Showing papers on "Bounded function published in 1984"
TL;DR: In this paper, the effects of unmodeled high frequency dynamics and bounded disturbances on stability and performance of adaptive control schemes are analyzed using simple examples, and a procedure is used to construct Lyapunov-like functions for a modified adaptive controller applied to a dominant plant of relative degree one, in the presence of parasitics and disturbances.
553 citations
TL;DR: Coifman and Meyer as discussed by the authors showed the LP-boundedness of the first Calderon commutator, which is the first non-convolution operator associated to a kernel which satisfies certain size and smoothness properties comparable to those of the kernel of the Hilbert transform.
Abstract: In 1965, A. P. Calderon showed the L2-boundedness of the so-called first Calderon commutator. This is one of the first examples of a non-convolution operator associated to a kernel which satisfies certain size and smoothness properties comparable to those of the kernel of the Hilbert transform. These properties, together with the L2-boundedness, imply the LP-boundedness for all p's in ]1, + oo[. Many operators in analysis, such as certain classes of pseudo-differential operators and the Cauchy integral operator on a curve, are associated with kernels having these properties. For these operators, one of the major questions is if they are bounded on L2. We are going to give necessary and sufficient conditions for such an operator to be bounded on L2. They are essentially that the images of the function 1 under the actions of the operator and its adjoint both lie in BMO. In the case of the aforementioned first commutator this can be checked by an integration by parts. In the first section we present some basic notions and state the theorem, which is proved in Sections 2 and 3. In Section 4 we show how to recover some classical results. In Sections 5 and 6 we construct a functional calculus for small perturbations of A, and in Section 7 we show a connection between the theory of Calderon-Zygmund operators and Kato's conjecture. It is a pleasure to express our thanks to R. R. Coifman and Y. Meyer for suggesting many elegant simplifications in our proofs and most of the applications. We also wish to thank Stephen Semmes for several pertinent remarks.
514 citations
TL;DR: In this paper, a window selection rule is considered, which can be interpreted in terms of cross-validation, under the mild assumption that the unknown density and its one-dimensional marginals are bounded.
Abstract: Kernel estimates of an unknown multivariate density are investigated, with mild restrictions being placed on the kernel. A window selection rule is considered, which can be interpreted in terms of cross-validation. Under the mild assumption that the unknown density and its one-dimensional marginals are bounded, the rule is shown to be asymptotically optimal. This strengthens recent results of Peter Hall.
419 citations
TL;DR: The determinant, characteristic polynomial and adjoint over an arbitrary commutative ring with unity can be computed by a circuit with size O(n3.496) and depth O(log2n).
395 citations
TL;DR: In this paper, the authors considered the critical exponent γ associated with the expected cluster sizex and the structure of then-site connection probabilities τ =τn(x 1,..., xn) and showed that quite generally γ⩾ 1.
Abstract: Various inequalities are derived and used for the study of the critical behavior in independent percolation models. In particular, we consider the critical exponent γ associated with the expected cluster sizex and the structure of then-site connection probabilities τ=τn(x1,..., xn). It is shown that quite generally γ⩾ 1. The upper critical dimension, above which γ attains the Bethe lattice value 1, is characterized both in terms of the geometry of incipient clusters and a diagramatic convergence condition. For homogeneousd-dimensional lattices with τ(x, y)=O(¦x -y¦−(d−2+η), atp=p
c, our criterion shows that γ=1 if η> (6-d)/3. The connectivity functions τn are generally bounded by tree diagrams which involve the two-point function. We conjecture that above the critical dimension the asymptotic behavior of τn, in the critical regime, is actually given by such tree diagrams modified by a nonsingular vertex factor. Other results deal with the exponential decay of the cluster-size distribution and the function τ2
(x, y).
315 citations
06 Jun 1984
TL;DR: It is shown that if the persistent excitation of the reference input is larger than the perturbation in some sense, the solutions will be globally bounded.
Abstract: The paper addresses an open problem concerned with the boundedness of signals in an adaptive loop when external perturbations are present. A complete solution is provided for the case of a first order plant with an unknown parameter by analyzing a nonlinear differential equation in R2. It is shown that if the persistent excitation of the reference input is larger than the perturbation in some sense, the solutions will be globally bounded. The same methodology appears to be applicable to the general adaptive control problem.
284 citations
TL;DR: An algebraic approach is presented to the proof that a linear system with matrices (A, B) is null–controllable using bounded inputs if and only if it is null-controllersable (with unbounde...
Abstract: In this paper we present an algebraic approach to the proof that a linear system with matrices (A, B) is null–controllable using bounded inputs if and only if it is null–controllable (with unbounde...
235 citations
TL;DR: A theoretical analysis of self-adaptive equalization for data-transmission is carried out starting from known convergence results for the corresponding trained adaptive filter and it can be proved that the algorithm is bounded.
Abstract: A theoretical analysis of self-adaptive equalization for data-transmission is carried out starting from known convergence results for the corresponding trained adaptive filter. The development relies on a suitable ergodicity model for the sequence of observations at the output of the transmission channel. Thanks to the boundedness of the decision function used for data recovery, it can be proved that the algorithm is bounded. Strong convergence results can be reached when a perfect (noiseless) equalizer exists: the algorithm will converge to it if the eye pattern is initially open. Otherwise convergence may take place towards certain other stationary points of the algorithm for which domains of attraction have been defined. Some of them will result in a poor error rate. The case of a noisy channel exhibits limit points for the algorithm that differ from those of the classical (trained) algorithm. The stronger the noise, the greater the difference is. One of the principal results of this study is the proof of the stability of the usual decision feedback algorithms once the learning period is over.
190 citations
TL;DR: In this article, a sufficient condition for stochastic boundedness persistence of a top predator in generalized Lotka-Volterra-type Stochastic Food Web models in arbitrary bounded regions of state space is given.
185 citations
TL;DR: In this article, the authors define an invariant AX(z) which is associated with each point z in the boundary of a smoothly bounded pseudoconvex domain in Cn.
Abstract: The purpose of this paper is to describe an invariant AX(z) which is associated with each point z in the boundary of a smoothly bounded pseudoconvex domain in Cn. The motivation for defining the invariant AX(z), referred to as the multitype of z, comes from the study of the boundary regularity properties of solutions of the d-Neumann problem on domains of finite type. By a domain of finite type, we mean one that satisfies the definition given by D'Angelo [5], namely a domain such that at any boundary point the maximum order of contact of one-dimensional complex-analytic varieties with the boundary is bounded. In [4] the author showed how one can give a proof of global regularity of the a-Neumann problem for pseudoconvex domains of finite type if there is an invariant such as the one described in this paper. In a forthcoming article this invariant will be used to obtain a proof of subelliptic estimates for the same class of domains. Before giving the definition of the multitype AX(z), we must introduce some
176 citations
TL;DR: The method introduces a generalization of the ring of integers, called well-endowed rings, which possesses a very efficient parallel implementation of the basic (+,−,×) ring operations.
Abstract: It is shown that a probabilistic Turing acceptor or transducer running within space bound S can be simulated by a time S2 parallel machine and therefore by a space S2 deterministic machine. (Previous simulations ran in space S6.) In order to achieve these simulations, known algorithms are extended for the computation of determinants in small arithmetic parallel time to computations having small Boolean parallel time, and this development is applied to computing the completion of stochastic matrices. The method introduces a generalization of the ring of integers, called well-endowed rings. Such rings possess a very efficient parallel implementation of the basic (+,−,×) ring operations.
TL;DR: This work considers how large these approximations have to be, if they prevent convergence when the objective function is bounded below and continuously differentiable, and obtains a useful convergence result in the case when there is a bound on the second derivative approximation that depends linearly on the iteration number.
Abstract: Many trust region algorithms for unconstrained minimization have excellent global convergence properties if their second derivative approximations are not too large [2]. We consider how large these approximations have to be, if they prevent convergence when the objective function is bounded below and continuously differentiable. Thus we obtain a useful convergence result in the case when there is a bound on the second derivative approximations that depends linearly on the iteration number.
TL;DR: In this article, the authors extend Clark's formula to the more general class of weakly H-differentiable functions, and give a simple proff based on Malliavin's calculus.
Abstract: If F is a Frechet differentiable functional on is a Brownian motion, and clark's formula states that where is the measure defining the Frechet derivative of F at b.In this paper we extend Clark's formula to the more general class of weakly H-differentiablefunctionals, and we give a simple proff based on Malliavin's calculus. again using Malliavin calculus techniques, we also derive Haussmann's stochastic integral representation of a function F(y) of the diffusion process In doing this, we show that is weakly H-differentiable if m and have bounded, continuous, first derivatives in y.
TL;DR: An algorithm is described for solving this problem for which the amount of computation is bounded by a polynomial in E, independently of x, allowing as steps tests of independence in M and additions, subtractions, and comparisons of numbers.
TL;DR: The categorical duality which exists between bounded distributive lattices and compact totally order disconnected spaces is discussed in this article, where the authors present a dictionary of mutually dual properties.
Abstract: An account is given of the categorical duality which exists between bounded distributive lattices and compact totally order disconnected spaces. During the past decade, a wide range of structural problems concerning distributive lattices have been solved by the topological and order theoretic techniques provided by duality, and a representative selection of these is presented. In addition, certain related dualities are briefly considered, as are compact totally order disconnected spaces in their own right. The paper ends with a 'dictionary' of mutually dual properties.
TL;DR: In this article, it was shown that a bounded operator on a Hilbert space is similar to a contraction if and only if it is completely polynomially bounded, which is a partial answer to Problem 6 of Halmos.
TL;DR: In this paper, a quasilinear skew-self-adjoint form of hyperbolic systems of conservation laws augumented with an entropy inequality is studied. But it is not shown that such systems can be written in a (quasileinear) skew self-joint form under the smooth regime, nor can they be constructed under the nonsmooth regime.
TL;DR: In this article, the authors studied the Hilbert space of analytic functions with finite Dinchlet integral in the open unit disc and identified the functions whose polynomial multiples are dense in this space.
Abstract: We study the Hilbert space of analytic functions with finite Dinchlet integral in the open unit disc. We try to identify the functions whose polynomial multiples are dense in this space. Theorems 1 and 2 confirm a special case of the following conjecture: if IJ(z)I > Ig(z)l at all points and if g is cyclic, thenJis cyclic. Theorems 3-5 give a sufficient condition (t is an outer function with some smoothness and the boundary zero set is at most countable) and a necessary condition (the radial limit can vanish only for a set of loganthmic capacity zero) for a function J to be cyclic. Introduction. In this paper we shall study the (Hilbert) space of analytic functions in the open unit disc a in the complex plane that have a finite Dirichlet integral: JJ If t12 dx dy [g(z)l for some cyclic g, and all z? Question 4 asks if f must be cyclic whenever f and l/f are both in the space. No examples are known where either of these questions has a negative answer. In §2 we begin the study of cyclic vectors in the Dirichlet space D. Theorems 1 and 2 give a partial answer to Question 3 above, for this space. This section also contains 2 propositions (10, 11) and 4 questions (7-10). Proposition 11 says that if f and g are bounded functions in D whose product is cyclic, then bothf and g must be cyclic. Theorem 2 gives a partial converse (we require that [gl be Dini continuous on Received by the editors July 21, 1983. 1980 Mathematics Subject Classification. Primary 30H05; Secondary 46E15, 46E20, 47B37.
TL;DR: A new algorithm is presented that computes the probability that there is an operating path from a node s to a node t in a stochastic network and the complexity of other connectedness reliability problems with respect to the number of cutsets and pathsets in the network is examined.
Abstract: We present a new algorithm that computes the probability that there is an operating path from a node s to a node t in a stochastic network. The computation time of this algorithm is bounded by a polynomial in the number of s, t-cuts in the network. We also examine the complexity of other connectedness reliability problems with respect to the number of cutsets and pathsets in the network. These problems are distinguished as either having algorithms that are polynomial in the number of such sets, or having no such algorithms unless P = NP.
TL;DR: In this article, the authors give a necessary and sufficient condition on the modulus of continuity of the coefficients of an elliptic operator in divergence form in order that the corresponding Poisson kernel for the Dirichlet problem exists.
Abstract: Our purpose in this paper is to give a necessary and sufficient condition on the modulus of continuity of the coefficients of an elliptic operator in divergence form in order that the corresponding Poisson kernel for the Dirichlet problem exist. This condition on the coefficients is global continuity together with the additional property that the modulus of continuity along some nontangential direction at each boundary point be bounded uniformly in these points and directions by a function 7(t) satisfying the Dini-type condition
TL;DR: Theorem 1 is satisfied whenever M is a knot manifold as discussed by the authors, i.e. the complement of an open tubular neighborhood of a nontrivial knot in S 3.
Abstract: This generalizes and strengthens the main theorem of [13]. Note that the hypothesis of Theorem 1 is satisfied whenever M is a knot manifold, i.e. the complement of an open tubular neighborhood of a nontrivial knot in S 3. (The theorem of [13] gives no information for a knot manifold.) In this case various versions of Theorem 1 have been conjectured by L.P. Neuwirth. For example, Conjecture A of [11], that every knot group is a free product of two proper subgroups amalgamated along a free group, is an immediate corollary to Theorem 1. The following result can be derived from Theorem 1 above in the same way that [13, Theorem 2] is derived from [13, Theorem 1]. Because the proof parallels so precisely that of [13, Theorem 2], we shall omit it.
TL;DR: In this paper, the authors considered the strong Hamburger moment problem for a given double sequence of real numbers C = { c n } ∞ − ∞, does there exist a real-valued, bounded, non-decreasing function ψ on (−∞, ∞) with infinitely many points of increase such that for every integer n, c n = ∝ ∞−∞ (− t ) n dψ (t ) ndψ( t )?
TL;DR: In this paper, it was shown that there are many approach regions which are not contained in any nontangential region but for which the conclusions of Fatou's theorem remain true.
TL;DR: In this paper, a viscous incompressible fluid enclosed in a bounded region of ℝ 2 or 3 was considered and subjected to time dependent forces, and bound state estimates for the Schrodinger operator were obtained for the characteristic exponents, entropy (Kolmogorov-Sinai invariant), and Hausdorff dimension of attracting sets.
Abstract: We consider a viscous incompressible fluid enclosed in a bounded region of ℝ2 or ℝ3, and subjected to time dependent forces. Using bound state estimates for the Schrodinger operator, we obtain rigorous bounds for the characteristic exponents, entropy (Kolmogorov-Sinai invariant), and Hausdorff dimension of attracting sets. Our methods are of potential use for more general time evolutions described by nonlinear partial differential equations.
TL;DR: A multilevel algorithm for the numerical solution of symmetric indefinite problems which arise, e.g. from mixed finite element approximations of the Stokes equation, by introducing a scale of mesh-dependent norms.
Abstract: We describe a multilevel algorithm for the numerical solution of symmetric indefinite problems which arise, e.g. from mixed finite element approximations of the Stokes equation. The main difficulty, besides the indefiniteness, is the lack of regularity of the solution of the corresponding continuous problem. This is overcome by introducing a scale of mesh-dependent norms. The convergence rate of the described algorithm is bounded independently of the meshsize. For convenience we only discuss Jacobi relaxation as smoothing operator in detail. In the last section we comment on Lanczos-type smoothing procedures.
01 Dec 1984
TL;DR: Two (closely-related) propositional probabilistic temporal logics based on temporallogics of branching time as introduced by Ben-Ari, Pnueli and Manna and by Clarke and Emerson are presented.
Abstract: We present two (closely-related) propositional probabilistic temporal logics based on temporal logics of branching time as introduced by Ben-Ari, Pnueli and Manna and by Clarke and Emerson. The first logic, PTLf, is interpreted over finite models, while the second logic, PTLb, which is an extension of the first one, is interpreted over infinite models with transition probabilities bounded away from 0. The logic PTLf allows us to reason about finite-state sequential probabilistic programs, and the logic PTLb allows us to reason about (finite-state) concurrent probabilistic programs, without any explicit reference to the actual values of their state-transition probabilities. A generalization of the tableau method yields exponential-time decision procedures for our logics, and complete axiomatizations of them are given. Several meta-results, including the absence of a finite-model property for PTLb, and the connection between satisfiable formulae of PTLb and finite state concurrent probabilistic programs, are also discussed.
01 Mar 1984
TL;DR: The primary result is a variation that is shown to be "bounded-complete"-the method obtains a solution whenever a solution consisting of a bounded number of motions exists.
Abstract: In this paper we explore a method for automatic planning of robot fine-motion programs, first described in [Lozano-Perez, Mason, and Taylor 1983]. The primary result is a variation that is shown to be "bounded-complete"-the method obtains a solution whenever a solution consisting of a bounded number of motions exists.
TL;DR: In this paper, a weak convergence criterion for stochastic differential equations with bounded coefficients is derived for evolution equations with memory, where A(t) is the quasigenerator of U(t,s), V(t), a bounded variation process, and Z(t)-a semimartingale.
Abstract: A stopped Doob inequality is proved for stochastic convolution integrals in Hilbert space, where M is a square integrable Hilbert space valued cadlag martingale, ⊘ an operator valued predictable function and U(t, s) a contraction-type evolution operator. This allows to obtain the mild solution for evolution equations (with memory) where A(t) is the quasigenerator of U(t,s), V(t) a bounded variation process, and Z(t) a semimartingale, under the same weak assumptions on B and D as for stochastic differential equations with bounded coefficients, i .e ., (A( t) = 0) . Moreover, a weak convergence criterion for is derived.
01 Dec 1984
TL;DR: In this paper, necessary and sufficient conditions are given for a control sequence belonging to a polyhedral constraint set to stabilize the system under the condition that the state is restricted to the polyhedral state constraint set.
Abstract: For linear discrete time dynamical systems, necessary and sufficient conditions are given for a control sequence, belonging to a polyhedral constraint set, to stabilize the system under the condition that the state is restricted to a polyhedral state constraint set. A variable structure linear state feedback controller, given in terms of the controls at the vertices of the polyhedral state constraint set, is presented.
TL;DR: In this article, the existence of nonconstant bounded harmonic functions on certain classes of non-compact Riemannian manifolds was proved by defining and solving an asymptotically defined Dirichlet problem for harmonic functions.
Abstract: We define the asymptotic Dirichlet problem and give a sufficient condition for solving it. This proves an existence of nontrivial bounded harmonic functions on certain classes of noncompact complete Riemannian manifolds. 0. Introduction. In this paper we will prove the existence of nonconstant bounded harmonic functions on certain classes of noncompact Riemannian manifolds by defining and solving an asymptotically defined Dirichlet problem for harmonic functions. The motivation comes from the classical uniformization theorem of Riemann surfaces which says that a simply connected Riemann surface is biholo- morphic to the Riemann sphere S2, the complex plane C, or the unit disk D. This is a geometric theorem, but its original proof due to Koebe relies heavily on function theory. The function-theoretic interpretation of this theorem is the following: Among the noncompact simply connected surfaces, C is characterized by the fact that it admits no nonconstant bounded harmonic functions, and D by that it admits nonconstant bounded harmonic functions. The geometric aspect of the uniformization theorem could be roughly stated as follows: Let M be a simply connected Riemann surface equipped with a complete Riemannian metric with Gaussian curvature KM, if KM > c > 0, then M is biholo- morphic to S2; if KM < — c < 0, then M is biholomorphic to D; if KM is "close" to zero, then M is biholomorphic to C. The following precise version is due to Greene and Wu (GW1, p. 120).