Search results for "Set theory"

showing 10 items of 751 documents

Weakly algebraizable logics

2000

AbstractIn the paper we study the class of weakly algebraizable logics, characterized by the monotonicity and injectivity of the Leibniz operator on the theories of the logic. This class forms a new level in the non-linear hierarchy of protoalgebraic logics.

AlgebraPhilosophyClass (set theory)HierarchyLogicLeibniz operatorMonotonic functionT-norm fuzzy logicsMathematicsJournal of Symbolic Logic
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POSITIVE DEFINITE FUNCTIONS OF DIAGONAL LIMITS OF FINITE ALTERNATING GROUPS

2004

The normalized positive definite class functions are determined for all those direct limits of finite alternating groups for which the embeddings are natural in the sense that every non-trivial -orbit in is natural.

AlgebraPure mathematicsClass (set theory)General MathematicsDiagonalPositive-definite matrixOrbit (control theory)MathematicsJournal of the London Mathematical Society
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The polyhedral Hodge number $h^{2,1}$ and vanishing of obstructions

2000

We prove a vanishing theorem for the Hodge number $h^{2,1}$ of projective toric varieties provided by a certain class of polytopes. We explain how this Hodge number also gives information about the deformation theory of the toric Gorenstein singularity derived from the same polytope. In particular, the vanishing theorem for $h^{2,1}$ implies that these deformations are unobstructed.

AlgebraPure mathematicsClass (set theory)Mathematics::Algebraic GeometrySingularityMathematics::Commutative AlgebraGeneral MathematicsDeformation theoryPolytope52B2014M25Mathematics::Symplectic GeometryMathematicsTohoku Mathematical Journal
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Tensor product characterizations of mixed intersections of non quasianalytic classes and kernel theorems

2009

Mixed intersections of non quasi-analytic classes have been studied in [12]. Here we obtain tensor product representations of these spaces that lead to kernel theorems as well as to tensor product representations of intersections of non quasi-analytic classes on product of open or of compact sets (© 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

AlgebraPure mathematicsCompact spaceTensor productTensor product of algebrasKernel (set theory)General MathematicsTensor (intrinsic definition)Product (mathematics)Tensor product of Hilbert spacesTensor product of modulesMathematicsMathematische Nachrichten
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Formal Description of Rough Sets

1994

In the paper we present a formal description of rough sets within the limits of the generalized set theory, which is interpreted in the approximation of set theory. The rough sets are interpreted as an approximations, which are defined by means of the Pawlak’s rough sets.

AlgebraSimple objectRough setSet theoryFormal descriptionMathematics
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Algebraic Results on Quantum Automata

2004

We use tools from the algebraic theory of automata to investigate the class of languages recognized by two models of Quantum Finite Automata (QFA): Brodsky and Pippenger’s end-decisive model, and a new QFA model whose definition is motivated by implementations of quantum computers using nucleo-magnetic resonance (NMR). In particular, we are interested in the new model since nucleo-magnetic resonance was used to construct the most powerful physical quantum machine to date. We give a complete characterization of the languages recognized by the new model and by Boolean combinations of the Brodsky-Pippenger model. Our results show a striking similarity in the class of languages recognized by th…

AlgebraSurface (mathematics)Class (set theory)Pure mathematicsAlgebraic theoryQuantum machineQuantum finite automataAlgebraic numberComputer Science::Formal Languages and Automata TheoryQuantum computerMathematicsAutomaton
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Lawvere–Tierney sheaves in Algebraic Set Theory

2009

We present a solution to the problem of defining a counterpart in Algebraic Set Theory of the construction of internal sheaves in Topos Theory. Our approach is general in that we consider sheaves as determined by Lawvere-Tierney coverages, rather than by Grothendieck coverages, and assume only a weakening of the axioms for small maps originally introduced by Joyal and Moerdijk, thus subsuming the existing topos-theoretic results.

Algebraic setPure mathematicsLogicMathematics - Category TheoryMathematics - LogicTopos theoryPhilosophyMathematics::LogicMathematics::Algebraic GeometryMathematics::Category TheoryFOS: MathematicsCategory Theory (math.CT)Algebraic Set Theory sheavesLogic (math.LO)03C90 03G30 03F50AxiomMathematics
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Documenting carved stones from 3D models. Part II - Ambient occlusion to reveal carved parts.

2021

10 pages; International audience; Revealing carved parts in rock art is of primary importance and remains a major challenge for archaeological documentation. Computational geometry applied to 3D imaging provides a unique opportunity to document rock art. This study evaluates five algorithms and derivatives used to compute ambient occlusion and sky visibility on 3D models of Mongolian stelae, also known as deer stones. By contrast with the previous companion work, models are processed directly in 3D, without preliminary projection. Volumetric obscurance gives the best results for the identification of carved figures. The effects of model resolution and parameters specific to ambient occlusio…

Archeology[SHS.ARCHEO]Humanities and Social Sciences/Archaeology and PrehistoryComputer scienceMaterials Science (miscellaneous)ComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISION02 engineering and technologyConservationDocumentation01 natural sciencesSoftwareComputer graphics (images)Rock artVolumetric obscuranceProjection (set theory)Deer stoneSpectroscopyComputingMethodologies_COMPUTERGRAPHICSbusiness.industry010401 analytical chemistryVisibility (geometry)Mongolia021001 nanoscience & nanotechnologyComputational geometry0104 chemical sciencesIdentification (information)ArchaeologyChemistry (miscellaneous)Late bronze ageAmbient occlusionRock art0210 nano-technologyScale (map)businessGeneral Economics Econometrics and Finance
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Cardinal invariants of cellular Lindelof spaces

2018

A space X is said to be cellular-Lindelof if for every cellular family $$\mathcal {U}$$ there is a Lindelof subspace L of X which meets every element of $$\mathcal {U}$$ . Cellular-Lindelof spaces generalize both Lindelof spaces and spaces with the countable chain condition. Solving questions of Xuan and Song, we prove that every cellular-Lindelof monotonically normal space is Lindelof and that every cellular-Lindelof space with a regular $$G_\delta $$ -diagonal has cardinality at most $$2^\mathfrak {c}$$ . We also prove that every normal cellular-Lindelof first-countable space has cardinality at most continuum under $$2^{<\mathfrak {c}}=\mathfrak {c}$$ and that every normal cellular-Lindel…

Arhangel’skii TheoremMathematics::General MathematicsDiagonalMathematics::General TopologyRank (differential topology)Space (mathematics)01 natural sciencesCombinatoricsCountable chain conditionCardinalityCardinal inequalityLindelöf spaceFOS: MathematicsContinuum (set theory)0101 mathematicsMathematicsMathematics - General TopologyAlgebra and Number TheoryApplied Mathematics010102 general mathematicsGeneral Topology (math.GN)Nonlinear Sciences::Cellular Automata and Lattice Gases· Elementary submodel010101 applied mathematicsMonotonically normal spaceMathematics::LogicComputational MathematicsLindelöf spaceCountable chain conditionGeometry and TopologyAnalysis
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OmniFlowNet: a Perspective Neural Network Adaptation for Optical Flow Estimation in Omnidirectional Images

2021

International audience; Spherical cameras and the latest image processing techniques open up new horizons. In particular, methods based on Convolutional Neural Networks (CNNs) now give excellent results for optical flow estimation on perspective images. However, these approaches are highly dependent on their architectures and training datasets. This paper proposes to benefit from years of improvement in perspective images optical flow estimation and to apply it to omnidirectional ones without training on new datasets. Our network, OmniFlowNet, is built on a CNN specialized in perspective images. Its convolution operation is adapted to be consistent with the equirectangular projection. Teste…

Artificial neural networkComputer sciencebusiness.industryDistortion (optics)Perspective (graphical)[INFO.INFO-RB] Computer Science [cs]/Robotics [cs.RO]ComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISIONImage processing02 engineering and technology010501 environmental sciences01 natural sciencesConvolutional neural networkConvolutionOptical flow estimation0202 electrical engineering electronic engineering information engineering[INFO.INFO-RB]Computer Science [cs]/Robotics [cs.RO]020201 artificial intelligence & image processingComputer visionArtificial intelligencebusinessProjection (set theory)0105 earth and related environmental sciences
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