Search results for "Bounded function"

showing 10 items of 508 documents

Coherent Conditional Previsions and Proper Scoring Rules

2012

In this paper we study the relationship between the notion of coherence for conditional prevision assessments on a family of finite conditional random quantities and the notion of admissibility with respect to bounded strictly proper scoring rules. Our work extends recent results given by the last two authors of this paper on the equivalence between coherence and admissibility for conditional probability assessments. In order to prove that admissibility implies coherence a key role is played by the notion of Bregman divergence.

Settore MAT/06 - Probabilita' E Statistica Matematicabregman divergenceproper scor- ing rulesConditional prevision assessmentsconditional scoring rulesstrong dominanceConditional probabilityweak dominanceCoherence (statistics)Bregman divergenceConditional prevision assessments coherence proper scoring rules conditional scoring rules weak dominance strong dominance admissibility Bregman divergence.proper scoring rulescoherenceBounded functionKey (cryptography)admissibilityConditional prevision assessments; conditional scoring rules; admissibility; proper scor- ing rules; weak dominance; strong dominanceEquivalence (measure theory)Mathematical economicsconditional prevision assessments; strong dominance; admissibility; proper scoring rules; bregman divergence; weak dominance; conditional scoring rules; coherenceMathematics
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Observer-based finite-time fuzzy H∞ control for discrete-time systems with stochastic jumps and time-delays

2014

This paper is concerned with the problem of observer-based finite-time H ∞ control for a family of discrete-time Markovian jump nonlinear systems with time-delays represented by Takagi-Sugeno (T-S) model. The main contribution of this paper is to design an observer-based finite-time H ∞ controller such that the resulting closed-loop system is stochastic finite-time bounded and satisfies a prescribed H ∞ disturbance attenuation level over the given finite-time interval. Sufficient criteria on stochastic finite-time H ∞ stabilization via observer-based fuzzy state feedback are presented for the solvability of the problem, which can be tackled by a feasibility problem in terms of linear matrix…

Signal processingObserver (quantum physics)Finite-time H∞ controlTakagi-Sugeno (T-S) modelMarkovian jump systemsFuzzy control systemFuzzy logicFinite-time H∞ control; Markovian jump systems; Observer-based control; Takagi-Sugeno (T-S) model; Electrical and Electronic Engineering; Control and Systems Engineering; Software; Signal Processing; 1707Nonlinear systemobserver-based controlTakagi–Sugeno (T–S) modelDiscrete time and continuous timeControl and Systems EngineeringControl theoryBounded functionSignal ProcessingComputer Vision and Pattern RecognitionState observerElectrical and Electronic Engineeringfinite-time H∞ controlfinite-time H infinity controlObserver-based controlSoftware1707Mathematics
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Collision Orbits in the Isosceles Rectilinear Restricted Problem

1995

In the study of the Collinear Three-Body Problem, McGehee (1974) introduced a new set of coordinates which had the effect of blowing up the triple collision singularity. Subsequently, his method has been used to analyze some other collision or singularities. Recently, Wang (1986) introduced another transformation which differs from the McGehee’s coordinates in the fact that the blowing-up factor is now the potential function, U, instead of the moment of inertia, I. Meyer and Wang (1993) have applied this method to the Restricted Isosceles Three-body Problem with positive energy and Cors and Llibre (1994) to the hyperbolic restricted three-body problem. In this paper we study the singulariti…

SingularityClassical mechanicsBounded functionMathematical analysisIsosceles triangleGravitational singularityNegative energyFunction (mathematics)Stable manifoldMathematicsBlowing up
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Further results on H<inf>∞</inf> control of switched linear time-delay systems

2012

In this note, we study the problems of stability analysis and H ∞ controller synthesis of discrete-time switched systems with time-varying delay. The system under consideration is firstly transformed into an interconnection system. Based on the system transformation and the scaled small gain theorem, the asymptotic stability of the original system is examined via the version of the bounded realness of the transformed forward system. The aim of the proposed approach is to reduce conservatism, which is made possible by a precise approximation of the time-varying delay and the input-output approach. The proposed stability condition is demonstrated to be much less conservative than most existin…

Small-gain theoremApproximation theoryExponential stabilityControl theoryBounded functionConvex optimizationTime-invariant systemLinear systemMathematics2012 12th International Conference on Control Automation Robotics & Vision (ICARCV)
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Boundedness and spectral invariance for standard pseudodifferential operators on anisotropically weighted LP-Sobolev spaces

1990

It is shown that pseudodifferential operators with symbols in the standard classes S ρ,δ m (ℝn) define bounded maps between large classes of weighted LP-Sobolev spaces where the growth of the weight does not have to be isotropic. Moreover, the spectrum is independent of the choice of the space.

Sobolev spaceAlgebra and Number TheoryPseudodifferential operatorsBounded functionMathematical analysisSpectrum (functional analysis)IsotropySpace (mathematics)AnalysisMathematicsIntegral Equations and Operator Theory
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Maximal potentials, maximal singular integrals, and the spherical maximal function

2014

We introduce a notion of maximal potentials and we prove that they form bounded operators from L to the homogeneous Sobolev space Ẇ 1,p for all n/(n − 1) < p < n. We apply this result to the problem of boundedness of the spherical maximal operator in Sobolev spaces.

Sobolev spaceMathematics::Functional AnalysisHomogeneousApplied MathematicsGeneral MathematicsBounded functionMathematical analysisMathematics::Analysis of PDEsMaximal operatorMaximal functionSingular integralMathematicsSobolev inequalityProceedings of the American Mathematical Society
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Uniform, Sobolev extension and quasiconformal circle domains

1991

This paper contributes to the theory of uniform domains and Sobolev extension domains. We present new features of these domains and exhibit numerous relations among them. We examine two types of Sobolev extension domains, demonstrate their equivalence for bounded domains and generalize known sufficient geometric conditions for them. We observe that in the plane essentially all of these domains possess the trait that there is a quasiconformal self-homeomorphism of the extended plane which maps a given domain conformally onto a circle domain. We establish a geometric condition enjoyed by these plane domains which characterizes them among all quasicircle domains having no large and no small bo…

Sobolev spacePartial differential equationGeneral MathematicsBounded functionMathematical analysisEquivalence (formal languages)QuasicircleAnalysisMathematicsSobolev spaces for planar domainsJournal d’Analyse Mathématique
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Analytic capacity and quasiconformal mappings with $W^{1,2}$ Beltrami coefficient

2008

We show that if $\phi$ is a quasiconformal mapping with compactly supported Beltrami coefficient in the Sobolev space $W^{1,2}$, then $\phi$ preserves sets with vanishing analytic capacity. It then follows that a compact set $E$ is removable for bounded analytic functions if and only if it is removable for bounded quasiregular mappings with compactly supported Beltrami coefficient in $W^{1,2}$.

Sobolev spaceQuasiconformal mappingComputer Science::GraphicsCompact spaceMathematics::Complex VariablesGeneral MathematicsBounded functionMathematical analysisAnalytic capacityAnalytic functionMathematicsMathematical Research Letters
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Dynamics and spectra of composition operators on the Schwartz space

2017

[EN] In this paper we study the dynamics of the composition operators defined in the Schwartz space of rapidly decreasing functions. We prove that such an operator is never supercyclic and, for monotonic symbols, it is power bounded only in trivial cases. For a polynomial symbol ¿ of degree greater than one we show that the operator is mean ergodic if and only if it is power bounded and this is the case when ¿ has even degree and lacks fixed points. We also discuss the spectrum of composition operators.

Space of rapidly decreasing functionsMathematics::Functional AnalysisPure mathematicsComposition operator010102 general mathematicsSpectrum (functional analysis)Power bounded operatorMonotonic functionFixed pointMean ergodic composition operator01 natural sciencesFunctional Analysis (math.FA)Mathematics - Functional Analysis010101 applied mathematicsOperator (computer programming)Schwartz spaceBounded functionSpectrumFOS: MathematicsErgodic theory0101 mathematicsMATEMATICA APLICADAAnalysisMathematics
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Spline-Based Wavelet Transforms

2018

The Lifting Scheme introduced in (Sweldens, Appl. Comput. Harmon. Anal. 3(2), 186–200 (1996) and Sweldens, SIAM J. Math. Anal. 29(2), 511–546 (1997).) [3, 4] is a method that constructs bi-orthogonal wavelet transforms of signals and provides their efficient implementation. The main feature of the lifting scheme is that all the constructions are derived directly in the spatial domain and therefore can be custom designed to more general and irregular settings such as non-uniformly spaced data samples and bounded intervals. In this chapter, we outline the lifting scheme and describe how to use the local quasi-interpolating splines, introduced in Chap. 6, for the construction of wavelet transf…

Spline (mathematics)Boundary effectsLifting schemeComputer scienceBounded functionWavelet transformSpatial domainAlgorithm
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