Search results for "Combinatorics"

showing 10 items of 1770 documents

The minimal free resolution of fat almost complete intersections in ℙ1 x ℙ1

2017

AbstractA current research theme is to compare symbolic powers of an ideal I with the regular powers of I. In this paper, we focus on the case where I = IX is an ideal deûning an almost complete intersection (ACI) set of points X in ℙ1 × ℙ1. In particular, we describe a minimal free bigraded resolution of a non-arithmetically Cohen-Macaulay (also non-homogeneous) set 𝒵 of fat points whose support is an ACI, generalizing an earlier result of Cooper et al. for homogeneous sets of triple points. We call 𝒵 a fat ACI.We also show that its symbolic and ordinary powers are equal, i.e, .

Current (mathematics)Ideal (set theory)General MathematicsPoints in ℙ1× ℙ1010102 general mathematicsComplete intersectionArithmetically Cohen-Macaulay; Points in ℙ1× ℙ1; Resolution; Symbolic powersSymbolic powers01 natural sciencesArithmetically Cohen-MacaulayCombinatoricsSet (abstract data type)Settore MAT/02 - AlgebraHomogeneous0103 physical sciencesArithmetically Cohen-Macaulay Points in ℙ1xℙ1 Resolution Symbolic powersSettore MAT/03 - Geometria010307 mathematical physics0101 mathematicsResolutionFocus (optics)Resolution (algebra)Mathematics
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Statistical Properties of Generalized Strain Criterion for Multiaxial Random Fatigue

1989

ABSTRACT Statistical properties of generalized criterion of the maximum shear and normal strains on the fracture plane have been presented, Functions of probability distribution and spectral density of the equivalent strain have been analysed on the assumption that a random tensor of strain state is a six-dimensional stationary and ergodic Gaussian process. The expected value and variance of the equivalent strain have been determined as well. From spectral analysis a new limitation has been derived for extension of some multiaxial cyclic fatigue criteria to random loadings. It is connected with the fact that in some cases the frequency band of the equivalent strain is greater than that for …

Cyclic stressFrequency bandMathematical analysisSpectral densityInfinitesimal strain theoryExpected valueCombinatoricsCondensed Matter::Materials Sciencesymbols.namesakesymbolsErgodic theoryProbability distributionGaussian processMathematics
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A Dido problem for domains in ?2 with a given inradius

1990

We find which are the simply connected domains in ℝ2 satisfying the Dido condition for a straight shoreline, with a given area A and a fixed inradius ϱ, which minimize the length of the free boundary. There are three different cases according to the values of A and ϱ.

DIDODiscrete mathematicsCombinatoricsDifferential geometryHyperbolic geometrySimply connected spaceBoundary (topology)Geometry and TopologyAlgebraic geometryIncircle and excircles of a triangleProjective geometryMathematicsGeometriae Dedicata
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New results for finding common neighborhoods in massive graphs in the data stream model

2008

AbstractWe consider the problem of finding pairs of vertices that share large common neighborhoods in massive graphs. We give lower bounds for randomized, two-sided error algorithms that solve this problem in the data-stream model of computation. Our results correct and improve those of Buchsbaum, Giancarlo, and Westbrook [On finding common neighborhoods in massive graphs, Theoretical Computer Science, 299 (1–3) 707–718 (2004)]

Data streamDiscrete mathematicsGeneral Computer ScienceExtremal graph theorySpace lower boundsModel of computationCommunication complexityGraph theoryUpper and lower boundsTheoretical Computer ScienceExtremal graph theoryCombinatoricsGraph algorithms for data streamsAlgorithms Theoretical Computer SciencedGraph algorithmsCommunication complexityComputer Science(all)MathematicsTheoretical Computer Science
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Quasi-Newton approach to nonnegative image restorations

2000

Abstract Image restoration, or deblurring, is the process of attempting to correct for degradation in a recorded image. Typically the blurring system is assumed to be linear and spatially invariant, and fast Fourier transform (FFT) based schemes result in efficient computational image restoration methods. However, real images have properties that cannot always be handled by linear methods. In particular, an image consists of positive light intensities, and thus a nonnegativity constraint should be enforced. This constraint and other ways of incorporating a priori information have been suggested in various applications, and can lead to substantial improvements in the reconstructions. Neverth…

DeblurringMathematical optimizationNumerical AnalysisAlgebra and Number TheoryPrinciple of maximum entropyFast Fourier transformCirculant matrixBlock Toeplitz matrixConjugate gradient methodReal imageQuasi-Newton methodImage restorationConjugate gradient methodRegularizationA priori and a posterioriQuasi-Newton methodDiscrete Mathematics and CombinatoricsGeometry and TopologyImage restorationMathematicsLinear Algebra and its Applications
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Bounds for the relative n-th nilpotency degree in compact groups

2009

The line of investigation of the present paper goes back to a classical work of W. H. Gustafson of the 1973, in which it is described the probability that two randomly chosen group elements commute. In the same work, he gave some bounds for this kind of probability, providing information on the group structure. We have recently obtained some generalizations of his results for finite groups. Here we improve them in the context of the compact groups.

Degree (graph theory)Group (mathematics)General MathematicsProbability (math.PR)20P05 22A05 28C10 22A20 43A05Context (language use)Group Theory (math.GR)Group structureCombinatoricsLine (geometry)FOS: MathematicsMathematics - Group TheoryMathematics - ProbabilityHaar measureMathematics
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Integral-geometrical consideration of density matrices

1995

The ensemble N-representability problem for the k-th order reduced density matrix (k-RDM) as well as the problem of reconstruction of the N-particle system density matrices (N-DM) from a given k-RDM are studied. The spatial parts of the k-RDM expansion in terms of spin tensorial operators {Theta}{sub {lambda}} are represented using particular values (at specially chosen {Xi} = {Xi}{sub o}) of the Radon transform D{sub N{lambda}} D{sub N{lambda}}({Xi}) of the N-DM spatial parts (or their sums) D{sub N{lambda}}({chi}{prime}{vert_bar}{chi}{double_prime}) (here, {Xi} is a d-plane in the n-space {Re}{double_prime} of {chi} = ({chi}{prime}, {chi}{double_prime}), with n = 6N, d = 3(N - k), {chi}{p…

Density matrixCombinatoricsOrder (ring theory)Reduced density matrixPhysical and Theoretical ChemistrySymmetry (geometry)Condensed Matter PhysicsLambdaAtomic and Molecular Physics and OpticsPrime (order theory)Spin-½International Journal of Quantum Chemistry
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Unambiguous recognizable two-dimensional languages

2006

We consider the family UREC of unambiguous recognizable two-dimensional languages. We prove that there are recognizable languages that are inherently ambiguous, that is UREC family is a proper subclass of REC family. The result is obtained by showing a necessary condition for unambiguous recognizable languages. Further UREC family coincides with the class of picture languages defined by unambiguous 2OTA and it strictly contains its deterministic counterpart. Some closure and non-closure properties of UREC are presented. Finally we show that it is undecidable whether a given tiling system is unambiguous.

DeterminismSettore INF/01 - InformaticaDeterministic context-free languageGeneral MathematicsTwo-dimensional languagesAutomata and formal languages; Determinism; Two-dimensional languages; UnambiguityComputer Science::Computation and Language (Computational Linguistics and Natural Language and Speech Processing)Class (philosophy)Computer Science ApplicationsUndecidable problemAutomata and Formal Languages. ; Unambiguity ; Determinism. .; Two-dimensional languagesCombinatoricsClosure (mathematics)Computer Science::Programming LanguagesAutomata and formal languagesDeterminism.ArithmeticComputer Science::Formal Languages and Automata TheorySoftwareUnambiguityMathematics
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Weak and strong recognition by 2-way randomized automata

1997

Languages weakly recognized by a Monte Carlo 2-way finite automaton with n states are proved to be strongly recognized by a Monte Carlo 2-way finite automaton with no(n) states. This improves dramatically over the previously known result by M.Karpinski and R.Verbeek [10] which is also nontrivial since these languages can be nonregular [5]. For tally languages the increase in the number of states is proved to be only polynomial, and these languages are regular.

Deterministic pushdown automatonCombinatoricsDeterministic automatonProbabilistic automatonPushdown automatonQuantum finite automataBüchi automatonTwo-way deterministic finite automatonNondeterministic finite automatonComputer Science::Computational ComplexityComputer Science::Formal Languages and Automata TheoryMathematics
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A note on rank 2 diagonals

2020

<p>We solve two questions regarding spaces with a (G<sub>δ</sub>)-diagonal of rank 2. One is a question of Basile, Bella and Ridderbos about weakly Lindelöf spaces with a G<sub>δ</sub>-diagonal of rank 2 and the other is a question of Arhangel’skii and Bella asking whether every space with a diagonal of rank 2 and cellularity continuum has cardinality at most continuum.</p>

DiagonalCardinal invariantsMathematics::General TopologyWeakly Lindelöflcsh:AnalysisSpace (mathematics)01 natural sciencesCombinatoricsBELLACardinalitydual propertiesCardinality boundsFOS: MathematicsRank (graph theory)Continuum (set theory)0101 mathematicsDual propertiesMathematics - General TopologyMathematicsweakly LindelofGδ- diagonallcsh:Mathematics010102 general mathematicsGeneral Topology (math.GN)neighbourhood assignmentGδ-diagonallcsh:QA299.6-433lcsh:QA1-939gδ-diagonal010101 applied mathematicscardinality boundsMathematics::LogicNeighbourhood assignmentSettore MAT/03 - GeometriaGeometry and Topologyweakly lindelöf
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