Boundary behavior in Hilbert spaces of vector-valued analytic functions

In this paper we study the boundary behavior of functions in Hilbert spaces of vector-valued analytic functions on the unit disc D. More specifically, we give operator-theoretic conditions on Mz, where Mz denotes the operator of multiplication by the identity function on D, that imply that all functions in the space have non-tangential limits a.e., at least on some subset of the boundary. The main part of the article concerns the extension of a theorem by Aleman, Richter and Sundberg in [A. Aleman, S. Richter, C. Sundberg, Analytic contractions and non-tangential limits, Trans. Amer. Math. Soc. 359 (2007)] to the case of vector-valued functions.     

Long-range predictive adaptive fuzzy relational control

A class of long-range predictive adaptive fuzzy relational controllers is presented. The plant behavior is described over an extended time horizon by a fuzzy relational model which is identified based on input-output closed-loop observations of the plant variables. In this class of adaptive controllers the control law attempts to minimize a quadratic cost over an extended control horizon. When used with linear models, this approach has revealed a significant potential for overcoming the limitations of one-step ahead schemes, such as the stabilization of non-minimum phase plants. Here, a uniform framework is adopted for implementing both the fuzzy model and the fuzzy controller, namely distributed fuzzy relational structures gaining from their massive parallel processing features and from the learning capabilities typical of the connectivist approaches. Issues such as maintenance during the adaptation process of the meaning of linguistic terms used at both fuzzy systems interfaces are addressed, namely by introducing a new design methodology for on-line fuzzy systems interface adaptation. The examples presented reinforce the claim of the usefulness of this new approach.     

Gas-liquid chromatography of perfluorocarboxylic thioesters

Perfluorocarboxylic thioesters R_FC(O)SR (R_F=CF₃(CF₂)_j, R=CH₃(CH₂)_i, i andj=0–5) were studied for the first time by GLC on packed columns using SE-30, SKTFT-50X, and XE-60 as the stationary phase. The values of thermodynamics functions of sorption were calculated. The correlations between these functions and the molecular structures as well as the conditions of analysis were established. The insertion of the S atom into the molecules of derivatives of perfluorocarboxylic acids causes a decrease in the contribution of the orientation interaction and an increase in the dispersion interaction of thioesters with the stationary phases compared to esters and amides of perfluorocarboxylic acids studied previously. For Part 1, see Ref. 1. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 6, pp. 1165–1168, June, 1997.     

Rational approximation in the complex plane using a τ-method and computer algebra

Numerous versions of the Lanczos τ-methods have been extensively used to produce polynomial approximations for functions verifying a linear differential equation with polynomial coefficients. In the case of an initial-value problem, an adapted τ-method based on Chebyshev series and the use of symbolic computation lead to a rational approximation of the solution on a region of the complex plane. Numerical examples show that the simplicity of the method does not prevent a high accuracy of results. This revised version was published online in June 2006 with corrections to the Cover Date.     

On the Seneta Sequences

In this paper, we prove some properties of the Seneta sequences and functions, and in particular we prove a representation theorem in the Karamata sense for the sequences from the Seneta class SOc.     

New numerical methods and some applied aspects of the p-regularity theory

The theory of p-regularity is applied to optimization problems and to singular ordinary differential equations (ODE). The special variant of the method of the modified Lagrangian function proposed by Yu.G. Evtushenko for constrained optimization problems with inequality constraints is justified on the basis of the 2-factor transformation. An implicit function theorem is given for the singular case. This theorem is used to show the existence of solutions to a boundary value problem for a nonlinear differential equation in the resonance case. New numerical methods are proposed including the p-factor method for solving ODEs with a small parameter.     

Traces of harmonic functions,capacities, and traces of symmetric Markov processes

We derive explicit isomorphism formulas between weighted Dirichlet integrals for harmonic functions and boundary Dirichlet forms. Applications yield results on traces of Markov processes and convergence quasieverywhere of harmonic functions.     

A class of nonlinear equations in Hilbert space and its application to completeness problems

Nonlinear equations arising in the spectral theory of self-adjoint operator functions and related completeness problems for eigenvectors are studied. A separation theorem about the values of the Rayleigh functional on solutions of a nonlinear equation is proved. This theorem is used, as a new approach to establish completeness of eigenvectors for some classes of self-adjoint operator functions. Examples from matrix pencils are given.