Kernel estimation for stationary density of Markov chains with general state space

Let {X _n } _n ≥0 be a Markov chain with stationary distributionf(x)ν(dx), ν being a σ-finite measure onE⊂R ^d . Under strict stationarity and mixing conditions we obtain the consistency and asymptotic normality for a general class of kernel estimates off(·). When the assumption of stationarity is dropped these results are extended to geometrically ergodic chains. Partially supported by CAPES. Partially supported by CNPq, PROCAD/CAPES, PRONEX/FAPDF and FINATEC/UnB.     

Entire functions of exponential type bounded on the real axis and fourier transforms of distributions with bounded supports

On the complexification of the dual spaceE′ of a real Banach spaceE′ of infinite dimension, there is an entire complex valued function of exponential type, bounded onE′, hence slowly increasing onE′, which is not the Fourier transform of any distribution with bounded support onE. Partially supported by the Centro Brasileiro de Pesquisas Físicas, Rio de Janeiro, GB, Brasil and by the National Science Foundation, Washington, DC, USA. Attendance at the International Symposium on Partial Differential Equations and the Geometry of Normed Spaces was possible in part thanks to a grant from CAPES, Brasil.     

Minimal surfaces of rotation in Finsler space with a Randers metric

 We consider Finsler spaces with a Randers metric F=α+β, on the three dimensional real vector space, where α is the Euclidean metric and β=bdx ₃ is a 1-form with norm b,0≤b<1. By using the notion of mean curvature for immersions in Finsler spaces introduced by Z. Shen, we get the ordinary differential equation that characterizes the minimal surfaces of rotation around the x ₃ axis. We prove that for every b,0≤b<1, there exists, up to homothety, a unique forward complete minimal surface of rotation. The surface is embedded, symmetric with respect to a plane perpendicular to the rotation axis and it is generated by a concave plane curve. Moreover, for every there are non complete minimal surfaces of rotation, which include explicit minimal cones. Received: 30 November 2001 / Published online: 10 February 2003 RID="⋆" ID="⋆" Partially supported by CAPES RID="⋆⋆" ID="⋆⋆" Partially supported by CNPq and PROCAD.     

On a Modified Subgradient Algorithm for Dual Problems via Sharp Augmented Lagrangian*

We study convergence properties of a modified subgradient algorithm, applied to the dual problem defined by the sharp augmented Lagrangian. The primal problem we consider is nonconvex and nondifferentiable, with equality constraints. We obtain primal and dual convergence results, as well as a condition for existence of a dual solution. Using a practical selection of the step-size parameters, we demonstrate the algorithm and its advantages on test problems, including an integer programming and an optimal control problem. *Partially Supported by 2003 UniSA ITEE Small Research Grant Ero2. Supported by CAPES, Brazil, Grant No. 0664-02/2, during her visit to the School of Mathematics and Statistics, UniSA.     

Analysis of an iterative method for variable density incompressible fluids

We derive error bounds for an iterative method used by Okamoto to prove the existence of strong solutions for the equations of nonhomogeneous incompressible fluids. The authors Ortega-Torres and Rojas-Medar are partially supported by FONDECYT-Chile grant No. 1040205 and No. 7040187. The authors Braz e Silva and Rojas-Medar are partially supported by CAPES/MECD-DGU Brazil/Spain grant No. 117/06.     

Examples of ill-behaved central paths in convex optimization

This paper presents some examples of ill-behaved central paths in convex optimization. Some contain infinitely many fixed length central segments; others manifest oscillations with infinite variation. These central paths can be encountered even for infinitely differentiable data.Mathematics Subject Classification (2000): 90C25, 90C51Research partially supported by CAPES, Brazil.Research partially supported by CAPES and CNPq, Brazil.     

Critical Gevrey index for hypoellipticity of parabolic operators and Newton polygones

Summary In this paper we give geometrical expressions of the (non) hypoellipticity in Gevrey spaces of parabolic operators via Newton polygones. We also determine the critical Gevrey class for which the hypoellipticity holds.Partially supported by GNAFA, CNR, Italy.Partially supported by JSPS, Japan and a grant MM-410/94 with MES, Bulgaria.Partially supported by Chuo University special research fund.     

Stratifications distinguées comme outil en géométrie semi-analytique

We introduce the distinguish stratifications as a new tool in order to give new proofs of some essential facts in the semi-analytic geometry in an easier way, for example the property of regular separation.

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Partially supported by KBN grant PB 1219/2/91

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Partially supported by KBN grant PB 1219/2/91

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Partially supported by DGICYT.     

The full automorphism groups of hyperelliptic Riemann surfaces

For every integer g≥2 we obtain the complete list of groups acting as the full automorphisms groups on hyperelliptic Riemann surfaces of genus g. Partially supported by DGICYT PB 89-201 and Science Plan 910021 Partially supported by DGICYT PB 89/379/C02/01 and Science Plan 910021 Partially supported by DGICYT After the typing of this paper we have heard about a Ph.D. Thesis by Britta Krapp on questions related to the problem studied here.     

Convergence analysis and error estimates for a parallel algorithm for solving the Navier-Stokes equations

Summary. This paper is concerned with the analysis of the convergence and the derivation of error estimates for a parallel algorithm which is used to solve the incompressible Navier-Stokes equations. As usual, the main idea is to split the main differential operator; this allows to consider independently the two main difficulties, namely nonlinearity and incompressibility. The results justify the observed accuracy of related numerical results. Received April 20, 2001 / Revised version received May 21, 2001 / Published online March 8, 2002 RID="*" ID="*" Partially supported by D.G.E.S. (Spain), Proyecto PB98–1134 RID="**" ID="**" Partially supported by D.G.E.S. (Spain), Proyecto PB96–0986 RID="**" ID="**" Partially supported by D.G.E.S. (Spain), Proyecto PB96–0986 RID="*" ID="*" Partially supported by D.G.E.S. (Spain), Proyecto PB98–1134 RID="**" ID="**" Partially supported by D.G.E.S. (Spain), Proyecto PB96–0986 RID="**" ID="**" Partially supported by D.G.E.S. (Spain) Proyecto PB96–0986     

A Bernstein type theorem on a Randers space

We consider Finsler spaces with a Randers metric F=+, on the three-dimensional real vector space, where is the Euclidean metric and is a 1-form with norm b,0 b1. By using the notion of mean curvature for immersions in Finsler spaces, introduced by Z. Shen, we obtain the partial differential equation that characterizes the minimal surfaces which are graphs of functions. For each b, 0 b1/, we prove that it is an elliptic equation of mean curvature type. Then the Bernstein type theorem and other properties, such as the nonexistence of isolated singularities, of the solutions of this equation follow from the theory developped by L. Simon. For b 1/, the differential equation is not elliptic. Moreover, for every b, 1/b1 we provide solutions, which describe minimal cones, with an isolated singularity at the origin.Partially supported by CAPES/PROCAD.Partially supported by NSF grant DMS-0072242.Partially supported by CNPq and CAPES/PROCAD.     

Generic representations for the unitary group in three variables

We show that for the quasi-split unitary group in three variables every tempered packet of cuspidal automorphic representations contains a globally generic representation. Partially supported by a Minerva grant. Partially supported by NSF grant DMS 9619766 and 9988611. Partially supported by NSF grant DMS 9700950.     

Non-negative hereditary polynomials in a free *−algebra

We prove a non-negative-stellensatz and a null-stellensatz for a class of polynomials called hereditary polynomials in a free *-algebra.Partially supported by NSF, DARPA and Ford Motor Co.Partially supported by NSF grant DMS-0140112Partially supported by NSF grant DMS-0100367     

Identities with involution for the matrix algebra of order two in characteristic<Emphasis Type="Italic">p</Emphasis>

LetM ₂ (K) be the matrix algebra of order two over an infinite fieldK of characteristicp≠2. IfK is algebraically closed then, up to isomorphism, there are two involutions of first kind onM ₂ (K), namely the transpose and the symplectic. IfK is not algebraically closed, studying *-identities it is still sufficient to consider only these two involutions. We describe bases of the polynomial identities with involution in each of these cases. Supported by PhD grant from CNPq. Partially supported by CNPq and by CAPES.     

On the eigenvalues of matrices with given upper triangular part

We give necessary and sufficient conditions for a set of numbers to be the eigenvalues of a completion of a matrix prescribed in its upper triangular part.Partially supported by the NSF Grant DMS-8701615-02Partially supported by the NSF Grant DMS-8802836 and United States-Israel Binational Science Foundation Grant 88-00304/I.     

A note on the Beck-Fiala Theorem

In this note we slightly improve the Beck-Fiala Theorem on discrepancy.Partially supported by PSC-CUNY Grant No. 665524.Partially supported by DAAD HSPII/AUFE grant.     

Testing for parameter changes in ARCH models

The paper develops the asymptotic theory for CUSUM-type tests for a change point in parameters of an ARCH(∞) model. Special attention is given to asymptotics under local alternatives. Research partially supported by EPSRC grant GR/L/78222 from the University of Liverpool. Partially supported by NATO grant CRG 960503. Partially supported by the Lithuanian State Science and Studies Foundation, Grant K-014. Published in Lietuvos Matematikos Rinkinys, Vol. 39, No. 2, pp. 231–247, April–June, 1999.     

Jackson’s integral of the Hurwitz zeta function

We give a Jacksonq-integral analogue of Euler’s logarithmic sine integral established in 1769 from several points of view, specifically from the one relating to the Hurwitz zeta function. Partially supported by Grant-in-Aid for Exploratory Research No. 15654003. Partially supported by Grant-in-Aid for Scientific Research (B) No. 15340003. Partially supported by Grant-in-Aid for Scientific Research (B) No. 15340012.     

Entropy of flows, revisited

We introduce a concept of measure-theoretic entropy for flows and study its invariance under measure-theoretic equivalences. Invariance properties of the corresponding topological entropy is studied too. We also answer a question posed by Bowen-Walters in [3] concerning the equality between the topological entropy of the time-one map of an expansive flow and the time-one map of its symbolic suspension.Partially supported by FAPESP-Brasil, Grant #96/11671-6.Partially supported by CNPq-Brasil, Grant #300557/89-2.     

A Floquet Operator with Purely Point Spectrum and Energy Instability

An example of Floquet operator with purely point spectrum and energy instability is presented. In the unperturbed energy eigenbasis its eigenfunctions are exponentially localized. CRdeO was partially supported by CNPq (Brazil). MSS was supported by CAPES (Brazil). Submitted: September 21, 2006. Accepted: December 12, 2006.