Search results for "Mink"

showing 10 items of 115 documents

Overlapping self-affine sets of Kakeya type

2009

We compute the Minkowski dimension for a family of self-affine sets on the plane. Our result holds for every (rather than generic) set in the class. Moreover, we exhibit explicit open subsets of this class where we allow overlapping, and do not impose any conditions on the norms of the linear maps. The family under consideration was inspired by the theory of Kakeya sets.

Class (set theory)Applied MathematicsGeneral Mathematics010102 general mathematicsMinkowski–Bouligand dimensionDynamical Systems (math.DS)Type (model theory)16. Peace & justice01 natural sciencesCombinatoricsSet (abstract data type)Mathematics - Classical Analysis and ODEs0103 physical sciencesClassical Analysis and ODEs (math.CA)FOS: Mathematics28A80 37C45010307 mathematical physicsAffine transformationMathematics - Dynamical Systems0101 mathematicsMathematicsErgodic Theory and Dynamical Systems
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Systematisation of Systems Solving Physics Boundary Value Problems

2020

A general conservation law that defines a class of physical field theories is constructed. First, the notion of a general field is introduced as a formal sum of differential forms on a Minkowski manifold. By the action principle the conservation law is defined for such a general field. By construction, particular field notions of physics, e.g., magnetic flux, electric field strength, stress, strain etc. become instances of the general field. Hence, the differential equations that constitute physical field theories become also instances of the general conservation law. The general field and the general conservation law together correspond to a large class of relativistic hyperbolic physical …

Class (set theory)Conservation lawField (physics)numeeriset menetelmätDifferential equationDifferential formAction (physics)AlgebraMinkowski spacelaskennallinen tiedeBoundary value problemfysiikkadifferentiaaliyhtälötnumerical mathematics
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Hausdorff dimension from the minimal spanning tree

1993

A technique to estimate the Hausdorff dimension of strange attractors, based on the minimal spanning tree of the point distribution is extensively tested in this work. This method takes into account in some sense the infimum requirement appearing in the definition of the Hausdorff dimension. It provides accurate estimates even for a low number of data points and it is especially suited to high-dimensional systems.

CombinatoricsDiscrete mathematicsHausdorff distancePacking dimensionHausdorff dimensionMathematicsofComputing_NUMERICALANALYSISMinkowski–Bouligand dimensionDimension functionHausdorff measureUrysohn and completely Hausdorff spacesEffective dimensionMathematicsPhysical Review E
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Hausdorff measures and dimension

1995

CombinatoricsHausdorff distancePacking dimensionHausdorff dimensionMinkowski–Bouligand dimensionDimension functionHausdorff measureOuter measureEffective dimensionMathematics
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Cotype 2 estimates for spaces of polynomials on sequence spaces

2002

We give asymptotically correct estimations for the cotype 2 constant C2(P(mXn)) ofthe spaceP(mXn) of allm-homogenous polynomials onXn, the span of the firstn sequencesek=(\gdkj)j in a Banach sequence spaceX. Applications to Minkowski, Orlicz and Lorentz sequence spaces are given.

CombinatoricsMathematics::Functional AnalysisSequencesymbols.namesakeSpan (category theory)General MathematicsLorentz transformationMinkowski spaceMathematics::Optimization and ControlsymbolsAlgebra over a fieldConstant (mathematics)Mathematics
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Semimodular Locally Projective Lattices of Rank 4 from v.Staudt’s Point of View

1981

We consider groups of projectivities in a certain kind of lattices called “Spaces”,also comprising the circle planes, and give theorems of v.Staudtian type, which characterize those Spaces which can be represented by a sublattice of a projective geometry of rank 4.

CombinatoricsMinkowski planeTranslation planeTangentPoint (geometry)Rank (differential topology)Type (model theory)Projective testProjective geometryMathematics
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The Poincaré inequality is an open ended condition

2008

Let p > 1 and let (X,d,µ) be a complete metric measure space with µ Borel and doubling that admits a (1,p)-Poincare inequality. Then there exists e > 0 such that (X,d,µ) admits a (1,q)-Poincare inequality for every q > p - e, quantitatively.

Combinatoricssymbols.namesakeMathematics (miscellaneous)Mathematical analysisMetric (mathematics)symbolsPoincaré inequalityStatistics Probability and UncertaintyMinkowski inequalitySpace (mathematics)Measure (mathematics)MathematicsAnnals of Mathematics
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On the Euler-Lagrange inequality of a convex variational integral in Orlicz spaces

1987

Convex analysisInequalitymedia_common.quotation_subjectMathematical analysisRegular polygonLinear matrix inequalityMinkowski inequalityGeneral Earth and Planetary SciencesApplied mathematicsBirnbaum–Orlicz spaceLp spaceJensen's inequalityGeneral Environmental Sciencemedia_commonMathematicsBanach Center Publications
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Monte Carlo Studies of Relations between Fractal Dimensions in Monofractal Data Sets

1998

Within the fractal approach to studying the distribution of seismic event locations, different fractal dimension definitions and estimation algorithms are in use. Although one expects that for the same data set, values of different dimensions will be different, it is usually anticipated that the direction of fractal dimension changes among different data sets will be the same for every fractal dimension. Mutual relations between the three most popular fractal dimensions, namely: the capacity, cluster and correlation dimensions, have been investigated in the present work. The studies were performed on the Monte Carlo generated data sets. The analysis has shown that dependence of the fractal …

Correlation dimensionGeophysicsFractalFractal dimension on networksGeochemistry and PetrologyMinkowski–Bouligand dimensionGeometryMultifractal systemStatistical physicsEffective dimensionFractal analysisFractal dimensionMathematicsPure and Applied Geophysics
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Dimension of a measure

2000

Correlation dimensionPure mathematicsDimension (vector space)General MathematicsMinkowski–Bouligand dimensionMeasure (physics)MathematicsStudia Mathematica
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