On a new law of the iterated logarithm of Erdős and Révész

Research supported by the Fok Yingtung Education Foundation and by an NSERC Canada Scientific Exchange Award at Carleton University, Ottawa, Canada.     

Confidence bands for quantile function under random censorship

Some new confidence bands are established for the quantile function from randomly censored data. The method does not require estimation of the density function. As an application, we construct bands for the quantile function of the length of fractures in the granitic plutons near Lac du Bonnet, Manitoba, where an Underground Research Laboratory is being built for the nuclear waste disposal program in Canada.Geological Survey of Canada Contribution Number 10386.Research partially supported by an NSERC Canada Grant.Research done while at Carieton University, supported by NSERC Canada and EMR Canada Grants of M. Csörg.     

Bootstrapped confidence bands for percentile lifetime

Summary We propose bootstrapped confidence bands for the percentile lifetime function. Our method is based on a joint approximation of the empirical and quantile processes and their bootstrapped counterparts. Modest simulations support the results. Confidence bands are applied to quantile and median residual lifetimes of tractor rear brakes. Research done while at Carleton University Norman Paterson Centre: also partially supported by NSERC Canada grants of M. Cs?rgő. Research supported in part by a NSERC Canada operating grant. Research done while at Carleton University; also partially supported by NSERC Canada grants of m. Cs?rgő and D. A. Dawson and by an EMR Canada grant of M. Cs?gő. Research supported in part by a United States Department of Agriculture CSRS grant and a United States NSF grant of D. M. Bates, G. Wahba and B. S. Yandell.     

Diffusion approximations for re-entrant lines with a first-buffer-first-served priority discipline

The diffusion approximation is proved for a class of queueing networks, known as re-entrant lines, under a first-buffer-first-served (FBFS) service discipline. The diffusion limit for the workload process is a semi-martingale reflecting Brownian motion on a nonnegative orthant. This approximation has recently been used by Dai, Yeh and Zhou [21] in estimating the performance measures of the re-entrant lines with a FBFS discipline.Supported in part by a grant from NSERC (Canada).Supported in part by a grant from NSERC (Canada); the research was done while the author was visiting the Faculty of Commerce and Business Administration, UBC, Canada.     

Rate of convergence of transport processes with an application to stochastic differential equations

Summary We obtain a rate of convergence of uniform transport processes to Brownian motion, which we apply to the Wong and Zakai approximation of stochastic integrals.The research of both authors was supported by a NSERC Canada Grant and by an EMR Canada Grant of M. Csörgö at Carleton University, Ottawa     

On the existence of oscillatory solutions to nonlinear differential equations

Summary A general change of variable technique is combined with appropriate energy functions to show the existence of oscillatory solutions to nonlinear ordinary second order differential equations. Entrata in Redazione il 21 marzo 1974. Research supported by National Research Council of Canada grants NRC-A-7673 and NRC-A-7197 and Defence Research Board of Canada grand DRB-9540-28.     

A note on trivial nonmultidimensional superstable theories

Research supported by the NSERC of Canada     

Geometry of normed bilinear maps and the 16-square problem

Supported in part by NSERC of Canada     

Pro-2-Demuškin groups of rank ℵ0 as Galois groups of maximal 2-extensions of fields

Research supported in part by the Natural Sciences and Engineering Council of Canada     

Graded Betti numbers of some embedded rationaln-folds

Supported, in part, by the Natural Sciences and Engineering Research Council of Canada     

Automorphisms of split Cayley algebras over real closed fields

Research supported in part by NSERC Canada grant A7251.     

Applications of parametric programming and eigenvalue maximization to the quadratic assignment problem

We investigate new bounding strategies based on different relaxations of the quadratic assignment problem. In particular, we improve the lower bound found by using an eigenvalue decomposition of the quadratic part and by solving a linear program for the linear part. The improvement is accomplished by applying a steepest ascent algorithm to the sum of the two bounds.Both authors would like to thank the Natural Sciences and Engineering Research Council Canada and the Austrian Government for their support.This author would like to acknowledge partial support from the Department of Combinatorics and Optimization at the University of Waterloo.Research partially supported by Natural Sciences and Engineering Research Council Canada.     

Inverse programming and the linear vector maximization problem

This paper presents a new concept of efficient solution for the linear vector maximization problem. Briefly, these solutions are efficient with respect to the constraints, in addition to being efficient with respect to the multiple objectives. The duality theory of linear vector maximization is developed in terms of this solution concept and then is used to formulate the problem as a linear program.This research has been partially supported by grants from the Canada Council and the National Research Council of Canada.     

A class of martingales with non-symmetric limit distributions

Summary A class of non-pathological martingales is exhibited to which current martingale central limit theory does not apply. The problem consists in the convergence of the normalized sums of squares being only in distribution. The class is that of degenerate U-statistics.This work was done while the first two authors were on Sabbatical leave at the Technion.Work supported in part by National Research Council of Canada, Grant No. A-9068Work supported in part by National Research Council of Canada, Grant No. A-9076     

On a result of Birkhoff

The research of the first two authors was supported by the NSERC of Canada.     

An extended descent framework for variational inequalities

In this paper, we develop a very general descent framework for solving asymmetric, monotone variational inequalities. We introduce two classes of differentiable merit functions and the associated global convergence frameworks which include, as special instances, the projection, Newton, quasi-Newton, linear Jacobi, and nonlinear methods. The generic algorithm is very flexible and consequently well suited for exploiting any particular structure of the problem.This research was supported by the National Science and Engineering Research Council of Canada, Grant A5789, and by the Department of National Defence of Canada, Grant FUHBP.     

Ring analogues of Baer's norm and P. Hall's margins

Supported by the Natural Sciences and Engineering Research Council of Canada, Grant No. A3961.     

The ring of upper triangular invariants as a module over the Dickson invariants

This research is supported in part by the Natural Sciences and Engineering Research Council of Canada     

Evaluation of the discrepancy of the linear congruential pseudo-random number sequencies

The discrepancy of a pseudo-random number (PRN) sequence has been defined as a quantity which measures the deviation of the sequence's distribution from the ideal uniform distribution. In this paper, we give three algorithms for computer evaluation of the discrepancy of PRN sequences. The computational results for the discrepancy of PRN sequences generated by a linear congruential method are included.This research is partially funded by Natural Sciences and Engineering Research Council of Canada, Grant No. 0GP00089. A research grant from IBM Canada through the Supercomputer Center, University of New Brunswick, is gratefully acknowledged.     

On derivations and commutativity in prime rings

Supported by the Natural Sciences and Engineering Research Council of Canada, Grant No. A3961.