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     

Directional derivative of the value function in parametric optimization

This paper presents with elementary proofs some results on the directional derivative of the optimal value of a finite dimensional optimization problem with parameters.This research was supported by the Natural Sciences and Engineering Research Council of Canada under Grant A-9273.     

Idempotent reducts of abelian groups

In this paper we construct two maps between the polynomials of abelian groups and the polynomials of idempotent reducts of abelian groups and show that these can be used to “lift” the finite basis property from abelian groups to their idenpotent reducts. It follows that this equational class of all idempotent reducts of abelian groups has the finite basis property. The research of this author was supported by a grant from the National Research Council of Canada. Presented by J. Mycielski     

Finding the largest suborder of fixed width

Finding the largest suborder of fixed width in a partially ordered set is an interesting combinatorial problem with applications in combinatorial optimization and scheduling. We present a polynomial time solution for this problem by transforming it into a minimum cost network flow problem in an appropriate auxiliary network.This research was supported in part by the Natural Sciences and Engineering Research Council of Canada, under Grant No. A1798.     

Switching between modified Newton and fix-point iteration for implicit ode-solvers

In this paper we discuss the automatic switch between modified Newton iteration with the Jacobian not equal zero and fix-point iteration, i.e. the Jacobian equal zero. The switching strategy is based on the ratio between the norm of the displacement and the norm of the residual. Several examples are discussed both from non-stiff and stiff systems. These examples show that our strategy is working as predicted.This work was supported by NATO Research Grant Programme, project RG 096.80 and by National Sciences and Engineering Research Council of Canada, Grants: A1244, A3597, A4076, A8111, A8239, A8639.     

Products of idempotent endomorphisms of free acts of infinite rank

In 1966, J. M. Howie characterized the self-maps of a set which can be written as a product (i.e., composite) of idempotent self-maps of that set. Using a wreath product construction introduced by V. Fleischer, the first-named author was recently able to describe products of idempotent endomorphisms of a freeS-act of finite rank whereS is any monoid. The purpose of the present paper is to extend this result to freeS-acts of infinite rank.Research supported by Natural Sciences and Engineering Research Council of Canada Research Grant A4494     

Exact penalization and stationarity conditions of mathematical programs with equilibrium constraints

Using the theory of exact penalization for mathematical programs with subanalytic constraints, the theory of error bounds for quadratic inequality systems, and the theory of parametric normal equations, we derive various exact penalty functions for mathematical programs subject to equilibrium constraints, and we also characterize stationary points of these programs. The research of this author is based on work supported by the National Sciences and Engineering Research Council of Canada under grant OPG0090391. The research of this author is based on work supported by the National Science Foundation under grants DDM-9104078 and CCR-9213739. Part of this paper was completed while he was visiting The University of Melbourne and The University of New South Wales. The research of this author is based on work supported by the Australian Research Council.     

On the continuity of the minimum in parametric quadratic programs

This paper establishes results on the lower semicontinuity and continuity of the optimal objective value of a parametric quadratic program with continuous dependence of the coefficients on parameters. The results established herein generalize directly well-known results on parametric linear programs.This research was supported by the Natural Sciences and Engineering Research Council of Canada under Grant No. A8189.     

On the discretization of differential and Volterra integral equations with variable delay

In this paper we analyze the attainable order ofm-stage implicit (collocation-based) Runge-Kutta methods for differential equations and Volterra integral equations of the second kind with variable delay of the formqt (0<q<1). It will be shown that, in contrast to equations without delay, or equations with constant delay, collocation at the Gauss (-Legendre) points will no longer yield the optimal (local) orderO(h ^2m ). This work was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC Research Grant OGP0009406).     

The functor A min on p-local spaces

In a previous paper, the authors gave the finest functorial decomposition of the loop suspension of a p-torsion suspension. The purpose of this paper is to generalize this theorem to the loop suspension of arbitrary p-local path connected spaces. The authors are grateful for support from National Sciences Engineering Research Council of Canada and National University of Singapore.     

Input optimization: I. Optimal realizations of mathematical models

Mathematical models are considered as input-output systems. The input is data (technological coefficients, available energy, prices) and the output is the feasible set, the set of optimal solutions, and the optimal value. We study when output is a continuous function of input and identify optimal (minimal) realizations of mathematical models. These are states of the model having the property that every stable perturbation of input results in a locally worse (higher) value of the optimal value function. In input optimization we “optimize” mathematical model rather than a specific mathematical program. This research was supported in part by the Natural Sciences and Engineering Research Council of Canada, and in part by the Gouvernement du Québec, programme de formation de chercheurs et d’action concertée.     

Characterizing an optimal input in perturbed convex programming

When every feasible stable perturbation of data results in a non-improvement of the optimal value function, then we talk about an ‘optimal input’ or an ‘optimal selection of data”. In this paper we describe such data for convex programs using perturbed saddle points. Research partly supported by Natural Sciences and Engineering Council of Canada and le Ministère de l'Education du Québec (F.C.A.C.). Presented in part at the Third Symposium on Mathematical Programming with Data Perturbations, The George Washington University, Washington, D.C. (May 21–22, 1981).     

The nonemptiness of thef-core of a game without side payments

We prove the nonemptiness of the core of a continuum game without side payments where only small coalitions — ones bounded in absolute size of finite cardinality — are permitted. This result covers assignment games with a continuum of players and includes combinations of several assignment games, such as housing and automobile markets.The authors thank two anonymous referees for many helpful comments. The second author is indebted primarily to the Natural Sciences and Engineering Research Council of Canada for financial support and also the Social Sciences and Humanities Research Council of Canada.     

A unified framework for linear control problems with state-variable inequality constraints

This paper briefly reviews the literature on necessary optimality conditions for optimal control problems with state-variable inequality constraints. Then, it attempts to unify the treatment of linear optimal control problems with state-variable inequality constraints in the framework of continuous linear programming. The duality theory in this framework makes it possible to relate the adjoint variables arising in different formulations of a problem; these relationships are illustrated by the use of a simple example. This framework also allows more general problems and admits a simplex-like algorithm to solve these problems.This research was partially supported by Grant No. A4619 from the National Research Council of Canada to the first author. The first author also acknowledges the support provided by the Brookhaven National Laboratory, where he conducted his research.     

A saddle-point characterization of Pareto optima

This paper provides an answer to the following basic problem of convex multi-objective optimization: Find a saddle-point condition that is both necessary and sufficient that a given point be Pareto optimal. No regularity condition is assumed for the constraints or the objectives.Research partly supported by the Natural Sciences and Engineering Research Council of Canada.Corresponding author.Contribution of this author is a part of her M.Sc. Thesis in Applied Mathematics.     

On Pairs of Linear Equations in Three Prime Variables

In this paper, we consider the simultaneous representation of pairs of integers as linear combinations in three prime variables and obtain a related numerical bound.     

On the normalizer problem for integral group rings of torsion groups

In this paper, we investigate the normalizer property for the integral group ring of a torsion group. We show that this property holds for locally finite nilpotent groups. A necessary and sufficient condition for this property to hold for any torsion group is also given. This research was supported in part by a research grant from the Natural Sciences and Engineering Research Council of Canada.     

Formally real fields,pythagorean fields,C-fields andW-groups

Supported in part by the National Science Foundation and the Natural Sciences and Engineering Research Council of Canada     

A simple linear model for the optimal exploitation of renewable resources

This paper describes a simple linearized model for the optimal control of a natural resource stock. Applications of the model to fisheries and forestry, as well as to mineral exploration and recovery, are discussed.Research supported partially by the National Research Council of Canada, Grant A-3990.     

An algebraic dependence over the quasi-centre

Summary The authors study a class of rings generalizing both ξ-rings and rings which are (1) quasi-radical over their normalizer. The results are quite complete in the Noetherian case. In application several conditions on rings are shown to force the right duo condition. In particular it is shown that ξ-rings, algebras over the rationals satisfying (1), and algebraic algebras having no non central nilpotent elements (or a more general condition) are right duo or duo rings. Entrata in Redazione il 28 luglio 1972. This research has been supported by grant A7876 of the National Research Council of Canada. This research has been supported by grant A7877 of the National Research Council of Canada.