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.     

Large Sets and Overlarge Sets of Triangle-Decomposition

There are six types of triangles:undirected triangle,cyclic triangle,transitive triangle,mixed-1triangle,mixed-2 triangle and mixed-3 triangle.The triangle-decompositions for the six types of triangles havealready been solved.For the first three types of triangles,their large sets have already been solved,and theiroverlarge sets have been investigated.In this paper,we establish the spectrum of LT_i(v,λ),OLT_i(v)(i=1,2),and give the existence of LT_3(v,λ)and OLT_3(v,λ)with λ even.     

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.     

Precomplete Clones on Infinite Sets which are Closed under Conjugation

We show that on an infinite set, there exist no other precomplete clones closed under conjugation except those which contain all permutations. Since on base sets of some infinite cardinalities, in particular on countably infinite ones, the precomplete clones containing the permutations have been determined, this yields a complete list of the precomplete conjugation-closed clones in those cases. In addition, we show that there exist no precomplete submonoids of the full transformation monoid which are closed under conjugation except those which contain the permutations; the monoids of the latter kind are known.     

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。     

Bohr Sets in Triple Products of Large Sets in Amenable Groups

We answer a question of Hegyvári and Ruzsa concerning effective estimates of the Bohr-regularity of certain triple sums of sets with positive upper Banach densities in the integers. Our proof also works for any discrete amenable group, and it does not require all addends in the triple products we consider to have positive (left) upper Banach densities; one of the addends is allowed to only have positive upper asymptotic density with respect to a (possibly very sparse) ergodic sequence.

     

On Large Systems of Sets with No Large Weak Δ-subsystems

weak Δ-system if the cardinality of the intersection of any two sets is the same. We elaborate a construction by R?dl and Thoma [9] and show that for large n, there exists a family ℱ of subsets of without weak Δ-systems of size 3 with . Received: October 1, 1997     

A Construction of Difference Sets

In this paper, we will give a construction of a family of -difference sets in thegroup , where q is any power of 2, K is any group with and G is an abelian 2-group of order which contains anelementary abelian subgroup of index 2.     

Planar Point Sets With Large Minimum Convex Decompositions

We show the existence of sets with $n$ points ( $n\ge 4$ ) for which every convex decomposition contains more than $\frac{35}{32}n-\frac{3}{2}$ polygons, which refutes the conjecture that for every set of $n$ points there is a convex decomposition with at most $n+C$ polygons. For sets having exactly three extreme points we show that more than $n+\sqrt{2(n-3)}-4$ polygons may be necessary to form a convex decomposition.     

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.     

Functions of Two Variables with Large Tangent Plane Sets

We show that there exist a C¹function,f, of two variables and a setE ⊆ R²of zero Lebesgue measure such that using the natural three-dimensional parametrization of planesz = ax + by + ctangent to the surfacez = f(x, y), the (three-dimensional) interior of the set of parameter values, (a, b, c), of tangent planes corresponding to points (x, y) inEis nonempty. From the Morse–Sard theorem it follows that there are no such C²functions. We also study briefly the relationship of our example with the Denjoy–Young–Saks theorem.     

Lattice Points in Large Borel Sets and Successive Minima

Let B be a Borel set in E^d with volume V(B) = ∞. It is shown that almost all lattices L in E^d contain infinitely many pairwise disjoint d-tuples, that is sets of d linearly independent points in B. A consequence of this result is the following: let S be a star body in E^d with V(S ) = ∞. Then for almost all lattices L in E^d the successive minima λ₁(S,L),..., λ_d(S,L) of S with respect to L are 0. A corresponding result holds for most lattices in the Baire category sense. A tool for the latter result is the semi-continuity of the successive minima.     

Sparse Systems of Functions Closed on Large Sets in RN

Let E(Z) = {e^inx}_nZ denote the trigonometrical exponential system.It is well known that E(Z) forms an orthogonal basis in thespace L²(0, 2). In 1964, H. Landau discovered that the trigonometricalsystem has the following property: certain small perturbationsof E(Z) yield exponential systems which are complete in L² onany finite union of 2-periodic translations of any interval(, 2–), 0 < < .     

Large Deviations in Random Perturbations of Axiom a Basic Sets

The paper first proves a result on the upper semi-continuityof the entropy map of random bundle maps, and then proves somelarge deviation results for random maps perturbations of anAxiom A diffeomorphism.     

Homeomorphisms of Manifolds with Prescribed Behaviour on Large Dense Sets

It is shown that MA₁ for -centred partial orders implies forany compact n-manifold M(n > 1) and any two ₁-dense subsetsof M there is an autohomeomorphism of M which is a bijectionbetween the two ₁-dense sets.     

Sparse Variational Analysis of Linear Mixed Models for Large Data Sets

It is increasingly common to be faced with longitudinal or multi-level data sets that have large numbers of predictors and/or a large sample size. Current methods of fitting and inference for mixed effects models tend to perform poorly in such settings. When there are many variables, it is appealing to allow uncertainty in subset selection and to obtain a sparse characterization of the data. Bayesian methods are available to address these goals using Markov chain Monte Carlo (MCMC), but MCMC is very computationally expensive and can be infeasible in large p and/or large n problems. As a fast approximate Bayes solution, we recommend a novel approximation to the posterior relying on variational methods. Variational methods are used to approximate the posterior of the parameters in a decomposition of the variance components, with priors chosen to obtain a sparse solution that allows selection of random effects. The method is evaluated through a simulation study, and applied to an epidemiological application.