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Showing papers on "Bounded function published in 1990"


Book
01 Jan 1990
TL;DR: In this paper, the authors present a probabilistic model for convexity in the Euclidean plane and a model of the massless damped spring, which is based on the Euler-Lagrange equations.
Abstract: 1. Probabilistic Modelling: Pros and Cons. Preliminary considerations. Probabilistic modelling in mechanics. Reliability of structures. Sensitivity of failure probability. Some quotations on the limitations of probabilistic methods. 2. Mathematics of Convexity. Convexity and Uncertainty. What is convexity? Geometric convexity in the Euclidean plane. Algebraic convexity in Euclidean space. Convexity in function spaces. Set-convexity and function-convexity. The structure of convex sets. Extreme points and convex hulls. Extrema of linear functions on convex sets. Hyperplane separation of convex sets. Convex models. 3. Uncertain Excitations. Introductory examples. The massless damped spring. Excitation sets. Maximum responses. Measurement optimization. Vehicle vibration. Introduction. The vehicle model. Uniformly bounded substrate profiles. Extremal responses on uniformly bounded substrates. Duration of acceleration excursions on uniformly bounded substrates. Substrate profiles with bounded slopes. Isochronous obstacles. Solution of the Euler-Lagrange equations. Seismic excitation. Vibration measurements. Introduction. Damped vibrations: full measurement. Example: 2-dimensional measurement. Damped vibrations: partial measurement. Transient vibrational acceleration. 4. Geometric Imperfections. Dynamics of thin bars. Introduction. Analytical formulation. Maximum deflection. Duration above a threshold. Maximum integral displacements. Impact loading of thin shells. Introduction. Basic equations. Extremal displacement. Numerical example. Buckling of thin shells. Introduction. Bounded Fourier coefficients: first-order analysis. Bounded Fourier coefficients: second-order analysis. Uniform bounds on imperfections. Envelope bounds on imperfections. Estimates of the knockdown factor. First and second-order analyses. 5. Concluding Remarks. Bibliography. Index.

801 citations


Journal ArticleDOI
TL;DR: In this article, Martin et al. developed fundamental results on the existence and behavior of solutions to semilinear functional differential equations in a Banach space setting, including differential inequalities, invariant sets, and Lyapunov functions.
Abstract: FUNCTIONAL DIFFERENTIAL EQUATIONS AND REACTION-DIFFUSION SYSTEMS R. H. MARTIN, JR. AND H. L. SMITH ABSTRACT. Several fundamental results on the existence and behavior of solutions to semilinear functional differential equations are developed in a Banach space setting. The ideas are applied to reaction-diffusion systems that have time delays in the nonlinear reaction terms. The techniques presented here include differential inequalities, invariant sets, and Lyapunov functions, and therefore they provide for a wide range of applicability. The results on inequalities and especially strict inequalities are new even in the context of semilinear equations whose nonlinear terms do not contain delays. Several fundamental results on the existence and behavior of solutions to semilinear functional differential equations are developed in a Banach space setting. The ideas are applied to reaction-diffusion systems that have time delays in the nonlinear reaction terms. The techniques presented here include differential inequalities, invariant sets, and Lyapunov functions, and therefore they provide for a wide range of applicability. The results on inequalities and especially strict inequalities are new even in the context of semilinear equations whose nonlinear terms do not contain delays. Suppose Q is a bounded domain in RN with aQ smooth and A is the Laplacian operator on Q. Also, let m be a positive integer, z a positive number, and f = (fi)m a continuous, bounded function from [0, xc] x Q x C([-z, 0])m into Rm where C([-T, 0]) is the space of continuous functions from [-z, 0] into R. The purpose of this paper is to apply abstract results for semilinear functional differential equations in Banach spaces to reactiondiffusion systems with time delays having the form a tu(x, t) = diAu' (x, t) + ?i(t, x, ut(x, *)), t>a, xeQ, i=1,...,m, (RDD) ai(x)ui(x, t) + au i(x, t) = ,81(x, t), t > a , x EaQ u'(x , a + 0) = X'(x , 0) 5 -T 0, di > 0, and ca:Q * [0,o ) is C' and ,i:Q x [0, oo) R is C2. Here an is the outward normal derivative on aQ and if di = 0 it is assumed that no boundary conditions are specified for this i. Also, tu'(x, t) denotes the partial with respect to t, whereas ut(x, *) denotes the member of C([-z, 0]) defined by 0 -u(x, t + 0) = (u'(x, t + 0))M. Our techniques provide basic existence criteria, but the main point is that they can also be effectively applied to obtain estimates for solutions, especially Received by the editors October 7, 1987 and, in revised form, October 7, 1988. 1980 Mathematics Subject Classification (1985 Revision). Primary 35R10, 34K30.

503 citations


Book
19 Dec 1990
TL;DR: In this paper, the authors provide an introduction to the new techniques of subharmonic functions and analytic multifunctions in spectral theory, including functional analysis, bounded operations on Banach algebras, and applications of spectral subharmonicity.
Abstract: This textbook provides an introduction to the new techniques of subharmonic functions and analytic multifunctions in spectral theory. Topics include the basic results of functional analysis, bounded operations on Banach algebras, and applications of spectral subharmonicity. Each chapter is followed by exercises of varying difficulty. Much of the subject matter, particularly in spectral theory, operator theory and Banach algebras, contains new results.

443 citations


Journal ArticleDOI
TL;DR: In this article, the existence and regularity of diffeomorphisms in bounded open sets was studied. But the authors focused on the existence of diffEomorphisms and not on the regularity.
Abstract: Let Ω ⊂ ℝn a bounded open set and f > 0 in Ω ¯ satisfying ∫ Ω f ( x ) d x = meas Ω . We study existence and regularity of diffeomorphisms u : Ω ¯ → Ω ¯ such that { det ∇ u ( x ) = f ( x ) , x ∈ Ω u ( x ) = x , x ∈ ∂ Ω .

389 citations


Journal ArticleDOI
22 Oct 1990
TL;DR: It is shown how to triangulate a planar point set or a polygonally bounded domain with triangles of bounded aspect ratio, and how to produce a linear-size Delaunay triangulation of a multidimensional point set by adding a linear number of extra points.
Abstract: Several versions of the problem of generating triangular meshes for finite-element methods are studied. It is shown how to triangulate a planar point set or a polygonally bounded domain with triangles of bounded aspect ratio, how to triangulate a planar point set with triangles having no obtuse angles, how to triangulate a point set in arbitrary dimension with simplices of bounded aspect ratio, and how to produce a linear-size Delaunay triangulation of a multidimensional point set by adding a linear number of extra points. All the triangulations have size within a constant factor of optimal and run in optimal time O(n log n+k) with input of size n and output of size k. No previous work on mesh generation simultaneously guarantees well-shaped elements and small total size. >

358 citations


Journal ArticleDOI
TL;DR: In this article, a polynomial test for observability is given and a notion of resiliency is defined for observers, and a test for resilient observability and a procedure for the construction of a resilient observer are presented.
Abstract: A finite state automaton is adopted as a model for discrete event dynamic systems (DEDS). Observations are assumed to be a subset of the event alphabet. Observability is defined as having perfect knowledge of the current state at points in time separated by bounded numbers of transitions. A polynomial test for observability is given. It is shown that an observer may be constructed and implemented in polynomial time and space. A bound on the cardinality of the observer state space is also presented. A notion of resiliency is defined for observers, and a test for resilient observability and a procedure for the construction of a resilient observer are presented. >

310 citations


Journal ArticleDOI
TL;DR: In this paper, a vector field on a bounded Lipschitz domain in R 3 is shown to be square integrable if and only if its divergence and curl can be squared integrably bounded.
Abstract: Let ~ u be a vector field on a bounded Lipschitz domain in R 3 , and let ~ u together with its divergence and curl be square integrable. If

299 citations


Journal ArticleDOI
TL;DR: In this article, a characterization of a class of classical Lorentz spaces on which the Hardy Littlewood maximal operator is bounded is given by determining the weights for which Hardy's inequality holds for nonincreasing functions.
Abstract: A characterization is given of a class of classical Lorentz spaces on which the Hardy Littlewood maximal operator is bounded. This is done by determining the weights for which Hardy's inequality holds for nonincreasing functions. An alternate characterization, valid for nondecreasing weights, is also derived.

239 citations


Journal ArticleDOI
TL;DR: In this article, the problem of output tracking for a single-input single-output non-linear system in the presence of uncertainties is studied, and a control law is designed for minimum-phase nonlinear systems which results in tracking of this signal by the output.
Abstract: The problem of output tracking for a single-input single-output non-linear system in the presence of uncertainties is studied. The notions relative degree and minimum-phase for non-linear systems are reviewed. Given a bounded desired tracking signal with bounded derivatives, a control law is designed for minimum-phase non-linear systems which results in tracking of this signal by the output. This control law is modified in the presence of uncertainties associated with the model vector fields to reduce the effects of these uncertainties on the tracking errors. Two types of uncertainties are considered: those satisfying a generalized matching condition but otherwise unstructured, and linear parametric uncertainties. It is shown that for systems with the first type of uncertainty, high-gain control laws can result in small tracking errors of O(∊), where e is a small design parameter. An alternative scheme based on variable structure control strategy is shown to yield zero tracking errors. Adaptive control te...

233 citations


Journal ArticleDOI
TL;DR: In this article, the authors consider supersolutions of the Hamilton-Jacobi equation up to the boundary of a bounded open subset of a real-valued function, where the gradient of the unknown function u is the gradient gradient of u. The main motivation for this kind of solution comes from deterministic optimal control and differential games problems with constraints on the state of the system.
Abstract: In the present paper we consider Hamilton-Jacobi equations of the form H(x, u, Vu) = 0, x E Q, where Q is a bounded open subset of Rn H is a given continuous real-valued function of (x, s, p) E Q x R x Rn and Vu is the gradient of the unknown function u . We are interested in particular solutions of the above equation which are required to be supersolutions, in a suitable weak sense, of the same equation up to the boundary of Q. This requirement plays the role of a boundary condition. The main motivation for this kind of solution comes from deterministic optimal control and differential games problems with constraints on the state of the system, as well from related questions in constrained geodesics.

226 citations


Journal ArticleDOI
TL;DR: The proposed methods are illustrated through syntactic pattern recognition experiments in which a number of strings generated by ten given (source) non-k- TSSL grammars are used to infer ten k-TSSL stochastic automata, which are further used to classify newstrings generated by the same source Grammars.
Abstract: The inductive inference of the class of k-testable languages in the strict sense (k-TSSL) is considered. A k-TSSL is essentially defined by a finite set of substrings of length k that are permitted to appear in the strings of the language. Given a positive sample R of strings of an unknown language, a deterministic finite-state automation that recognizes the smallest k-TSSL containing R is obtained. The inferred automation is shown to have a number of transitions bounded by O(m) where m is the number of substrings defining this k-TSSL, and the inference algorithm works in O(kn log m) where n is the sum of the lengths of all the strings in R. The proposed methods are illustrated through syntactic pattern recognition experiments in which a number of strings generated by ten given (source) non-k-TSSL grammars are used to infer ten k-TSSL stochastic automata, which are further used to classify new strings generated by the same source grammars. The results of these experiments are consistent with the theory and show the ability of (stochastic) k-TSSLs to approach other classes of regular languages. >

Journal ArticleDOI
Christian Ronse1
TL;DR: It is shown that it is also necessary for a mathematically coherent application of morphological operators to grey-level images, and dilations and erosions can be defined directly with lattice-theoretic methods, without recourse to umbras.

Journal ArticleDOI
P. M. Vaidya1
TL;DR: The worst-case running time of the algorithm is better than that of Karmarkar's algorithm by a factor of $$\sqrt {m + n} $$ .
Abstract: We present an algorithm for linear programming which requires O(((m+n)n 2+(m+n)1.5 n)L) arithmetic operations wherem is the number of constraints, andn is the number of variables. Each operation is performed to a precision of O(L) bits.L is bounded by the number of bits in the input. The worst-case running time of the algorithm is better than that of Karmarkar's algorithm by a factor of $$\sqrt {m + n} $$ .

Journal Article
TL;DR: In this article, the conditions générales d'utilisation (http://www.numdam.org/conditions) of the agreement with the Scuola Normale Superiore di Pisa are described.
Abstract: © Scuola Normale Superiore, Pisa, 1990, tous droits réservés. L’accès aux archives de la revue « Annali della Scuola Normale Superiore di Pisa, Classe di Scienze » (http://www.sns.it/it/edizioni/riviste/annaliscienze/) implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/conditions). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright.

Journal ArticleDOI
TL;DR: Two different approaches to parameter estimation when the data are corrupted by unknown but bounded errors are reviewed and compared, the first based on a recursive parameter ellipsoidal- bounding algorithm, the other on an orthotopic-bounding set, obtained by solving linear programming problems.

Journal ArticleDOI
TL;DR: In this paper, a rigorous proof is given in the standard map associated with a Frenkel-Kontorowa model for the existence of chaotic trajectories with unbounded momenta for large enough coupling constant k > k 0.

Journal ArticleDOI
TL;DR: In this paper, the free creeping viscous incompressible plane flow of a finite region, bounded by a simple smooth closed curve and driven solely by surface tension, is analysed.
Abstract: The free creeping viscous incompressible plane flow of a finite region, bounded by a simple smooth closed curve and driven solely by surface tension, is analysed. The shape evolution is described in terms of a time-dependent mapping function z = Ω (ζ, t) of the unit circle, conformal on |ζ| [les ] 1. An equation giving the time evolution of the Ω (ζ, t) is derived. In practice, it has been necessary to guess a parametric form, i.e. Ω (ζ, t) = Ω[ζ; a1(t), a2(t), …], whose validity must be verified using the shape-evolution equation. Polynomial and proper rational mappings with no repeated factors are apparently always valid in principle. Solutions are given for (i) regions bounded initially by a regular epitrochoid, (ii) the limiting case of a half-plane bounded by a trochoid, and (iii) a class of rosettes whose mapping is rational. The two-lobed rosette gives the exact solution of the coalescence of equal cylinders. All these mappings involve limiting initial shapes having inward-pointing cusps. Useful parameterizations providing regions whose limiting shapes possess corners or outward-pointing cusps have not been found.

Book
30 Nov 1990
TL;DR: In this paper, the authors introduce the concept of almost periodic functions in space variables and show that these functions are almost periodic in the sense that they have a constant number of parameters.
Abstract: 1. Almost periodic functions.- 1. Almost periodic functions and Bohr compactilication.- 2. Besicovitch almost periodic functions and harmonic analysis.- 3. Structure of Bohr compactifications and spaces of almost periodic functions.- 4. Stepanov almost periodic functions.- 5. Weakly almost periodic functions.- 6. Spaces of smooth almost periodic functions on Rn.- Comments.- 2. Preliminaries.- 1. Some integral inequalities.- 2. Composition operators.- Comments.- 3. Solutions of evolution variational inequalities bounded and almost periodic in time.- 1. On variational inequalities.- 2. Bounded solutions.- 3. Regularity and almost periodicity of bounded solutions.- 4. The use of compactness.- 5. Almost periodicity in the sense of Besicovitch.- 6. Singular perturbation.- 7. Some examples and additional results.- Comments.- 4. Bounded and almost periodic solutions of certain evolution equations.- 1. Abstract evolution equations.- 2. Applications.- 3. Additional results.- Comments.- 5. Problems that are almost periodic in space variables.- 1. Nonlinear elliptic equations.- 2. Almost periodic first order systems.- 3. Symmetric hyperbolic systems with monotone nonlinearity.- 4. A nonlinear Schrodinger-type equation.- Comments.- Appendix 1. On certain linear evolution equations.- Appendix 2. On certain wave equations.- Appendix 3. Open questions.- References.

Journal ArticleDOI
TL;DR: Two algorithms for the k-satisfiability problem are presented and a probabilistic analysis is performed and it is shown that the first algorithm finds a solution with probability approaching one for a wide range of parameter values.

Journal ArticleDOI
TL;DR: In this article, the closed-form solution of the equations of motion of an ideal missile pursuing a nonmaneuvering target according to the pure proportional navigation law is obtained as a function of the polar coordinates for all real navigation constants N>or=2.
Abstract: The closed-form solution of the equations of motion of an ideal missile pursuing a nonmaneuvering target according to the pure proportional navigation law is obtained as a function of the polar coordinates for all real navigation constants N>or=2. The solution is given in the form of a uniformly convergent infinite product which reduces to a product of a finite number of factors if the navigation constant is a rational number. The solution is discussed, and necessary and sufficient conditions are stated for vanishing, bounded, and unbounded missile acceleration in the final phase of pursuit. >

Journal ArticleDOI
TL;DR: In this article, the authors define numerical Boltzmann schemes with finite speed of propagation corresponding to an equilibrium density function with bounded support, and obtain the compressible Euler equations with a convex entropy naturally associated to the convex function.
Abstract: Let H be a convex function. A Boltzmann equation is built following the B.G.K. model, for which H is an entropy. In the fluid limit, the compressible Euler equations are obtained with a convex entropy naturally associated to H. The motivation is to define numerical Boltzmann schemes with finite speed of propagation corresponding to an equilibrium density function with bounded support. The classical scheme, obtained with $H(f) = f\log (f)$, is based on the equilibrium density function $\exp ({{ - |v|^2 } / 2})$, which has infinite support.

Journal ArticleDOI
01 Oct 1990
TL;DR: G. Cybenko (1989) has demonstrated the existence of uniform approximations to any continuous f provided that sigma is continuous, relying on the Hahn-Branch theorem and the dual characterization of C(I/sup n/).
Abstract: A constructive algorithm for uniformly approximating real continuous mappings by linear combinations of bounded sigmoidal functions is given. G. Cybenko (1989) has demonstrated the existence of uniform approximations to any continuous f provided that sigma is continuous; the proof is nonconstructive, relying on the Hahn-Branch theorem and the dual characterization of C(I/sup n/). Cybenko's result is extended to include any bounded sigmoidal (even nonmeasurable ones). The approximating functions are explicitly constructed. The number of terms in the linear combination is minimal for first-order terms. >

Journal ArticleDOI
TL;DR: For bounded symmetric domains Ω in Cn, a notion of bounded mean oscillation in terms of the Bergman metric is introduced in this article, where the densely defined operator [Mƒ, P] ≡ MƒP − PMƒ on L2(Ω, dv) is bounded.

Journal ArticleDOI
TL;DR: In this article, the authors modify the original form by replacing 1(0) by a related integral 7(0), thereby removing all singularities and computational instabilities in the solution.
Abstract: are removable singularities, they may lead to computational instabilities in the solution. Especially bothersome is the fact that computational problems can occur where the true anomaly is near zero. These problems are avoided in the work of solution that does not involve 7(0), but their work is confined to elliptical orbits. The purpose of this Note is to modify the original form by replacing 1(0) by a related integral 7(0), thereby removing all singularities and computational instabilities. The resulting solution, in terms of /(0), is identical for hyperbolic, parabolic, or noncircular elliptic orbits, but the particular case determines the nature of the closed-form evaluation of 7(0). Application of this work to actual problems usually involves the solution of a two-point boundary-value problem and is not considered here. Although we emphasize the case of bounded thrust, the unbounded thrust case can also be investigated through the use of the simpler equations for unpowered flight, which we also present. If the maximum number of impulses is known for an optimal rendezvous in this case, the two-point boundary-value problem is reduced to a problem of parameter optimization on the velocity increments and their locations. We conjecture that the maximum of impulses for this problem is four. If the number of impulses is restricted to two, the problem is solved by methods similar to those of Weiss et al.11'12 For the case of bounded thrust, a method such as that used for the rendezvous problem near circular orbit16 can be applied with starting iteratives obtained from the related unbounded thrust case.

Journal ArticleDOI
TL;DR: In this article, the convergence and stability properties of the Kalman filter-based parameter estimator are established for linear stochastic time-varying regression models, where both the variances and sample path averages of the parameter tracking error are shown to be bounded.
Abstract: Convergence and stability properties of the Kalman filter-based parameter estimator are established for linear stochastic time-varying regression models. The main features are: both the variances and sample path averages of the parameter tracking error are shown to be bounded; the regression vector includes both stochastic and deterministic signals, and no assumptions of stationarity or independence are requires; and the unknown parameters are only assumed to have bounded variations in an average sense. >

Journal ArticleDOI
TL;DR: The main result is that every morphism from a free semigroup to a finite semigroup S admits a Ramseyan factorization forest of height at most 9|S|.

Proceedings ArticleDOI
17 Jun 1990
TL;DR: It is shown that feedforward networks having bounded weights are not undesirable restricted, but are in fact universal approximators, provided that the hidden-layer activation function belongs to one of several suitable broad classes of functions: polygonal functions, certain piecewise polynomial functions, or a class of functions analytic on some open interval.
Abstract: It is shown that feedforward networks having bounded weights are not undesirable restricted, but are in fact universal approximators, provided that the hidden-layer activation function belongs to one of several suitable broad classes of functions: polygonal functions, certain piecewise polynomial functions, or a class of functions analytic on some open interval. These results are obtained by trading bounds on network weights for possible increments to network complexity, as indexed by the number of hidden nodes. The hidden-layer activation functions used include functions not admitted by previous universal approximation results, so the present results also extend the already broad class of activation functions for which universal approximation results are available. A theorem which establishes the approximate ability of these arbitrary mappings to learn when examples are generated by a stationary ergodic process is given

Journal ArticleDOI
TL;DR: The Leray functor as discussed by the authors was introduced to define the cohomological Conley index of an isolated invariant set of a homeomorphism on a locally compact metric space.
Abstract: We introduce the Leray functor on the category of graded modules equipped with an endomorphism of degree zero and we use this functor to define the cohomological Conley index of an isolated invariant set of a homeomorphism on a locally compact metric space. We prove the homotopy and additivity properties for this index and compute the index in some examples. As one of applications we prove the existence of nonconstant, bounded solutions of the Euler approximation of a certain system of ordinary differential equations.

Journal ArticleDOI
TL;DR: A procedure has been developed to machine a pocket with a convex or concave free surface bounded by lines, circular arcs and free curves, and the cutter location data are computed directly with better computational efficiency than normal.
Abstract: In machining die cavities or mechanical parts, it is often necessary to remove material within a given boundary. Although this pocket cutting capability is implemented in many numerical control packages, most of them can handle only convex shaped pockets bounded by curves of limited types and numbers. A procedure has been developed to machine a pocket with a convex or concave free surface bounded by lines, circular arcs and free curves. The cutter location data are computed directly with better computational efficiency than normal, without using an iterative method.

Journal ArticleDOI
TL;DR: It is shown that if G is 2K2-free and has maximum degree Δ(G)=D, then G has at most 5D24 edges if D is even, and this bound can be improved to (5D2−2D+1)4.