Search results for "Transform"

showing 10 items of 3975 documents

Perturbations of surjective convolution operators

2002

Let μ 1 and μ 2 be (ultra)distributions with compact support which have disjoint singular supports. We assume that the convolution operator f → μ 1 *f is surjective when it acts on a space of functions or (ultra)distributions, and we investigate whether the perturbed convolution operator f→ (μ 1 + μ 2 ) * f is surjective. In particular we solve in the negative a question asked by Abramczuk in 1984.

Discrete mathematicsLaplace transformApplied MathematicsGeneral MathematicsDisjoint setsOperator theorySpace (mathematics)ConvolutionSurjective functionsymbols.namesakeDistribution (mathematics)Fourier transformsymbolsMathematicsProceedings of the American Mathematical Society
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The support localization property of the strongly embedded subspaces of banach function spaces

2015

[EN] Motivated by the well known Kadec-Pelczynski disjointifcation theorem, we undertake an analysis of the supports of non-zero functions in strongly embedded subspaces of Banach functions spaces. The main aim is to isolate those properties that bring additional information on strongly embedded subspaces. This is the case of the support localization property, which is a necessary condition fulflled by all strongly embedded subspaces. Several examples that involve Rademacher functions, the Volterra operator, Lorentz spaces or Orlicz spaces are provided.

Discrete mathematicsMathematics::Functional AnalysisPure mathematicsVolterra operatorFunctional analysisDisjoint sequenceStrongly embedded subspaceFunction spaceGeneral MathematicsLorentz transformationVector measure integrationBanach function spaceLinear subspacesymbols.namesakesymbolsInterpolation spaceBirnbaum–Orlicz spaceLp spaceMATEMATICA APLICADAMathematics
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Compactness of time-frequency localization operators on L2(Rd)

2006

Abstract In this paper, we consider localization operators on L 2 ( R d ) defined by symbols in a subclass of the modulation space M ∞ ( R 2 d ) . We show that these operators are compact and that this subclass is “optimal” for compactness.

Discrete mathematicsModulation spaceCompact operatorApproximation propertyShort-time Fourier transformModulation spaceLocalization operatorOperator theoryCompact operatorCompact operator on Hilbert spaceSubclassCompact spaceTheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGESShort-time Fourier transformAnalysisComputer Science::Formal Languages and Automata TheoryMathematicsJournal of Functional Analysis
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Equivariant Triviality of Quasi-Monomial Triangular $$\mathbb{G}_{a}$$-Actions on $$\mathbb{A}^{4}$$

2014

We give a direct and self-contained proof of the fact that additive group actions on affine four-space generated by certain types of triangular derivations are translations whenever they are proper. The argument, which is based on explicit techniques, provides an illustration of the difficulties encountered and an introduction to the more abstract methods which were used recently by the authors to solve the general triangular case.

Discrete mathematicsMonomialPure mathematicsArgumentEquivariant mapAffine transformationTrivialityMathematicsAdditive group
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Tensor product multiresolution analysis with error control for compact image representation

2002

A class of multiresolution representations based on nonlinear prediction is studied in the multivariate context based on tensor product strategies. In contrast to standard linear wavelet transforms, these representations cannot be thought of as a change of basis, and the error induced by thresholding or quantizing the coefficients requires a different analysis. We propose specific error control algorithms which ensure a prescribed accuracy in various norms when performing such operations on the coefficients. These algorithms are compared with standard thresholding, for synthetic and real images.

Discrete mathematicsMultiresolution analysisMathematicsofComputing_NUMERICALANALYSISWavelet transformImage processingReal imageThresholdingTensor productControl and Systems EngineeringSignal ProcessingComputer Vision and Pattern RecognitionElectrical and Electronic EngineeringChange of basisAlgorithmSoftwareMathematicsImage compressionSignal Processing
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An extension of the Burrows-Wheeler Transform and applications to sequence comparison and data compression

2005

We introduce a generalization of the Burrows-Wheeler Transform (BWT) that can be applied to a multiset of words. The extended transformation, denoted by E, is reversible, but, differently from BWT, it is also surjective. The E transformation allows to give a definition of distance between two sequences, that we apply here to the problem of the whole mitochondrial genome phylogeny. Moreover we give some consideration about compressing a set of words by using the E transformation as preprocessing.

Discrete mathematicsMultisetBurrows-Wheeler transform; Data Compression; Mitochondrial genome phylogenyBurrows–Wheeler transformMultiplicity (mathematics)Mitochondrial genome phylogenyBurrows-Wheeler transformData CompressionSurjective functionConjugacy classSequence comparisonPreprocessorAlgorithmMathematicsData compression
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An extension of the Burrows-Wheeler Transform

2007

AbstractWe describe and highlight a generalization of the Burrows–Wheeler Transform (bwt) to a multiset of words. The extended transformation, denoted by ebwt, is reversible. Moreover, it allows to define a bijection between the words over a finite alphabet A and the finite multisets of conjugacy classes of primitive words in A∗. Besides its mathematical interest, the extended transform can be useful for applications in the context of string processing. In the last part of this paper we illustrate one such application, providing a similarity measure between sequences based on ebwt.

Discrete mathematicsMultisetSimilarity (geometry)General Computer ScienceBurrows–Wheeler transformGeneralizationAlignment-free distance measure; Burrows-Wheeler transform; Sequence comparisonContext (language use)Similarity measureBurrows-Wheeler transformSequence comparisonTheoretical Computer ScienceConjugacy classBijectionAlignment-free distance measureBurrows–Wheeler transformComputer Science::Formal Languages and Automata TheoryComputer Science(all)Mathematics
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Language Recognition Power and Succinctness of Affine Automata

2016

In this work we study a non-linear generalization based on affine transformations of probabilistic and quantum automata proposed recently by Diaz-Caro and Yakaryilmaz [6] referred as affine automata. First, we present efficient simulations of probabilistic and quantum automata by means of affine automata which allows us to characterize the class of exclusive stochastic languages. Then, we initiate a study on the succintness of affine automata. In particular, we show that an infinite family of unary regular languages can be recognized by 2-state affine automata, whereas the number of states of any quantum and probabilistic automata cannot be bounded. Finally, we present the characterization …

Discrete mathematicsNested word0102 computer and information sciences02 engineering and technologyω-automatonNonlinear Sciences::Cellular Automata and Lattice Gases01 natural sciencesMobile automaton010201 computation theory & mathematicsContinuous spatial automaton0202 electrical engineering electronic engineering information engineeringAutomata theoryQuantum finite automata020201 artificial intelligence & image processingAffine transformationComputer Science::Formal Languages and Automata TheoryMathematicsQuantum cellular automaton
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A Vector Approach to Euler's Line of a Triangle

1992

Among the many interesting properties that triangles possess there is one that quickly attracts our curiosity and stays easily in our mind: The centroid, circumcentre and orthocentre all lie in a common line (Euler's Line). An elementary simple proof can be obtained using metric and affine properties of the points involved, [1]. Our aim here is to illustrate a proof using vectors. We identify points in the plane with their position vectors. It is easy to see that the centroid G of the triangle ABC is given by the identity

Discrete mathematicsPlane (geometry)General MathematicsCentroidTopologysymbols.namesakeIdentity (mathematics)Simple (abstract algebra)Line (geometry)Metric (mathematics)Euler's formulasymbolsAffine transformationMathematicsThe American Mathematical Monthly
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A note on Sturmian words

2012

International audience; We describe an algorithm which, given a factor of a Sturmian word, computes the next factor of the same length in the lexicographic order in linear time. It is based on a combinatorial property of Sturmian words which is related with the Burrows-Wheeler transformation.

Discrete mathematicsProperty (philosophy)General Computer ScienceSettore INF/01 - Informatica010102 general mathematics[INFO.INFO-DS]Computer Science [cs]/Data Structures and Algorithms [cs.DS]Sturmian word0102 computer and information sciencesSturmian wordsLexicographical order01 natural sciencesTheoretical Computer ScienceCombinatoricsTransformation (function)010201 computation theory & mathematicsFactor (programming language)combinatorics0101 mathematicscomputerTime complexitycomputer.programming_languageMathematics
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