and the eigenvalue problem. Key words. perturbation theory, random matrix, linear system, least squares, eigenvalue, eigenvector, invariant subspace, singular value AMS(MOS) subject classifications. 15A06, 15A12, 15A18, 15A52, 15A60 1. Introduction. Let A be a matrix and let F be a matrix valued function of A

towards programming languages, but the same methods appear to be relevant also in the study of natural anguages. 1. Introduction. Let

Let X be a Banach space and G be a closed subspace of X. We say G is 2−simultaneously proximinal in X if for any x1, x2 in X, there exists some y ∈ G such that ‖x1 − y ‖ + ‖x2 − y ‖ = inf{‖x1 − z‖+ ‖x2 − z ‖ : z ∈ G} = d({x1, x2},G). In this paper, we give a formula for d({x1, x2},G) in vector

by combining domain knowledge with statistical data. 1 Introduction Many techniques for learning rely heavily on data. In contrast, the knowledge encoded in expert systems usually comes solely from an expert. In this paper, we examine a knowledge representation, called a Bayesian network, that lets us have

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ABSTRACT. This paper studies closed subspaces L of the Hardy spaces Hp which are g-invariant (i.e., gÐL L) where g is inner, g  ≥ 1. If p ≥ 2, the Wold decomposition theorem implies that there is a countable “g-basis ” f1, f2,... of L in the sense that L is a direct sum of spaces fj Ð H2[g] where H2[g] ≥ ff Ž g j f 2 H2g. The basis elements fj satisfy the additional property that RT jfj j2gk ≥ 0, k ≥ 1, 2,.... We call such functions g-2-inner. It also follows that any f 2 H2 can be factored f ≥ hf,2 Ð (F2 Ž g) where hf,2 is g-2-inner and F is outer, generalizing the classical Riesz factorization. Using Lp estimates for the canonical decomposition of H2, we find a factorization f ≥ hf,pÐ(FpŽg) for f 2 Hp. If p 1 and g is a finite Blaschke product we obtain, for any g-invariant L Hp, a finite g-basis of g-p-inner functions.

Abstract. In this paper we introduce for the first time the fusion of information on infinite discrete frames of discernment and we give general results of the fusion of two such masses using the Dempster’s rule and the PCR5 rule for Bayesian and non-Bayesian cases. Introduction. θ = x, x,..., x

Abstract. In this paper we introduce for the first time the fusion of information on infinite discrete frames of discernment and we give general results of the fusion of two such masses using the Dempster’s rule and the PCR5 rule for Bayesian and non-Bayesian cases. Introduction. θ = x, x,..., x

. Introduction and

: 30C45 1. Introduction and