Search results for " function"

showing 10 items of 9395 documents

Three-page encoding and complexity theory for spatial graphs

2004

We construct a series of finitely presented semigroups. The centers of these semigroups encode uniquely up to rigid ambient isotopy in 3-space all non-oriented spatial graphs. This encoding is obtained by using three-page embeddings of graphs into the product of the line with the cone on three points. By exploiting three-page embeddings we introduce the notion of the three-page complexity for spatial graphs. This complexity satisfies the properties of finiteness and additivity under natural operations.

Discrete mathematics[ MATH.MATH-GT ] Mathematics [math]/Geometric Topology [math.GT]Algebra and Number TheoryDegree (graph theory)Semigroup010102 general mathematicsGeometric topologyGeometric Topology (math.GT)01 natural sciences57M25 57M15 57M05Combinatorics010104 statistics & probabilityMathematics - Geometric TopologyCone (topology)Additive functionEncoding (memory)[MATH.MATH-GT]Mathematics [math]/Geometric Topology [math.GT]FOS: Mathematics0101 mathematicsUnit (ring theory)Ambient isotopyMathematics[MATH.MATH-GT] Mathematics [math]/Geometric Topology [math.GT]MathematicsofComputing_DISCRETEMATHEMATICS
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New Encodings of Pseudo-Boolean Constraints into CNF

2009

International audience; This paper answers affirmatively the open question of the existence of a polynomial size CNF encoding of pseudo-Boolean (PB) constraints such that generalized arc consistency (GAC) is maintained through unit propagation (UP). All previous encodings of PB constraints either did not allow UP to maintain GAC, or were of exponential size in the worst case. This paper presents an encoding that realizes both of the desired properties. From a theoretical point of view, this narrows the gap between the expressive power of clauses and the one of pseudo-Boolean constraints.

Discrete mathematics[INFO.INFO-CC]Computer Science [cs]/Computational Complexity [cs.CC]Polynomial021103 operations researchUnit propagation[INFO.INFO-DS]Computer Science [cs]/Data Structures and Algorithms [cs.DS]0211 other engineering and technologies[INFO.INFO-DS] Computer Science [cs]/Data Structures and Algorithms [cs.DS]02 engineering and technologyComputer Science::Computational ComplexityExpressive powerExponential functionCombinatorics[ INFO.INFO-CC ] Computer Science [cs]/Computational Complexity [cs.CC]Encoding (memory)0202 electrical engineering electronic engineering information engineeringLocal consistency020201 artificial intelligence & image processingPoint (geometry)[INFO.INFO-CC] Computer Science [cs]/Computational Complexity [cs.CC][ INFO.INFO-DS ] Computer Science [cs]/Data Structures and Algorithms [cs.DS]Mathematics
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Local dimensions of measures on infinitely generated self-affine sets

2014

We show the existence of the local dimension of an invariant probability measure on an infinitely generated self-affine set, for almost all translations. This implies that an ergodic probability measure is exactly dimensional. Furthermore the local dimension equals the minimum of the local Lyapunov dimension and the dimension of the space. We also give an estimate, that holds for all translation vectors, with only assuming the affine maps to be contractive.

Discrete mathematicsmatematiikka28A80Applied Mathematicsta111Minkowski–Bouligand dimensionDimension functionMetric Geometry (math.MG)Dynamical Systems (math.DS)Complex dimensionEffective dimensionPacking dimensionMathematics - Metric GeometryHausdorff dimensionFOS: MathematicsdimensionsMathematics - Dynamical SystemsDimension theory (algebra)Inductive dimensionulottuvuudetAnalysisMathematicsJournal of Mathematical Analysis and Applications
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Weighted norm inequalities in a bounded domain by the sparse domination method

2019

AbstractWe prove a local two-weight Poincaré inequality for cubes using the sparse domination method that has been influential in harmonic analysis. The proof involves a localized version of the Fefferman–Stein inequality for the sharp maximal function. By establishing a local-to-global result in a bounded domain satisfying a Boman chain condition, we show a two-weight p-Poincaré inequality in such domains. As an application we show that certain nonnegative supersolutions of the p-Laplace equation and distance weights are p-admissible in a bounded domain, in the sense that they support versions of the p-Poincaré inequality.

Discrete mathematicsosittaisdifferentiaaliyhtälötInequalityGeneral Mathematicsmedia_common.quotation_subject010102 general mathematicsPoincaré inequalityharmoninen analyysi01 natural sciences35A23 (Primary) 42B25 42B37 (Secondary)Harmonic analysis010104 statistics & probabilitysymbols.namesakeMathematics - Analysis of PDEsNorm (mathematics)Bounded functionFOS: MathematicssymbolsMaximal function0101 mathematicsepäyhtälötAnalysis of PDEs (math.AP)Mathematicsmedia_common
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Embedding of analytic function spaces with given mean growth of the derivative

2006

MSC (2000) 30D55 If φ is a positive function defined in (0,1) and 0 <p< ∞, we consider the space L(p, φ) which consists of all functions f analytic in the unit disc D for which the integral means of the derivative Mp(r, f � )= " 1 2π Rπ −π þ f � (re iθ ) þ p dθ "1/p , 0 <r< 1, satisfy M p(r, f � )=O (φ(r)) ,a sr → 1. In this paper, for any given p ∈ (0,1), we characterize the functions φ, among a certain class of weight functions, to be able to embedd L(p, φ) into classical function spaces. These results complement other previously obtained by the authors for p ≥ 1. c

Discrete mathematicssymbols.namesakeComplement (group theory)Function spaceGeneral MathematicssymbolsEmbeddingDerivativeHardy spaceSpace (mathematics)Unit (ring theory)MathematicsAnalytic functionMathematische Nachrichten
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A Constructive Minimal Integral which Includes Lebesgue Integrable Functions and Derivatives

2000

In this paper we provide a minimal constructive integration process of Riemann type which includes the Lebesgue integral and also integrates the derivatives of differentiable functions. We provide a new solution to the classical problem of recovering a function from its derivative by integration, which, unlike the solution provided by Denjoy, Perron and many others, does not possess the generality which is not needed for this purpose.The descriptive version of the problem was treated by A. M. Bruckner, R. J. Fleissner and J. Foran in [2]. Their approach was based on the trivial observation that for the required minimal integral, a function F is the indefinite integral of f if and only if F'…

Discrete mathematicssymbols.namesakeDifferentiation of integralsGeneral MathematicssymbolsRiemann–Stieltjes integralLocally integrable functionRiemann integralDaniell integralDifferentiable functionLebesgue integrationLebesgue–Stieltjes integrationMathematicsJournal of the London Mathematical Society
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Performance analysis of optical imaging systems based on the fractional fourier transform

1998

Some image quality parameters, such as the Strehl ratio and the optical transfer function, are analysed in the generalized phase-space, or x-p domain, of the fractional Fourier transform associated with a modified one-dimensional pupil function. Some experimental results together with computer simulations are performed which illustrate the tolerance to defocus of different apertures.

Discrete-time Fourier transformStrehl ratioIngenieríaDiscrete Fourier transformsymbols.namesakePupil functionOpticsOptical transfer functionPupil functionComputer Science::Distributed Parallel and Cluster ComputingCiencias ExactasPhysicsbusiness.industryPhysicsAstrophysics::Instrumentation and Methods for AstrophysicsShort-time Fourier transformStrehl ratioOpticsDiscrete Fourier transformFourier analysisAtomic and Molecular Physics and OpticsFractional Fourier transformFractional Fourier transformOptical transfer functionFourier analysisShort-time Fourier transformsymbolsbusinessDiscrete-time Fourier transformJournal of Modern Optics
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On Multiresolution Transforms Based on Weighted-Least Squares

2014

This work is devoted to construct Harten’s multiresolution transforms using Weighted-Least squares for different discretizations. We establish a relation between the filters obtained using some decimation operators. Some properties and examples of filters are presented.

Discrete-time signalWeight functionDecimationRelation (database)Applied mathematicsConstruct (python library)Mathematics
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The Line Element-less Method Analysis of orthotropic beam for the De Saint Venant torsion problem

2010

Abstract This paper deals with the extension of a novel numerical technique, labelled line element-less method (LEM), in order to provide approximate solutions of the De Saint Venant torsion problem for orthotropic beams having simply and multiply connected cross-section. A suitable transformation of coordinates allows to take full advantage of the theory of analytic complex functions as in the isotropic case. A complex potential function analytic in all the transformed domain whose real and imaginary parts are related to the shear stress components and to the orthotropic ratio is introduced and expanded in the double-ended Laurent series involving harmonic polynomials. An element-free weak…

DiscretizationLine elementMechanical EngineeringLaurent seriesMathematical analysisIsotropyTorsion (mechanics)GeometryOrthotropic materialCondensed Matter PhysicsOrthotropic materialanalytic functiontorsion problemAlgebraic equationMechanics of MaterialsShear stressGeneral Materials ScienceSettore ICAR/08 - Scienza Delle CostruzioniCivil and Structural EngineeringMathematics
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Perimeter symmetrization of some dynamic and stationary equations involving the Monge-Ampère operator

2017

We apply the perimeter symmetrization to a two-dimensional pseudo-parabolic dynamic problem associated to the Monge-Ampere operator as well as to the second order elliptic problem which arises after an implicit time discretization of the dynamical equation. Curiously, the dynamical problem corresponds to a third order operator but becomes a singular second order parabolic equation (involving the 3-Laplacian operator) in the class of radially symmetric convex functions. Using symmetrization techniques some quantitative comparison estimates and several qualitative properties of solutions are given.

DiscretizationMathematical analysisPerimeter symmetrizationPseudoparabolic dynamic Monge-Ampère equationThird orderOperator (computer programming)Dynamic problemSettore MAT/05 - Analisi MatematicaTwo-dimensional domainSymmetrizationOrder (group theory)AmpereConvex functionMathematics
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