On the Minimal Number of Even Submatrices of 0-1 Matrices

An asymptotic formula for the minimum possible number of even p x q submatrices of an m x n 0-1 matrix A is obtained. It is shown that if Ais considered random and pq is even, then the distributionof the number of the even p x q submatricesof A is highly skewed to the right, the left endpointof the distribution being very close to its mean, while its rightendpoint is twice the mean. A relation to Turán numbersis indicated.     

New Classes of Groups Containing Menon Difference Sets

A theorem due to Davis on the existence of Menon difference sets in 2-groups is generalised to non-2-groups. The existence of Menon difference sets in many new non-abelian groups is established.     

Bounded influence regression using high breakdown scatter matrices

In this paper we estimate the parameters of a regression model using S-estimators of multivariate location and scatter. The approach is proven to be Fisher-consistent, and the influence functions are derived. The corresponding asymptotic variances are obtained and it is shown how they can be estimated in practice. A comparison with other recently proposed robust regression estimators is made.     

Commutativity preserving linear maps and Lie automorphisms of strictly triangular matrix space

In this paper we classify linear maps preserving commutativity in both directions on the space N(F) of strictly upper triangular (n+1)×(n+1) matrices over a field F. We show that for n3 a linear map on N(F) preserves commutativity in both directions if and only if =^′+f where ^′ is a product of standard maps on N(F) and f is a linear map of N(F) into its center.     

复亚正定矩阵的几个行列式不等式

讨论了复亚正定矩阵的几个行列式不等式的问题，并在复亚正定矩阵的基础上推广了几个行列式不等式，修正并推广了现有的结果。     

Inferences on interclass and intraclass correlations in multivariate familial data

Inference procedures for interelass and intraclass correlations are given in the multivariate context of familial data for which measurements are taken on more than one characteristic. Unified estimators are proposed based on a certain class of unbiased estimators of covariance matrices. Asymptotic distributions of the proposed estimators are derived under the assumption of multivariate normality. The results can be used to construct approximate confidence intervals and test procedures.Research supported by the Department of Statistics, the Pennsylvania State University and the Air Force Office of Scientific Research under Grant AFSO-88-0030.Institute of Statistical Mathematics     

Gainfree Leontief substitution flow problems

Leontief substitution systems have been studied by economists and operations researchers for many years. We show how such linear systems are naturally viewed asLeontief substitution flow problems on directed hypergraphs, and that important solution properties follow from structural characteristics of the hypergraphs. We give a strongly polynomial, non-simplex algorithm for Leontief substitution flow problems that satisfy againfree property leading to acyclic extreme solutions. Integrality conditions follow easily from this algorithm. Another structural property,support disjoint reachability, leads to necessary and sufficient conditions for extreme solutions to be binary. In a survey of applications, we show how the Leontief flow paradigm links polyhedral combinatorics, expert systems, mixed integer model formulation, and some problems in graph optimization.Dedicated to the memory of Robert G. JeroslowSee Acknowledgement section.Research supported in part by the ONR (Office of Naval Research) under URI Grant number N00014-86-K-0689, and Center for Operations Research and Econometrics, Universite Catholique de Louvain.     

SINGULAR INTEGRAL OPERATORS ANDSINGULAR QUADRATURE OPERATORSASSOCIATED WITH SINGULAR INTEGRAL EQUATIONS

1IntroductionSingUlarlintegralequations(SIEs)withCauchytypekernelsoftheformappearfrequelltlyinproblemsOfthetheoriesofelasticity.Heretheinputfunctionsa)b,f,l,aretheH5lder-continuousfunctionsfortheirvariables,Aisagivenconstant,anditisrequiredtofindthesolutionWintheclassho[1,2].Theclassicaltheoryoftheseequationsisrathercomplete[1,2].Inthepasttwentyyearsagreatdealofinteresthasarisenintheirnumericalsolution.VariouscollocationmethodsforSIEshaveappeared,forwhichsomereferencescanbefoundinthesurv…     

Adaptive Wavelet Methods II—Beyond the Elliptic Case

This paper is concerned with the design and analysis of adaptive wavelet methods for systems of operator equations. Its main accomplishment is to extend the range of applicability of the adaptive wavelet-based method developed in [17] for symmetric positive definite problems to indefinite or unsymmetric systems of operator equations. This is accomplished by first introducing techniques (such as the least squares formulation developed in [26]) that transform the original (continuous) problem into an equivalent infinite system of equations which is now well-posed in the Euclidean metric. It is then shown how to utilize adaptive techniques to solve the resulting infinite system of equations. This second step requires a significant modification of the ideas from [17]. The main departure from [17] is to develop an iterative scheme that directly applies to the infinite-dimensional problem rather than finite subproblems derived from the infinite problem. This rests on an adaptive application of the infinite-dimensional operator to finite vectors representing elements from finite-dimensional trial spaces. It is shown that for a wide range of problems, this new adaptive method performs with asymptotically optimal complexity, i.e., it recovers an approximate solution with desired accuracy at a computational expense that stays proportional to the number of terms in a corresponding wavelet-best N -term approximation. An important advantage of this adaptive approach is that it automatically stabilizes the numerical procedure so that, for instance, compatibility constraints on the choice of trial spaces, like the LBB condition, no longer arise.