可分解的Hybrid三元系大集和超大集的构造

An LRHTS(v)(or LARHTS(v)) is a collection of {(X, B i) : 1 ≤ i ≤ 4(v-2)},where X is a v-set, each(X, B i) is a resolvable(or almost resolvable) HTS(v), and all B i s form a partition of all cycle triples and transitive triples on X. An OLRHTS(v)(or OLARHTS(v))is a collection {(Y \{y}, A j y) : y ∈ Y, j = 0, 1, 2, 3}, where Y is a(v + 1)-set, each(Y \{y}, A j y)is a resolvable(or almost resolvable) HTS(v), and all A j y s form a partition of all cycle and transitive triples on Y. In this paper, we establish some directed and recursive constructions for LRHTS(v), LARHTS(v), OLRHTS(v), OLARHTS(v) and give some new results.     

组合设计的大集

组合设计中的大集问题有着悠久的历史和广泛的应用．由于它的难度，长期进展很慢．近二十多年来，在一些新的方法和手段的推动下，大集研究呈现了很好的态势．本文力图对几类主要组合设计大集的概念和研究进展给予概要介绍，以期引起更多的关注。     

Large Sets of Orthogonal Arrays and Multimagic Squares

Large sets of orthogonal arrays (LOA) have been used to construct resilient functions and zigzag functions by D. R. Stinson. In this paper, a special kind of LOA, strong double large sets of orthogonal arrays (SDLOA), is introduced and some constructions are provided. Meanwhile, a construction of multimagic squares based on SDLOAs is also given. As its application, it is proved that a t‐multimagic square of order exists whenever q is a prime power and , , which improves a similar result by H. Derksen et al. from primes to prime powers in Amer. Math. Monthly (2007).     

Further Results on Large Sets of Resolvable Idempotent Latin Squares

An idempotent Latin square of order v is called resolvable and denoted by RILS(v) if the off‐diagonal cells can be resolved into disjoint transversals. A large set of resolvable idempotent Latin squares of order v, briefly LRILS(v), is a collection of RILS(v)s pairwise agreeing on only the main diagonal. In this paper, it is established that there exists an LRILS(v) for any positive integer , except for , and except possibly for .     

Planar Digraphs without Large Acyclic Sets

Given a directed graph, an acyclic set is a set of vertices inducing a directed subgraph with no directed cycle. In this note, we show that for all integers , there exist oriented planar graphs of order n and digirth g for which the size of the maximum acyclic set is at most . When this result disproves a conjecture of Harutyunyan and shows that a question of Albertson is best possible.     

Semiregular Large Sets

We develop the notion of t-homogeneous, G-semiregular large sets of t-designs, show that there are infinitely many 3-homogeneous PSL(2, q)-semiregular large sets when q 3 mod 4, two sporadic 3-homogeneous AL(1,32)-semiregular large sets, and no other interesting t-homogeneous G-semiregular large sets for t 3.     

不相交斯泰纳和柯克曼三元系大集两定理(一)

给定一个斯泰纳或柯克曼三元系,介绍其大集的生成方法;得到其大集存在条件的判据是一个位差各异的循环数;柯克曼三元系其大集判据是,不能分解的柯克曼三元系有大集,能分解的无大集.     

Large Cardinals and Ramifiability for Directed Sets

The notion of “ramifiability” (or “tree‐property”), usually applied to cardinals, can be extended to directed sets and is put in relation here with familiar “large cardinal” properties.     

Large Sets of Wrapped K–K Hamilton Cycle Decompositions of Complete Bipartite 3‐Uniform Hypergraphs

Using the Katona–Kierstead (K–K) definition of a Hamilton cycle in a uniform hypergraph, we investigate the existence of wrapped K–K Hamilton cycle decompositions of the complete bipartite 3‐uniform hypergraph and their large sets, settling their existence whenever n is prime.     

Overlarge sets of disjoint Steiner quadruple systems

In this article, we construct overlarge sets of disjoint S(3, 4, 3ⁿ − 1) and overlarge sets of disjoint S(3, 4, 3ⁿ + 1) for all n ≥ 2. Up to now, the only known infinite sequence of overlarge sets of disjoint S(3, 4, v) were the overlarge sets of disjoint S(3, 4, 2ⁿ) obtained from the oval conics of desarguesian projective planes of order 2ⁿ. © 1999 John Wiley & Sons, Inc. J Combin Design 7: 311–315, 1999     

Laws of Large Numbers for Exchangeable Random Sets in Kuratowski-Mosco Sense

Abstract

Most of the results for laws of large numbers based on Banach space valued random sets assume that the sets are independent and identically distributed (IID) and compact, in which Rådström embedding or the refined method for collection of compact and convex subsets of a Banach space plays an important role. In this paper, exchangeability among random sets as a dependency, instead of IID, is assumed in obtaining strong laws of large numbers, since some kind of dependency of random variables may be often required for many statistical analyses. Also, the Hausdorff convergence usually used is replaced by another topology, Kuratowski-Mosco convergence. Thus, we prove strong laws of large numbers for exchangeable random sets in Kuratowski-Mosco convergence, without assuming the sets are compact, which is weaker than Hausdorff sense.     

Extremal Forex Returns in Extremely Large Data Sets

Exciting information for risk and investment analysis is obtained from an exceptionally large and automatically filtered high frequency data set containing all the forex quote prices on Reuters during a ten-year period. It is shown how the high frequency data improve the efficiency of the tail risk cum loss estimates. We demonstrate theoretically and empirically that the heavy tail feature of foreign exchange rate returns implies that position limits for traders calculated under the industry standard normal model are either not prudent enough, or are overly conservative depending on the time horizon.     

Difference Sets and Recursion Theory

There is a recursive set of natural numbers which is the difference set of some recursively enumerable set but which is not the difference set of any recursive set.     

The spectrum for overlarge sets of hybrid triple systems

A hybrid triple system of order v and index λ,denoted by HTS(v,λ),is a pair(X,B) where X is a v-set and B is a collection of cyclic triples and transitive triples on X,such that every ordered pair of X belongs to λ triples of B. An overlarge set of disjoint HTS(v,λ),denoted by OLHTS(v,λ),is a collection {(Y {y},Ai)}i,such that Y is a(v+1)-set,each(Y {y},Ai) is an HTS(v,λ) and all Ais form a partition of all cyclic triples and transitive triples on Y.In this paper,we shall discuss the existence problem of OLHTS(v,λ) and give the following conclusion: there exists an OLHTS(v,λ) if and only if λ=1,2,4,v ≡ 0,1(mod 3) and v≥4.     

拟正则双序集用矩形双序集的余扩张

称双序集E为双序集F用矩形双序集的余扩张,若存在满双序集态射θ：E→F,使对每个α∈F,αθ－1是E的矩形双序子集．本文讨论了拟正则双序集的这种余扩张的性质,给出了它们的结构．作为应用,证明了拟正则的硬双序集实为正则双序集．     

A Random Set Extension of a Strong Law of Large Numbers of Cantrell and Rosalsky

Abstract

A strong law of large numbers under conditions irrespective of the joint distribution of the sequence is extended to random sets. The extension is such that the role of events of the form {||V _n || ≤ b _n } (where V _n is a random element of a separable Banach space) is played by events of the form {X _n  ? B _n } (where X _n is a random closed bounded set).     

Tripling Construction for Large Sets of Resolvable Directed Triple Systems

In this paper, we first define a doubly transitive resolvable idempotent quasigroup （DTRIQ）, and show that aDTRIQ of order v exists if and only ifv ≡0（mod3） and v ≠ 2（mod4）. Then we use DTRIQ to present a tripling construction for large sets of resolvable directed triple systems, which improves an earlier version of tripling construction by Kang （J. Combin. Designs, 4 （1996）, 301-321）. As an application, we obtain an LRDTS（4·3^n） for any integer n ≥ 1, which provides an infinite family of even orders.     

A Completion of the Spectrum for the Overlarge Sets of Pure Mendelsohn Triple Systems

A pure Mendelsohn triple system of order v, denoted by PMTS(v), is a pair \((X,\mathcal {B})\) where X is a v-set and \(\mathcal {B}\) is a collection of cyclic triples on X such that every ordered pair of X belongs to exactly one triple of \(\mathcal {B}\) and if \(\langle a,b,c\rangle \in \mathcal {B}\) implies \(\langle c,b,a\rangle \notin \mathcal {B}\). An overlarge set of PMTS(v), denoted by OLPMTS(v), is a collection \(\{(Y{\setminus }\{y_i\},{\mathcal {A}}_i)\}_i\), where Y is a \((v+1)\)-set, \(y_i\in Y\), each \((Y{\setminus }\{y_i\},{\mathcal {A}}_i)\) is a PMTS(v) and these \({\mathcal {A}}_i\)s form a partition of all cyclic triples on Y. It is shown in [3] that there exists an OLPMTS(v) for \(v\equiv 1,3\) (mod 6), \(v>3\), or \(v \equiv 0,4\) (mod 12). In this paper, we shall discuss the existence problem of OLPMTS(v)s for \(v\equiv 6,10\) (mod 12) and get the following conclusion: there exists an OLPMTS(v) if and only if \(v\equiv 0,1\) (mod 3), \(v>3\) and \(v\ne 6\).     

闭模糊集构成凸模糊集的充要条件

本文通过引入弱拟凸模糊集的概念，针对欧几里空间上的闭模糊集，给出了它构成凸模糊集的一个充要条件，从而丰富了凸模糊集的理论及其应用。