Search results for "Linear"

showing 10 items of 7165 documents

Implications of quantum automata for contextuality

2014

We construct zero error quantum finite automata (QFAs) for promise problems which cannot be solved by bounded error probabilistic finite automata (PFAs). Here is a summary of our results: There is a promise problem solvable by an exact two way QFA in exponential expected time but not by any bounded error sublogarithmic space probabilistic Turing machine (PTM). There is a promise problem solvable by an exact two way QFA in quadratic expected time but not by any bounded error o(loglogn) space PTMs in polynomial expected time. The same problem can be solvable by a one way Las Vegas (or exact two way) QFA with quantum head in linear (expected) time. There is a promise problem solvable by a Las …

Discrete mathematicsProbabilistic finite automataTheoryofComputation_COMPUTATIONBYABSTRACTDEVICESQuantum automata0102 computer and information sciencesConstruct (python library)Nonlinear Sciences::Cellular Automata and Lattice Gases01 natural sciencesKochen–Specker theoremTheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES010201 computation theory & mathematics0103 physical sciencesQuantum finite automataPromise problem010306 general physicsComputer Science::Formal Languages and Automata TheoryMathematics
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Property (R) for Bounded Linear Operators

2011

We introduce the spectral property (R), for bounded linear operators defined on a Banach space, which is related to Weyl type theorems. This property is also studied in the framework of polaroid, or left polaroid, operators.

Discrete mathematicsProperty (philosophy)Settore MAT/05 - Analisi MatematicaApproximation propertyGeneral MathematicsBounded functionLinear operatorsBanach spaceProperty (R) polaroid operatorsOperator theoryType (model theory)Operator normMathematicsMediterranean Journal of Mathematics
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On linear extension operators from growths of compactifications of products

1996

Abstract We obtain some results on product spaces. Among them we prove that for noncompact spaces X 1 and X 2 , the norm of every linear extension operator from C ( β ( X 1 × X 2 ) β ( X 1 × X 2 )) into C ( β ( X 1 × X 2 )) is greater or equal than 2, and also that β ( X 1 × X 2 ) β ( X 1 × X 2 ) is not a neighborhood retract of β ( X 1 × X 2 ).

Discrete mathematicsPseudocompact spacePseudocompact spaceCrystallographyOperator (computer programming)Linear extensionProduct (mathematics)RetractStone-Čech compactificationStone–Čech compactificationLinear extension operatorProduct topologyGeometry and TopologyProduct spaceMathematicsTopology and its Applications
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Indecomposable modules over the Virasoro Lie algebra and a conjecture of V. Kac

1991

We consider a class of indecomposable modules over the Virasoro Lie algebra that we call bounded admissible modules. We get results concerning the center and the dimensions of the weight spaces. We prove that these modules always contain a submodule with one-dimensional weight spaces. From this follows the proof of a conjecture of V. Kac concerning the classification of simple admissible modules.

Discrete mathematicsPure mathematics17B10Statistical and Nonlinear PhysicsUniversal enveloping algebraLie superalgebraAffine Lie algebra17B68Lie conformal algebraGraded Lie algebraAlgebra representationVirasoro algebraMathematics::Representation TheoryIndecomposable moduleMathematical PhysicsMathematicsCommunications in Mathematical Physics
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Fixed-Point Theorems in Complete Gauge Spaces and Applications to Second-Order Nonlinear Initial-Value Problems

2013

We establish fixed-point results for mappings and cyclic mappings satisfying a generalized contractive condition in a complete gauge space. Our theorems generalize and extend some fixed-point results in the literature. We apply our obtained results to the study of existence and uniqueness of solution to a second-order nonlinear initial-value problem.

Discrete mathematicsPure mathematicsArticle Subjectlcsh:MathematicsFixed-point theoremGauge (firearms)Space (mathematics)lcsh:QA1-939Nonlinear systemSettore MAT/05 - Analisi MatematicaInitial value problemOrder (group theory)UniquenessCoincidence pointfixed point gauge spaces initial-value problemAnalysisMathematics
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From quantale algebroids to topological spaces: Fixed- and variable-basis approaches

2010

Using the category of quantale algebroids the paper considers a generalization of the classical Papert-Papert-Isbell adjunction between the categories of topological spaces and locales to partial algebraic structures. It also provides a single framework in which to treat the concepts of quasi, standard and stratified fuzzy topology.

Discrete mathematicsPure mathematicsBasis (linear algebra)LogicAlgebraic structureGeneralizationQuantaleTopological spaceAdjunctionArtificial IntelligenceMathematics::Category TheoryCategory of topological spacesQuantaloidMathematicsFuzzy Sets and Systems
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On certain linear operators in spaces of ultradifferentiable functions

1996

Let ω be a weight in the sense of Braun, Meise, Taylor, which defines a non-quasianalytic class. Let H be a compact subset of ℝn. It is proved that for every function ƒ on ℝn which belongs to the non-quasianalytic (ω)-class, there is an element g of the same class which is analytic on ℝn\H and such that Dαƒ(x) = Dαg(x) for every x ∈ H and α ∈ ℕ0n. A similar result is proved for functions of the Roumieu type. Continuous linear extension operators of Whitney jets with additional properties are also obtained.

Discrete mathematicsPure mathematicsClass (set theory)Mathematics (miscellaneous)Applied MathematicsLinear operatorsFunction (mathematics)Continuous linear extensionElement (category theory)Type (model theory)MathematicsResults in Mathematics
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Linear invariants of Riemannian almost product manifolds

1982

Using the decomposition of a certain vector space under the action of the structure group of Riemannian almost product manifolds, A. M. Naveira (9) has found thirty-six distinguished classes of these manifolds. In this article, we prove that this decomposition is irreducible by computing a basis of the space of invariant quadratic forms on such a space.

Discrete mathematicsPure mathematicsCurvature of Riemannian manifoldsGeneral MathematicsLinear invariantsFundamental theorem of Riemannian geometryRiemannian geometryManifoldsymbols.namesakeRicci-flat manifoldProduct (mathematics)symbolsDifferential topologyMathematics::Differential GeometryMathematicsMathematical Proceedings of the Cambridge Philosophical Society
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On sets of subspaces closed under reguli

1992

Using a representation of chain geometries where points are certain subspaces of a projective space and chains are reguli, we give an algebraic description of the weak subspaces of the chain geometry (i.e. the subsets of the pointset which are closed with respect to reguli).

Discrete mathematicsPure mathematicsDifferential geometryChain (algebraic topology)Hyperbolic geometryProjective spaceGeometry and TopologyAlgebraic geometryAlgebraic numberLinear subspaceMathematicsProjective geometryGeometriae Dedicata
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Automatic continuity of generalized local linear operators

1980

In this note, we present a general automatic continuity theory for linear mappings between certain topological vector spaces. The theory applies, in particular, to local operators between spaces of functions and distributions, to algebraic homomorphisms between certain topological algebras, and to linear mappings intertwining generalized scalar operators.

Discrete mathematicsPure mathematicsGeneral MathematicsLocally convex topological vector spaceTopological tensor productDiscontinuous linear mapSpectral theoremOperator theoryTopological spaceTopological vector spaceContinuous linear operatorMathematicsManuscripta Mathematica
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