Search results for "Lemma"

showing 10 items of 210 documents

Stent oversizing or not-oversizing? An unresolved dilemma

2021

Primary PCI plus stent implantation is indicated for treatment of acute coronary syndrome. Technically, due to the difference in lumen diameter between vessel portions and stent size in some coronary arteries, post-expansion of the stent is usually necessary to match proximal reference diameter and optimize stent apposition. Incomplete stent apposition has been associated with increased risk of in stent restenosis (ISR) and stent thrombosis (1) despite new stent technologies have largely reduced this risk (2-3). Although new antiplatelet drugs showed a more rapid onset of action and a stronger effect (4-5), stent apposition remains an important risk factor for stent thrombosis. As stent pos…

Dilemmamedicine.medical_specialtybusiness.industrymedicine.medical_treatmentmedicineMEDLINEStentStentsbusinessstent PCICardiology and Cardiovascular MedicineBlood Vessel ProsthesisSurgeryMinerva Cardiology and Angiology
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On the Shuffle of Star-Free Languages

2012

Motivated by the general problem to characterize families of languages closed under shuffle, we investigate some conditions under which the shuffle of two star-free languages is star-free. Some of the special cases here approached give rise to new problems in combinatorics on words.

Discrete mathematicsAlgebra and Number TheorySettore INF/01 - Informaticapure submonoidGeneral problemAbstract family of languagesRegular languageComputer Science::Computation and Language (Computational Linguistics and Natural Language and Speech Processing)Star (graph theory)star-free languageCone (formal languages)shuffle of languagePumping lemma for regular languagesTheoretical Computer ScienceCombinatorics on wordsComputational Theory and MathematicsRegular languagecombinatorics on words.Information SystemsMathematicsFundamenta Informaticae
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Generalized Lebesgue points for Sobolev functions

2017

In this article, we show that a function $f\in M^{s,p}(X),$ $0<s\leq 1,$ $0<p<1,$ where $X$ is a doubling metric measure space, has generalized Lebesgue points outside a set of $\mathcal{H}^h$-Hausdorff measure zero for a suitable gauge function $h.$

Discrete mathematicsDominated convergence theoremmedian010102 general mathematicsLebesgue's number lemmaRiemann integralSobolev spaceLebesgue integration01 natural sciencesLebesgue–Stieltjes integrationFunctional Analysis (math.FA)Mathematics - Functional Analysis010101 applied mathematicssymbols.namesakemetric measure spaceDifferentiation of integralsSquare-integrable function46E35 28A78FOS: MathematicssymbolsLocally integrable function0101 mathematicsgeneralized Lebesgue pointMathematicsCzechoslovak Mathematical Journal
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On block pumpable languages

2016

Ehrenfeucht, Parikh and Rozenberg gave an interesting characterisation of the regular languages called the block pumping property. When requiring this property only with respect to members of the language but not with respect to nonmembers, one gets the notion of block pumpable languages. It is shown that these block pumpable are a more general concept than regular languages and that they are an interesting notion of their own: they are closed under intersection, union and homomorphism by transducers; they admit multiple pumping; they have either polynomial or exponential growth.

Discrete mathematicsGeneral Computer ScienceAbstract family of languagesComputer Science::Computation and Language (Computational Linguistics and Natural Language and Speech Processing)0102 computer and information sciences02 engineering and technology01 natural sciencesCone (formal languages)Pumping lemma for regular languagesTheoretical Computer ScienceCombinatoricsRegular languageIntersection010201 computation theory & mathematicsBlock (programming)0202 electrical engineering electronic engineering information engineering020201 artificial intelligence & image processingHomomorphismPumping lemma for context-free languagesComputer Science::Formal Languages and Automata TheoryMathematicsTheoretical Computer Science
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Periodicity and repetitions in parameterized strings

2008

AbstractOne of the most beautiful and useful notions in the Mathematical Theory of Strings is that of a Period, i.e., an initial piece of a given string that can generate that string by repeating itself at regular intervals. Periods have an elegant mathematical structure and a wealth of applications [F. Mignosi and A. Restivo, Periodicity, Algebraic Combinatorics on Words, in: M. Lothaire (Ed.), Cambridge University Press, Cambridge, pp. 237–274, 2002]. At the hearth of their theory, there are two Periodicity Lemmas: one due to Lyndon and Schutzenberger [The equation aM=bNcP in a free group, Michigan Math. J. 9 (1962) 289–298], referred to as the Weak Version, and the other due to Fine and …

Discrete mathematicsLemma (mathematics)Algebraic combinatoricsCombinatorics on wordsSettore INF/01 - InformaticaApplied MathematicsParameterized complexityParameterized stringsString searching algorithmString (physics)Periodic functionCombinatoricsCombinatorics on wordsDiscrete Mathematics and CombinatoricsString periodicityUniquenessCombinatorics on Words AlgorithmsMathematics
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On the points realizing the distance to a definable set

2011

Abstract We prove a definable/subanalytic version of a useful lemma, presumably due to John Nash, concerning the points realizing the Euclidean distance to an analytic submanifold of R n . We present a parameter version of the main result and we discuss the properties of the multifunction obtained.

Discrete mathematicsLemma (mathematics)Applied MathematicsSubanalytic setsdefinable setsSubmanifoldsubanalytic setsEuclidean distanceAlgebraMultifunctionsDefinable setDefinable setstame geometryAnalysisTame geometryMathematicsmultifunctions
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A multilinear Phelps' Lemma

2007

We prove a multilinear version of Phelps' Lemma: if the zero sets of multilinear forms of norm one are 'close', then so are the multilinear forms.

Discrete mathematicsMathematics::Functional AnalysisLemma (mathematics)CeroMultilinear mapbiologyApplied MathematicsGeneral MathematicsMathematics::Classical Analysis and ODEsComputer Science::Computational Complexitybiology.organism_classificationCombinatoricsNorm (mathematics)MathematicsProceedings of the American Mathematical Society
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Hoffman's Error Bound, Local Controllability, and Sensitivity Analysis

2000

Our aim is to present sufficient conditions ensuring Hoffman's error bound for lower semicontinuous nonconvex inequality systems and to analyze its impact on the local controllability, implicit function theorem for (non-Lipschitz) multivalued mappings, generalized equations (variational inequalities), and sensitivity analysis and on other problems like Lipschitzian properties of polyhedral multivalued mappings as well as weak sharp minima or linear conditioning. We show how the information about our sufficient conditions can be used to provide a computable constant such that Hoffman's error bound holds. We also show that this error bound is nothing but the classical Farkas lemma for linear …

Discrete mathematicsMaxima and minimaControllabilityLinear inequalityControl and OptimizationApplied MathematicsErgodicityVariational inequalityApplied mathematicsConstant (mathematics)Farkas' lemmaImplicit function theoremMathematicsSIAM Journal on Control and Optimization
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A restriction on the schur multiplier of nilpotent lie algebras

2011

An improvement of a bound of Yankosky (2003) is presented in this paper, thanks to a restriction which has been recently obtained by the authors on the Schur multiplier M(L) of a finite dimensional nilpotent Lie algebra L. It is also described the structure of all nilpotent Lie algebras such that the bound is attained. An important role is played by the presence of a derived subalgebra of maximal dimension. This allows precision on the size of M(L). Among other results, applications to the non-abelian tensor square L ⊗ L are illustrated.

Discrete mathematicsPure mathematicsAlgebra and Number TheorySchur multiplierSchur's lemmanilpotent Lie algebrasSchur algebrahomology of Lie algebraSchur's theoremLie conformal algebraNilpotent Lie algebraSettore MAT/02 - AlgebraAdjoint representation of a Lie algebraRepresentation of a Lie groupNilpotent groupMathematics::Representation TheoryMathematics
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On a normal form of symmetric maps of [0, 1]

1980

A class of continuous symmetric mappings of [0, 1] into itself is considered leaving invariant a measure absolutely continuous with respect to the Lebesgue measure.

Discrete mathematicsPure mathematicsLebesgue measureLebesgue's number lemmaStatistical and Nonlinear Physics58F20Absolute continuityLebesgue integrationLebesgue–Stieltjes integrationsymbols.namesakeNonlinear system28D05symbolsInvariant (mathematics)Borel measureMathematical PhysicsMathematicsCommunications in Mathematical Physics
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