Structural constrained controllers for discrete-time linear systems

In this paper, we present an approach for designing structural constrained controllers for discrete-time linear systems, based on a new stabilizability property of the Riccati equation solution. First, the feedback stabilization problem under a general structural constraint is considered and a simple numerical procedure to solve it is presented. Special attention is given to the output feedback stabilization problem, for which sufficient conditions for the existence and convergence toward a stabilizing matrix are provided. Some examples are solved and comparisons with other methods available in the literature are made.This research has been developed with the financial support of the Conselho Nacional de Desenvolvimento Científico e Tecnológico, CNPq, Brasília, Brazil.     

A simulation-based approach to two-stage stochastic programming with recourse

In this paper we consider stochastic programming problems where the objective function is given as an expected value function. We discuss Monte Carlo simulation based approaches to a numerical solution of such problems. In particular, we discuss in detail and present numerical results for two-stage stochastic programming with recourse where the random data have a continuous (multivariate normal) distribution. We think that the novelty of the numerical approach developed in this paper is twofold. First, various variance reduction techniques are applied in order to enhance the rate of convergence. Successful application of those techniques is what makes the whole approach numerically feasible. Second, a statistical inference is developed and applied to estimation of the error, validation of optimality of a calculated solution and statistically based stopping criteria for an iterative alogrithm. © 1998 The Mathematical Programming Society, Inc. Published by Elsevier Science B.V.Supported by CNPq (Conselho Nacional de Desenvolvimento Científico e Tecnológico), Brasília, Brazil, through a Doctoral Fellowship under grant 200595/93-8.     

A search strategy for the elementary cycles of a directed graph

The most successful known algorithms enumerating the elementary cycles of a directed graph are based on a backtracking strategy. Such existing algorithms are discussed and a new backtracking algorithm is proposed which is bounded byO(N +M(C + 1)) time, for a directed graph withN vertices,M edges andC elementary cycles.Research supported by the Conselho National de Desenvolvimento Científico e Tecnológico — CNPq — Brasil.     

Prime ideals and radicals of centred extensions and tensor products

In this paper, we study prime ideals and radicals of centred extensions of rings. Obtained results are applied to tensor products of algebras over commutative rings. This research was partially supported by Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), Brazil. The second-named author was also supported by KBN grant 2 P301 035 06.     

Large deviations for the contact process and two dimensional percolation

Summary The following results are proved: 1) For the upper invariant measure of the basic one-dimensional supercritical contact process the density of 1's has the usual large deviation behavior: the probability of a large deviation decays exponentially with the number of sites considered. 2) For supercritical two-dimensional nearest neighbor site (or bond) percolation the densityY of sites inside a square which belong to the infinite cluster has the following large deviation properties. The probability thatY deviates from its expected value by a positive amount decays exponentially with the area of , while the probability that it deviates from its expected value by a negative amount decays exponentially with the perimeter of . These two problems are treated together in this paper because similar techniques (renormalization) are used for both.Partially supported by the National Science Foundation and the U.S. Army Research Office through the Mathematical Sciences Institute at CornellPartially supported by Conselho Nacional de Desenvolvimento Científico e Tecnológico-CNPq (Brazil) and the U.S. Army Research Office through the Mathematical Sciences Institute at Cornell     

Rectilinear shortest paths in the presence of rectangular barriers

In this paper we address the following shortest-path problem. Given a point in the plane andn disjoint isothetic rectangles (barriers), we want to construct a shortestL ₁ path (not crossing any of the barriers) from the source point to any given query point. A restricted version of this problem (where the source and destination points are knowna priori) had been solved earlier inO(n ²) time. Our approach consists of preprocessing the source point and the barriers to obtain a planar subdivision where a query point can be located and a shortest path connecting it to the source point quickly transvered. By showing that any such path is monotone in at least one ofx ory directions, we are able to apply a plane sweep technique to divide the plane intoO(n) rectangular regions. This leads to an algorithm whose complexity isO(n logn) preprocessing time,O(n) space, andO(logn+k) query time, wherek is the number of turns on the reported path. If only the length of the path is sought,O(logn) query time suffices. Furthermore, we show an (n logn) time lower bound for the case where the source and destination points are known in advance, which implies the optimality of our algorithm in this case.A preliminary version of this paper appeared in theProceedings of the First Symposium on Computational Geometry (1985).Supported in part by CNPq-Conselho Nacional de Desenvolvimento Científico e Tecnológico (Brazil).Supported in part by the National Science Foundation under Grants MCS 8420814 and ECS 8340031.     

Optimal ℋ∞-state feedback control for continuous-time linear systemsfeedback control for continuous-time linear systems

This paper proposes a convex programming method to achieve optimal -state feedback control for continuous-time linear systems. State space conditions, formulated in an appropriate parameter space, define a convex set containing all the stabilizing control gains that guarantee an upper bound on the -norm of the closed-loop transfer function. An optimization problem is then proposed, in order to minimize this upper bound over the previous convex set, furnishing the optimal -control gain as its optimal solution. A limiting bound for the optimum -norm can easily be calculated, and the proposed method will achieve minimum attenuation whenever a feasible state feedback controller exists. Generalizations to decentralized and output feedback control are also investigated. Numerical examples illustrate the theory.This research has been supported in part by grants from Fundação de Amparo à Pesquisa do Estado de São Paulo—FAPESP and Conselho Nacional de Desenvolvimento Científico e Tecnológico, CNPq—Brazil. The authors are grateful to the anonymous referees for their useful comments on this paper.     

Solutions for a class of neutral differential equations with nonatomicD-operator

This paper is concerned with the existence and uniqueness of solutions to first-order linear differential equations of neutral type with a nonatomicD-operator. We use an algebraic approach, in the context of the theory of convolution operators. Necessary and sufficient conditions are given for the initial value problem to have unique solutions for a class of equations.This work was done while the author was at the Department of Mathematics, Virginia Polytechnic Institute and State University.Instituto de Desarrollo Tecnológico para la Industria Quimica (INTEC), dependent on Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET) and the Universidad Nacional del Litoral (UNL).     

Kelley-Morse+Types of well order is not a conservative extension of Kelley Morse

Summary Assuming the consistency ofZF + There is an inaccessible number of inaccessibles, we prove that Kelley Morse theory plus types is not a conservative extension of Kelley-Morse theory.This paper was partially supported by: Dirección de Investigación de la Pontificia Universidad Católica de Chile (DIUC); Fondo Nacional de Desarrollo Científico y Tecnológico (FONDECYT)     

Existence and nonexistence of homotopy formulas for the Mizohata complex

In connection with the question of local integrability of strongly pseudoconvex involutive structures of co-rank one, we prove existence and nonexistence of homotopy formulas on 1-forms for the Mizohata structure in ⁿ⁺¹ and relate them to local integrability.The work of both authors was partially supported by CNPq.     

Spectra of regular polytopes

In this paper we compute the spectra with multiplicities of the adjancency graphs of all regular polytopes in ⁿ : it turns out that all such eigenvalues are algebraic intergers of degree no greater than 3.Both authors receive continuous support from FINEP and CNPq, Brazil.     

Constraint decomposition algorithms in global optimization

Many global optimization problems can be formulated in the form min{c(x, y): x X, y Y, (x, y) Z, y G} where X, Y are polytopes in ^p , ⁿ , respectively, Z is a closed convex set in ^p+n, while G is the complement of an open convex set in ⁿ . The function c: ^p+n is assumed to be linear. Using the fact that the nonconvex constraints depend only upon they-variables, we modify and combine basic global optimization techniques such that some new decomposition methods result which involve global optimization procedures only in ⁿ . Computational experiments show that the resulting algorithms work well for problems with smalln.     

Properties of paradoxical sets in the plane

We show that every paradoxical subset of ² has empty interior, and every measurable paradoxical subset of ² has measure zero. We investigate how the proof fails in the hyperbolic plane, where there are paradoxical sets with interior points and with infinite measure.     

Boundedness of singular integrals of variable rough Calderón-Zygmund kernels along surfaces

Letn2. The authors establish theL ²( ⁿ )-boundedness of singular integrals with variable rough Calderón-Zygmund kernels associated to surfaces satisfying some conditions.The research is supported in part by the NNSF and the SEDF of China.     

An extended continuous Newton method

This paper describes a numerical realization of an extended continuous Newton method defined by Diener. It traces a connected set of locally one-dimensional trajectories which contains all critical points of a smooth functionf: ⁿ . The results show that the method is effectively applicable.The authors would like to thank L. C. W. Dixon for pointing out some errors in the original version of this paper and for several suggestions of improvements.     

Isotrope Kurventheorie aufS 2 × ℝ

In this note we define an isotropic metric on the threedimensional manifoldS ² × . This metric will allow an symmetric riemannian connection , wich will be used to do differential geometry on S² × . We develope theory of curves onS ² × and show some relations to the theory of curves of threedimensional isotropic spaceI ₃.     

Polyedrische 2-Mannigfaltigkeiten mit wenigen nicht-konvexen Ecken

LetP denote a polyhedral 2-manifold in ³, i.e. a 2-dimensional cell-complex in ³ whose underlying point-set is a closed connected 2-manifold. A vertexv ofP is called convex if at least one of the two components into whichP divides a sufficiently small ball centered atv is convex. It is shown that every polyhedral 2-manifold in ³ of genusg>–1 contains at least five non-convex vertices and that for every positive integerg this bound is attained, i.e. there exists a polyhedral 2-manifold in ³ of genusg with precisely five non-convex vertices.

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On the number of triple points of the tangent developable

We study the singularities of the tangent developable of a generic curve in ³ and prove that if the curve has no torsion zero points, the number of triple points of that surface must be even.     

Vandermonde matrices on the circle: Spectral properties and conditioning

Summary We study Vandermonde matrices whose nodes are given by a Van der Corput sequence on the unit circle. Our primary interest is in the singular values of these matrices and the respective (spectral) condition numbers. Detailed information about multiplicities and eigenvectors, however, is also obtained. Two applications are given to the theory of polynomials.Dedicated to R. S. Varga on the occasion of his sixtieth birthdayResearch of A. C. supported by the Fundación Andes, Chile, and by the German Academic Exchange Service (DAAD), Federal Republic of GermanyResearch of W. G. supported, in part, by the National Science Foundation, USA, (Grant CCR-8704404)Research of S. R. supported by the Fondo Nacional de Desarollo Cientßfico y Tecnológico (FONDECYT), Chile, (Grant 237/89), by the Universidad Técnica F. Santa Marßa, Valparaßso, Chile, (Grant 89.12.06), and by the German Academic Exchange Service (DAAD), Federal Republic of Germany     

Parabolic boundary integral operators symbolic representation and basic properties

In this paper we develop a theory of parabolic pseudodifferential operators in anisotropic spaces. We construct a symbolic calculus for a class of symbols globally defined on ⁿ⁺¹× ⁿ⁺¹, and then develop a periodisation procedure for the calculus of symbols on the cylinder ×. We show Gårding's inequality for suitable operators and precise estimates for the essential norm in anisotropic Sobolev spaces. These new mapping properties are needed in localization arguments for the analysis of numerical approximation methods.