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     

Cutting planes and column generation techniques with the projective algorithm

The problem studied is that of solving linear programs defined recursively by column generation techniques or cutting plane techniques using, respectively, the primal projective method or the dual projective method.This research has been supported in part by FCAR of Quebec, Grant Nos. CE-130 and EQ-3078, by NSERC of Canada, Grant No. A4152, and by the Fonds National Suisse de la Recherche Scientifique, Grant No. 1.467.0.86.     

Criteria for differentiable generalized monotone maps

First-order criteria for pseudomonotonicity and quasimonotonicity are given for differentiable maps on open convex sets. These criteria are proved stronger than those introduced earlier. This research was supported by the National Research Council of Canada, Grant No A8312.     

A note on table look-up

A more realistic bound for the average number of comparisons needed to match an incoming identifier by table look-up, when the table is still growing, is derived.Work carried out under a National Research Council of Canada Grant No. A-7700.     

Predictor-corrector methods for nonlinear Volterra integral equations of the second kind

Predictor-corrector methods for nonlinear Volterra integral equations are considered together with a theorem which provides a proof of the convergence of such methods. Some numerical examples are also included.This research was supported by the National Research Council of Canada under Grant A 8196.     

A set of geometric programming test problems and their solutions

This paper attempts to provide a set of standard test examples for researchers working in the area of geometric programming and general nonlinear, continuous, nonconvex programming algorithms. The examples consist partly of applications of nonlinear programming that have appeared in the literature and partly of original geometric programming applications. Solutions to all the problems are provided as well as the starting points from which these solutions were computed. Other computationally important aspects such as tolerances and degree of accuracy with which these problems were solved, are also included.This work was supported in part by Canada Council Grant #S74-0148 and National Research Council of Canada Grant #084-6319-32.     

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.     

Optimal control of a large turboalternator

The optimal torque and voltage control for a large turbogenerator is found by using the minimum norm formulation. It should be noted that the model used is highly nonlinear. Numerical results are presented.This work was supported in part by the National Research Council of Canada, Grant No. A4146.     

On the congruence lattice of a Scott-domain

We prove that the congruence lattice of a Scott-domain can be characterized as a complete lattice.Presented by V. Trnkova.The research of the first author was supported by the NSERC of Canada.The research of the second author was supported by the Hungarian National Foundation for Scientific Research, under Grant No. 1903.     

Finiteness conditions for finitely generated monoids

In this paper, we show that every finitely generated monoid, with a disjunctive zero 0 such that abc=0 implies cba=0, is finite. This research has been supported by Grant A7877 of the National Research Council of Canada.     

Optimal load frequency control with governor backlash

A new technique is described for designing an optimal controller for a system whose dynamical equations contain a backlash element. The approach is applied to the problem of load frequency control (LFC) of a single area steam power system.This work was supported in part by the National Research Council of Canada, Grant No. A4146.     

On strongly exposed points and frechet differentiability

Using properties of convex functionals, it is shown that closed and bounded convex sets in a class of Banach spaces which includes separable conjugate spaces are the closed convex hulls of their strongly exposed points. This research was supported by the National Research Council of Canada, Grant A-3999.     

Error bounds and convergence analysis of feasible descent methods: a general approach

We survey and extend a general approach to analyzing the convergence and the rate of convergence of feasible descent methods that does not require any nondegeneracy assumption on the problem. This approach is based on a certain error bound for estimating the distance to the solution set and is applicable to a broad class of methods.The research of the first author is supported by the Natural Sciences and Engineering Research Council of Canada, Grant No. OPG0090391, and the research of the second author is supported by the National Science Foundation, Grant No. CCR-9103804.     

A lower bound for the controlling parameters of the exact penalty functions

The purpose of this paper is to present new exact penalty functions and discuss their properties. A lower bound on the controlling parameters is given, for which above this value, the optimum of the exact penalty function coincides with the optimum of the nonlinear programming problem.This work was supported by the National Research Council of Canada under Grant A4414.     

On realizing symmetric 3-polytopes

We prove the analogue of Eberhard’s Theorem for symmetric convex 3-polytopes with a 4-valent graph, and disprove a conjecture of the late T. Motzkin about realizing symmetric convex 3-polytopes so that all of their geodesics are in planes. This research was supported by the National Research Council of Canada Grant A-3999.     

Schreier rewriting beyond the classical setting

Using actions of free monoids and free associative algebras, we establish some Schreiertype formulas involving ranks of actions and ranks of subactions in free actions or Grassmann-type relations for the ranks of intersections of subactions of free actions. The coset action of the free group is used to establish a generalization of the Schreier formula in the case of subgroups of infinite index. We also study and apply large modules over free associative and free group algebras. This work was supported by Natural Sciences and Engineering Research Council of Canada (Grant No. 227060-04), Yuri Bahturin, National Science Foundation (Grant No. DMS-0700811) and Russian Fund for Basic Research (Grant No. 08-01-00573), Alexander Olshanskii     

Subspace exit properties of extremal controls

In a linear control system setting, we derive conditions under which extremal controls give rise to trajectories which exit a given subspace. An application is in determining effectiveness of linear state restraints in time-optimal problems.This work was supported by the National Research Council of Canada under Grant No. A4641.     

On computing the number of linear extensions of a tree

An algorithm requiring O(n ²) arithmetic operations for computing the number of linear extensions of a poset whose covering graph is a tree is given.This research was partially funded by the National Science and Engineering Research Council of Canada under Grant Number A4219.     

The syntactic monoid of a hypercode

This paper gives a characterization of the syntactic monoid of a hypercode H over a finite alphabet X, a hupercode being a non empty set of non empty words over X, which are pairwise incomparable relatively to the embedding partial order of X. This research has been supported by Grant A7877 of the National Research Council of Canada.     

Decentralized optimum load frequency control of interconnected power systems

A new approach for designing a linear regulator for the problem of load frequency control (LFC) of interconnected power systems is developed. The control is specified to be of proportional-plus-integral (P-I) form and is only a function of the measurable states. The LFC problem is formulated as a parameter optimization problem.This work was supported in part by the National Research Council of Canada, Grant No. A4146.