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Stochastic Perturbation Theory
, 1988
"... . In this paper classical matrix perturbation theory is approached from a probabilistic point of view. The perturbed quantity is approximated by a firstorder perturbation expansion, in which the perturbation is assumed to be random. This permits the computation of statistics estimating the variatio ..."
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Cited by 907 (36 self)
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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
Semantics of ContextFree Languages
 In Mathematical Systems Theory
, 1968
"... "Meaning " may be assigned to a string in a contextfree language by defining "attributes " of the symbols in a derivation tree for that string. The attributes can be defined by functions associated with each production in the grammar. This paper examines the implications of th ..."
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Cited by 569 (0 self)
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towards programming languages, but the same methods appear to be relevant also in the study of natural anguages. 1. Introduction. Let
I. Introduction. Let X be a Banach space and G be a closed
"... 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 valu ..."
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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
A Tutorial on Learning Bayesian Networks
 Communications of the ACM
, 1995
"... We examine a graphical representation of uncertain knowledge called a Bayesian network. The representation is easy to construct and interpret, yet has formal probabilistic semantics making it suitable for statistical manipulation. We show how we can use the representation to learn new knowledge by c ..."
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Cited by 365 (12 self)
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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
1. Introduction. Let X be a Hilbert space and V: X! X be an isometry. The well
"... ABSTRACT. This paper studies closed subspaces L of the Hardy spaces Hp which are ginvariant (i.e., gÐL L) where g is inner, g Â ≥ 1. If p ≥ 2, the Wold decomposition theorem implies that there is a countable “gbasis ” f1, f2,... of L in the sense that L is a direct sum of spaces fj Ð H2[g] where ..."
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ABSTRACT. This paper studies closed subspaces L of the Hardy spaces Hp which are ginvariant (i.e., gÐL L) where g is inner, g Â ≥ 1. If p ≥ 2, the Wold decomposition theorem implies that there is a countable “gbasis ” 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 g2inner. It also follows that any f 2 H2 can be factored f ≥ hf,2 Ð (F2 Ž g) where hf,2 is g2inner 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 ginvariant L Hp, a finite gbasis of gpinner functions.
1 Introduction Let us consider the following classical hamiltonian model of a system of rotators:
"... ..."
Let
"... Abstract We consider transmission problems for general second or der linear hyperbolic systems having piecewise constant coecients in a bounded open connected set with smooth boundary and controlled through the Dirichlet boundary condition It is proved that such a sys tem is exactly controllable ..."
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in an appropriate function space provided the interfaces where the coecients have a jump discontinuity are all starshaped with respect to one and the same point and the coecients satisfy a certain monotonicity condition Introduction and main results
Let
, 1997
"... Abstract. The best constant in the usual L p norm inequality for the HardyLittlewood maximal function on R 1 is obtained for the class of all “bellshaped ” functions. A positive function on the line is called “bellshaped ” if it is smooth and has only one hump. The techniques we use include conve ..."
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convexity and an adaptation of the standard EulerLangrange variational method. 0. Introduction.
Let {}
"... 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 nonBayesian cases. Introduction. θ = x, x,..., x,... ..."
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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 nonBayesian cases. Introduction. θ = x, x,..., x
Let {}
"... 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 nonBayesian cases. Introduction. θ = x, x,..., x,... ..."
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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 nonBayesian cases. Introduction. θ = x, x,..., x
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