Bruck-Ryser abstract theorem and symmetric designs

In [3] U. Ott introduced a Bruck-Ryser abstract theorem concerning lattices of an R-module. As one of the applications of this theorem, he obtained a new proof of the Bruck-Ryser theorem for finite projective planes and studied p-curves in a projective plane. In this paper, we apply the Bruck-Ryser abstract theorem in order to give a new proof of the Bruck-Ryser-Chowla theorem for symmetric (v, k, )-design with (v, k, )=1, and to study p-curves in arbitrary symmetric designs.     

‘Outside’ as a primitive notion in constructive projective geometry

In intuitionistic (or constructive) geometry there are positive counterparts, apart and outside, of the relations = and incident. In this paper it is shown that the relation outside suffices to define incident, apart and equality. The equivalence of the new system with Heyting's system is shown and as a simple corollary one obtains duality for intuitionistic projective geometry.     

Invariant Subspaces for Positive Operators Acting on a Banach Space with Markushevich Basis

We introduce weak quasinilpotence for operators. Then, by substituting Markushevich basis and weak quasinilpotence at a nonzero vector for Schauder basis and quasinilpotence at a nonzero vector, respectively, we answer a question on the invariant subspaces of positive operators in [3].     

The Hyperbell Algorithm for Global Optimization: A Random Walk Using Cauchy Densities

This article presents a new algorithm, called theHyperbell Algorithm, that searches for the global extrema ofnumerical functions of numerical variables. The algorithm relies on theprinciple of a monotone improving random walk whose steps aregenerated around the current position according to a gradually scaleddown Cauchy distribution. The convergence of the algorithm is provenand its rate of convergence is discussed. Its performance is tested onsome hard test functions and compared to that of other recentalgorithms and possible variants. An experimental study of complexityis also provided, and simple tuning procedures for applications areproposed.     

Conformal spaces

A conformal space is a non-singular metric vector space to which has been adjoined a null-cone of points at infinity. We define a conformal space in terms of a higher dimensional coordinate space, and then state and prove a fundamental theorem of conformal geometry.     

On strong solutions of the Stokes equations in exterior domains

We construct strong solutionsu, p/of the general nonhomogeneous Stokes equations -u + p=f inG, ·u=g inG, u= on in an exterior domainG ⁿ (n3) with boundary of class C². Our approach uses a localization technique: With the help of suitable cut-off functions and the solution of the divergence equation ·=g inG, = 0 on , the exterior domain problem is reduced to the entire space problem and an interior problem.     

Five Kinds of Maximal Monotonicity

We discuss Gossez's type (D) maximal monotone multifunctions and the newer type (ED) subfamily (for which an analog of the Brøndsted-Rockafellar property holds). We then discuss the locally maximal monotone (= type (FP)) and maximal monotone locally (= type (FPV)) multifunctions of Fitzpatrick-Phelps and Fitzpatrick-Phelps-Verona-Verona. Finally, we discuss the strongly maximal monotone multifunctions. We prove that every maximal monotone multifunction of type (D) is locally maximal monotone, and every maximal monotone multifunction of type (ED) is both maximal monotone locally and strongly maximal monotone.     

Optimal transformations for prediction in continuous-time stochastic processes: finite past and future

In the classical Wiener-Kolmogorov linear prediction problem, one fixes a linear functional in the future of a stochastic process, and seeks its best predictor (in the L²-sense). In this paper we treat a variant of the prediction problem, whereby we seek the most predictable non-trivial functional of the future and its best predictor; we refer to such a pair (if it exists) as an optimal transformation for prediction. In contrast to the Wiener-Kolmogorov problem, an optimal transformation for prediction may not exist, and if it exists, it may not be unique. We prove the existence of optimal transformations for finite past and future intervals, under appropriate conditions on the spectral density of a weakly stationary, continuous-time stochastic process. For rational spectral densities, we provide an explicit construction of the transformations via differential equations with boundary conditions and an associated eigenvalue problem of a finite matrix.This research was partially supported by ARO (MURI grant) DAAH04-96-1-0445, NSF grant DMS-0074276, and CNPq grant 301179/00-0.     

Croissance lineaire et géométrie bornée

We show that on a noncompact manifold which has finite topology at infinity, there exists a Riemannian metric with bounded geometry and linear growth-type.     

Projections on Lp-spaces of polyanalytic functions

The fundamental result: for an arbitrary bounded, simply connected domain in , the subspace L_n,m ^p() of the space L^p(, ) ( is the plane Lebesgue measure, p 1), consisting of the (m, n)-analytic functions in , is complemented in LP(, ) (a function f is said to be (m, n)-analytic if (^m+n/¯Z^mZⁿ)f=0 in ). Consequently, by virtue of a theorem of J. Lindenstrauss and A. Pelczyski, the space L_n,m ^P() is linearly homeomorphic to lP. In particular, for m=n=1 we obtain that the space of all harmonic L^P-functions in is complemented in L^P(, ). This result has been known earlier only for smooth domains.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 190, pp. 15–33, 1991.     

Some New Transversality Properties

The theorems of Ceva and Menelaus are concerned with cyclic products of ratios of lengths of collinear segments of triangles or more general polygons. These segments have one endpoint at a vertex of the polygon and one at the intersection point of a side with a suitable line. To these classical results we have recently added a selftransversality theorem in which the suitable line is determined by two other vertices. Here we present additional transversality properties in which the suitable line is determined either by a vertex and the intersection point of two diagonals, or by the intersection points of two pairs of such diagonals. Unexpectedly it turns out that besides several infinite families of systematic cases there are also a few sporadic cases.     

Augmented non-quadratic penalty algorithms

Auslender, Cominetti and Haddou have studied, in the convex case, a new family of penalty/barrier functions. In this paper, we analyze the asymptotic behavior of augmented penalty algorithms using those penalty functions under the usual second order sufficient optimality conditions, and present order of convergence results (superlinear convergence with order of convergence 4/3). Those results are related to the analysis of pure penalty algorithms, as well as augmented penalty using a quadratic penalty function. Limited numerical examples are presented to appreciate the practical impact of this local asymptotic analysis.This research was partially supported by NSERC grant OGP0005491     

Chains and Trees: ‘Strong’–‘Weak’ Order in Job Scheduling

We present a summary of recent NP-hardness and polynomial time solvability results for the distinction between strong and weak precedence for chains and trees in scheduling. We distinguish between chains and proper trees which are not chains, and demonstrate that the strong-weak precedence distinction for chains is not inclusive with regards to NP-hardness, and conjecture that the same holds for strong-weak tree precedence. The objective is to show that different interpretations for chain and tree order relations in scheduling might have far reaching computational implications.     

Experiments with an interactive paired comparison simplex method for molp problems

In this paper, an interactive paired comparison simplex based method formultipleobjectivelinearprogramming (MOLP) problems is developed and compared to other interactive MOLP methods. Thedecisionmaker (DM)'s utility function is assumed to be unknown, but is an additive function of his known linearized objective functions. A test for utilityefficiency for MOLP problems is developed to reduce the number of efficient extreme points generated and the number of questions posed to the DM. The notion of strength ofpreference is developed for the assessment of the DM's unknown utility function where he can express his preference for a pair of extreme points as strong, weak, or almost indifferent. The problem of inconsistency of the DM is formalized and its resolution is discussed. An example of the method and detailed computational results comparing it with other interactive MOLP methods are presented. Several performance measures for comparative evaluations of interactive multiple objective programming methods are also discussed.All rights reserved. This study, or parts thereof, may not be reproduced in any form without written permission of the authors.     

Foundational Isomorphisms in Continuous Differentiation Theory

We provide an elementary proof of existence for the Foundational Isomorphism in each of the categories of convergence spaces, compactly generated topological spaces and sequential convergence spaces. This isomorphism embodies the germ of differentiation and its inverse the germ of integration.     

Local symmetries and conservation laws

Starting with Lie's classical theory, we carefully explain the basic notions of the higher symmetries theory for arbitrary systems of partial differential equations as well as the necessary calculation procedures. Roughly speaking, we explain what analogs of higher KdV equations are for an arbitrary system of partial differential equations and also how one can find and use them. The cohomological nature of conservation laws is shown and some basic results are exposed which allow one to calculate, in principle, all conservation laws for a given system of partial differential equations. In particular, it is shown that symmetry and conservation law are, in some sense, the dual conceptions which coincides in the self-dual case, namely, for Euler-Lagrange equations. Training examples are also given.Translated from the Russian by B. A. Kuperschmidt.     

An improved bound for the de Bruijn–Newman constant

The Riemann hypothesis is equivalent to the conjecture that the de Bruijn–Newman constant satisfies 0. However, so far all the bounds that have been proved for go in the other direction, and provide support for the conjecture of Newman that 0. This paper shows how to improve previous lower bounds and prove that –2.710^–9<. This can be done using a pair of zeros of the Riemann zeta function near zero number 10²⁰ that are unusually close together. The new bound provides yet more evidence that the Riemann hypothesis, if true, is just barely true.     

Central Limit Theorems for dependent variables. I

Summary This paper gives a flexible approach to proving the Central Limit Theorem (C.L.T.) for triangular arrays of dependent random variables (r.v.s) which satisfy a weak mixing condition called -mixing. Roughly speaking, an array of real r.v.s is said to be -mixing if linear combinations of its past and future are asymptotically independent. All the usual mixing conditions (such as strong mixing, absolute regularity, uniform mixing, -mixing and -mixing) are special cases of -mixing. Linear processes are shown to be -mixing under weak conditions. The main result makes no assumption of stationarity. A secondary result generalises a C.L.T. that Rosenblatt gave for strong mixing samples which are nearly second order stationary.     

Compressible flow induced by the transient motion of a wavemaker

The effect of fluid compressibility on the evolution of the pressure distribution and free surface elevation, following the initiation of a horizontal motion of a vertical wavemaker, is analysed. This effect is significant even in a liquid (like water) when the time scale of the motion is very short (e.g. impulsive motions).In the leading order the present problem is analogous to that of supersonic flow about a thin wing, thus the solution is represented by means of an appropriate supersonic source distribution. Closed-form results are obtained for the case of impulsive motion (i.e. a step function velocity). The pressure field corresponds to systems of double rarefaction and double compression waves traversing the fluid domain intermittently. Following the passage of a rarefaction (compression) wave, the free surface becomes locally concave (convex). The resulting free surface profile consists of an elongating wavetrain in front of a jet riding up the vertical wall.On the compressible time-scale the pressure and velocity fields approach a steady long-time limit. This limit corresponds to the short-time incompressible flow prevailing after the attenuation of the pressure waves. The spatial nonuniformity of the asymptotic expansion in the neighbourhood of the waterline is briefly discussed.     

Transient solution for a finite capacity M/G a,b /1 queueing system with vacations to the server

In this paper we consider a single server queueing system with Poisson input, general service and a waiting room that allows only a maximum of b customers to wait at any time. A minimum of a customers are required to start a service and the server goes for a vacation whenever he finds less than a customers in the waiting room after a service. If the server returns from a vacation to find less than a customers waiting, he begins another vacation immediately. Using the theory of regenerative processes we derive expressions for the time dependent system size probabilities at arbitrary epochs.