiting and the state entering counting processes. For analytical and illustrative purposes, we concentrate on the two state case. Two asymptotic expansions for the moment functions are proposed and evaluated both analytically and empirically. The two approximations are shown to be competitive in terms of absolute relative error, but the second approximation has a simpler analytical form which is useful in analyzing more complex stochastic processes having an underlying MRP structure.     

Approximate counting via random optimization

Let ℱ_n be a family of subsets of {1,…,n}. We propose a simple randomized algorithm to estimate the cardinality of ℱ_n from the maximum weight of a subset X∈ℱ_n in a random weighting of {1,…,n}. The examples include enumeration of perfect matchings in graphs, bases in matroids, and Hamiltonian cycles in graphs. © 1997 John Wiley & Sons, Inc. Random Struct. Alg., 11 , 187–198 (1997)     

In‐Situ Measurement of Local Particle Flux Densities in a Complex Two‐Phase Flow

An optical measuring technique is presented allowing the exact in‐situ measurement of local particle flux densities in a confined channel flow by counting single particles penetrating an optically well defined measuring volume. This enables a precise flux determination up to the direct vicinity of planar walls. The measurement set‐up and its calibration as well as the whole test facility are described in detail. This measurement technique is used to study the particle transport in electrostatic precipitators. Exemplarily, results of particle flux profiles as well as precipitation, as gained from balances of parts of the precipitator channel, are presented. Furthermore, the possibility to determine particle velocity fluctuations is demonstrated.