Search results for "Names"

showing 10 items of 6843 documents

Conjunction and Disjunction Among Conditional Events

2017

We generalize, in the setting of coherence, the notions of conjunction and disjunction of two conditional events to the case of n conditional events. Given a prevision assessment on the conjunction of two conditional events, we study the set of coherent extensions for the probabilities of the two conditional events. Then, we introduce by a progressive procedure the notions of conjunction and disjunction for n conditional events. Moreover, by defining the negation of conjunction and of disjunction, we show that De Morgan’s Laws still hold. We also show that the associative and commutative properties are satisfied. Finally, we examine in detail the conjunction for a family \(\mathcal F\) of t…

Discrete mathematicsSettore MAT/06 - Probabilita' E Statistica MatematicaComputer scienceConditional events · Conditional random quantities · Con- junction · Disjunction · Negation · Quasi conjunction · Coherent previ- sion assessments · Coherent extensions · De Morgan’s Laws02 engineering and technologyCoherence (philosophical gambling strategy)Settore MAT/01 - Logica Matematica01 natural sciencesDe Morgan's lawsConjunction (grammar)Set (abstract data type)010104 statistics & probabilitysymbols.namesakeNegation0202 electrical engineering electronic engineering information engineeringsymbols020201 artificial intelligence & image processing0101 mathematicsAlgorithmCommutative propertyAssociative propertyEvent (probability theory)
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Estimates of Jacobians by subdeterminants

2002

Let ƒ: Ω → ℝn be a mapping in the Sobolev space W1,n−1(Ω,ℝn), n ≥ 2. We assume that the determinant of the differential matrix Dƒ (x) is nonnegative, while the cofactor matrix D#ƒ satisfies\(|D^\sharp f|^{\frac{n}{{n - 1}}} \in L^P (\Omega )\), where Lp(Ω) is an Orlicz space. We show that, under the natural Divergence Condition on P, see (1.10), the Jacobian lies in Lloc1 (Ω). Estimates above and below Lloc1 (Ω) are also studied. These results are stronger than the previously known estimates, having assumed integrability conditions on the differential matrix.

Discrete mathematicsSpace (mathematics)OmegaDivergenceCombinatoricsSobolev spacesymbols.namesakeMatrix (mathematics)Differential geometryJacobian matrix and determinantsymbolsGeometry and TopologyDifferential (mathematics)Mathematics
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Classes of operators satisfying a-Weyl's theorem

2005

In this article Weyl's theorem and a-Weyl's theorem on Banach spaces are related to an important property which has a leading role in local spectral theory: the single-valued extension theory. We show that if T has SVEP then Weyl's theorem and a-Weyl's theorem for T are equivalent, and analogously, if T has SVEP then Weyl's theorem and a-Weyl's theorem for T are equivalent. From this result we deduce that a-Weyl's theorem holds for classes of operators for which the quasi-nilpotent part H0(I T ) is equal to ker (I T ) p for some p2N and every 2C, and for algebraically paranormal operators on Hilbert spaces. We also improve recent results established by Curto and Han, Han and Lee, and Oudghi…

Discrete mathematicsSpectral theoryGeneral MathematicsHilbert spaceBanach spacePropertySpectral theoremFredholm theorysymbols.namesakeKernel (algebra)Bounded functionsymbolsOperatorBounded inverse theoremtheorem holdsMathematics
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The cup product of Hilbert schemes for K3 surfaces

2003

To any graded Frobenius algebra A we associate a sequence of graded Frobenius algebras A [n] so that there is canonical isomorphism of rings (H *(X;ℚ)[2]) [n] ≅H *(X [n] ;ℚ)[2n] for the Hilbert scheme X [n] of generalised n-tuples of any smooth projective surface X with numerically trivial canonical bundle.

Discrete mathematicsSurface (mathematics)Hilbert series and Hilbert polynomialSequencePure mathematicsMathematics::Commutative AlgebraGeneral Mathematics010102 general mathematics01 natural sciencesCanonical bundlesymbols.namesakeHilbert schemeCup product0103 physical sciencesFrobenius algebrasymbols[MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG]010307 mathematical physicsIsomorphism0101 mathematicsComputingMilieux_MISCELLANEOUSMathematicsInventiones Mathematicae
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A Survey of Continuous-Time Computation Theory

1997

Motivated partly by the resurgence of neural computation research, and partly by advances in device technology, there has been a recent increase of interest in analog, continuous-time computation. However, while special-case algorithms and devices are being developed, relatively little work exists on the general theory of continuous- time models of computation. In this paper, we survey the existing models and results in this area, and point to some of the open research questions. Final Draft peerReviewed

Discrete mathematicsTheoretical computer scienceComputabilityComputationModel of computationneuraalilaskentaTuring machineTuring machinesymbols.namesakeModels of neural computationComputable functionOpen researchTheory of computationsymbolsHopfield networkcellular automatondifferential analyzerMathematics
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Probabilities to Accept Languages by Quantum Finite Automata

1999

We construct a hierarchy of regular languages such that the current language in the hierarchy can be accepted by 1-way quantum finite automata with a probability smaller than the corresponding probability for the preceding language in the hierarchy. These probabilities converge to 1/2.

Discrete mathematicsTheoretical computer scienceNested wordFinite-state machineHierarchy (mathematics)Computer scienceComputer Science::Computation and Language (Computational Linguistics and Natural Language and Speech Processing)Turing machinesymbols.namesakeNonlinear Sciences::Exactly Solvable and Integrable SystemsRegular languageProbabilistic automatonAnalytical hierarchysymbolsComputer Science::Programming LanguagesQuantum finite automataQuantum algorithmNondeterministic finite automaton
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Minimal nontrivial space complexity of probabilistic one- way turing machines

2005

Languages recognizable in o(log log n) space by probabilistic one — way Turing machines are proved to be regular. This solves an open problem in [4].

Discrete mathematicsTheoryofComputation_COMPUTATIONBYABSTRACTDEVICESSuper-recursive algorithmProbabilistic Turing machineLinear speedup theoremNSPACEDescription numberCombinatoricsTuring machinesymbols.namesakeTheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGESNon-deterministic Turing machinesymbolsTime hierarchy theoremComputer Science::Formal Languages and Automata TheoryMathematics
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Uncountable classical and quantum complexity classes

2018

It is known that poly-time constant-space quantum Turing machines (QTMs) and logarithmic-space probabilistic Turing machines (PTMs) recognize uncountably many languages with bounded error (A.C. Cem Say and A. Yakaryılmaz, Magic coins are useful for small-space quantum machines. Quant. Inf. Comput. 17 (2017) 1027–1043). In this paper, we investigate more restricted cases for both models to recognize uncountably many languages with bounded error. We show that double logarithmic space is enough for PTMs on unary languages in sweeping reading mode or logarithmic space for one-way head. On unary languages, for quantum models, we obtain middle logarithmic space for counter machines. For binary la…

Discrete mathematicsUnary operationComputer scienceGeneral MathematicsLinear spaceMagic (programming)Binary number0102 computer and information sciences02 engineering and technology01 natural sciencesComputer Science ApplicationsTuring machinesymbols.namesake010201 computation theory & mathematics0202 electrical engineering electronic engineering information engineeringComplexity classsymbols020201 artificial intelligence & image processingUncountable setTime complexitySoftwareRAIRO - Theoretical Informatics and Applications
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Ergodic properties of operators in some semi-Hilbertian spaces

2012

This article deals with linear operators T on a complex Hilbert space ℋ, which are bounded with respect to the seminorm induced by a positive operator A on ℋ. The A-adjoint and A 1/2-adjoint of T are considered to obtain some ergodic conditions for T with respect to A. These operators are also employed to investigate the class of orthogonally mean ergodic operators as well as that of A-power bounded operators. Some classes of orthogonally mean ergodic or A-ergodic operators, which come from the theory of generalized Toeplitz operators are considered. In particular, we give an example of an A-ergodic operator (with an injective A) which is not Cesaro ergodic, such that T  * is not a quasiaff…

Discrete mathematicsUnbounded operatorMathematics::Dynamical SystemsAlgebra and Number TheoryNuclear operatorHilbert spaceFinite-rank operatorOperator theoryCompact operator on Hilbert spaceQuasinormal operatorsymbols.namesakesymbolsOperator normMathematicsLinear and Multilinear Algebra
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An optimal extension of Marstrand?s plane-packing theorem

2003

We prove that if F is a subset of the 2-dimensional unit sphere in $\mathbb{R}^3$, with Hausdorff dimension strictly greater than 1, and E is a subset of $\mathbb{R}^3$ such that for each $e \in F$, E contains a plane perpendicular to the vector e, then E must have positive 3-dimensional Lebesgue measure.

Discrete mathematicsUnit spheresymbols.namesakePacking dimensionLebesgue measureGeneral MathematicsHausdorff dimensionsymbolsDimension functionHausdorff measureLebesgue covering dimensionEffective dimensionMathematicsArchiv der Mathematik
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