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.     

Polyboxes,Cube Tilings and Rigidity

A non-empty subset A of X=X ₁×???×X _d is a (proper) box if A=A ₁×???×A _d and A _i ?X _i for each i. Suppose that for each pair of boxes A, B and each i, one can only know which of the three states takes place: A _i =B _i , A _i =X _i ?B _i , A _i ?{B _i ,X _i ?B _i }. Let F and G be two systems of disjoint boxes. Can one decide whether ∪F=∪G? In general, the answer is ‘no’, but as is shown in the paper, it is ‘yes’ if both systems consist of pairwise dichotomous boxes. (Boxes A, B are dichotomous if there is i such that A _i =X _i ?B _i .) Several criteria that enable to compare such systems are collected. The paper includes also rigidity results, which say what assumptions have to be imposed on F to ensure that ∪F=∪G implies F=G. As an application, the rigidity conjecture for 2-extremal cube tilings of Lagarias and Shor is verified.     

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.

     

具有无界变差的连续函数研究进展

讨论了具有无界变差的连续函数的结构.首先按照局部结构和分形维数对连续函数进行了分类,给出了相应的例子.对这些具有无界变差的函数的性质进行了初步的讨论.对于新定义的奇异连续函数,给出了一个等价判别定理.基于奇异连续函数,又给出了局部分形函数和分形函数的定义.同时,分形函数又由奇异分形函数、非正则分形函数和正则分形函数组成.相应于不连续函数的情形也进行了简单的讨论.     

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。     

盒维数的一个等价定义及其应用

给出了盒维数的一个等价定义．该定义与盒维数的现有定义相比,从理论上更容易验证,在应用中更适合于数值计算．据此给出了计算盒维数的一个数值算法．     

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。