Search results for "COMPUTATION"

showing 10 items of 7362 documents

Polish G-spaces and continuous logic

2017

Abstract We extend the generalised model theory of H. Becker from [2] to the case of Polish G -spaces when G is an arbitrary Polish group. Our approach is inspired by logic actions of Polish groups which arise in continuous logic.

AlgebraModel theoryContinuous logic010201 computation theory & mathematicsLogicGroup (mathematics)010102 general mathematicsPolish G-spaces0102 computer and information sciences0101 mathematics01 natural sciencesMathematicsAnnals of Pure and Applied Logic
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Ein Axiomensystem f�r partielle affine R�ume

1994

A partial linear space with parallelism is called partial affine space if it is embeddable in an affine space with the same pointset preserving the parallelism. These partial affine spaces will be characterized by a system of three axioms for partial linear spaces with parallelism.

AlgebraParallelism (rhetoric)Linear spaceAffine spaceGeometry and TopologyAffine transformationComputer Science::Computational GeometryAxiomMathematicsJournal of Geometry
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Unification in superintuitionistic predicate logics and its applications

2018

AbstractWe introduce unification in first-order logic. In propositional logic, unification was introduced by S. Ghilardi, see Ghilardi (1997, 1999, 2000). He successfully applied it in solving systematically the problem of admissibility of inference rules in intuitionistic and transitive modal propositional logics. Here we focus on superintuitionistic predicate logics and apply unification to some old and new problems: definability of disjunction and existential quantifier, disjunction and existential quantifier under implication, admissible rules, a basis for the passive rules, (almost) structural completeness, etc. For this aim we apply modified specific notions, introduced in proposition…

AlgebraPhilosophyTheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGESMathematics (miscellaneous)Unification010201 computation theory & mathematicsLogic010102 general mathematics0102 computer and information sciencesPredicate (mathematical logic)0101 mathematics01 natural sciencesMathematicsReview of Symbolic Logic
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Some Problems on Homomorphisms and Real Function Algebras

2001

In this paper we solve a problem about the representation of all homomorphisms on a real function algebra as point evaluations and another two about function algebras in which homomorphisms are point evaluations on sequences in the algebra.

AlgebraPure mathematicsTheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGESReal-valued functionGeneral MathematicsComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATIONRepresentation (systemics)Algebra representationHomomorphismPoint (geometry)Function (mathematics)Algebra over a fieldMathematicsMonatshefte f�r Mathematik
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A Non-antisymmetric Tensor Contraction Engine for the Automated Implementation of Spin-Adapted Coupled Cluster Approaches

2015

We present a symbolic manipulation algorithm for the efficient automated implementation of rigorously spin-free coupled cluster (CC) theories based on a unitary group parametrization. Due to the lack of antisymmetry of the unitary group generators under index permutations, all quantities involved in the equations are expressed in terms of non-antisymmetric tensors. Given two tensors, all possible contractions are first generated by applying Wick's theorem. Each term is then put down in the form of a non-antisymmetric Goldstone diagram by assigning its contraction topology. The subsequent simplification of the equations by summing up equivalent terms and their factorization by identifying co…

AlgebraTheoretical computer scienceCoupled clusterFactorizationAntisymmetric tensorUnitary groupAntisymmetryTensorPhysical and Theoretical ChemistrySymbolic computationNetwork topologyComputer Science ApplicationsMathematicsJournal of Chemical Theory and Computation
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Learning from good examples

1995

The usual information in inductive inference for the purposes of learning an unknown recursive function f is the set of all input /output examples (n,f(n)), n ∈ ℕ. In contrast to this approach we show that it is considerably more powerful to work with finite sets of “good” examples even when these good examples are required to be effectively computable. The influence of the underlying numberings, with respect to which the learning problem has to be solved, to the capabilities of inference from good examples is also investigated. It turns out that nonstandard numberings can be much more powerful than Godel numberings.

AlgebraTransduction (machine learning)Inductive transferComputational learning theoryInductive biasbusiness.industryAlgorithmic learning theoryUnsupervised learningMulti-task learningArtificial intelligenceInstance-based learningbusinessMathematics
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Comparison between the shifted-Laplacian preconditioning and the controllability methods for computational acoustics

2010

Processes that can be modelled with numerical calculations of acoustic pressure fields include medical and industrial ultrasound, echo sounding, and environmental noise. We present two methods for making these calculations based on Helmholtz equation. The first method is based directly on the complex-valued Helmholtz equation and an algebraic multigrid approximation of the discretized shifted-Laplacian operator; i.e. the damped Helmholtz operator as a preconditioner. The second approach returns to a transient wave equation, and finds the time-periodic solution using a controllability technique. We concentrate on acoustic problems, but our methods can be used for other types of Helmholtz pro…

Algebraic multigrid methodFinite element methodHelmholtz equationPreconditionerSpectral element methodApplied MathematicsSpectral element methodMathematical analysisExact controllabilityComputational acousticsFinite element methodControllabilitysymbols.namesakeComputational MathematicsMultigrid methodHelmholtz free energysymbolsHelmholtz equationPreconditionerLaplace operatorMathematicsJournal of Computational and Applied Mathematics
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An algebraic multigrid based shifted-Laplacian preconditioner for the Helmholtz equation

2007

A preconditioner defined by an algebraic multigrid cycle for a damped Helmholtz operator is proposed for the Helmholtz equation. This approach is well suited for acoustic scattering problems in complicated computational domains and with varying material properties. The spectral properties of the preconditioned systems and the convergence of the GMRES method are studied with linear, quadratic, and cubic finite element discretizations. Numerical experiments are performed with two-dimensional problems describing acoustic scattering in a cross-section of a car cabin and in a layered medium. Asymptotically the number of iterations grows linearly with respect to the frequency while for lower freq…

Algebraic multigrid methodPhysics and Astronomy (miscellaneous)Helmholtz equationGMRESMathematics::Numerical Analysissymbols.namesakeMultigrid methodQuadratic equationHelmholtz equationäärellisten elementtien menetelmäMathematicsNumerical AnalysisPreconditionerApplied MathematicspohjustinMathematical analysisAlgebrallinen multigrid-menetelmäHelmholzin yhtälöComputer Science::Numerical AnalysisGeneralized minimal residual methodFinite element methodComputer Science ApplicationselementtimenetelmäComputational MathematicsModeling and SimulationHelmholtz free energysymbolsPreconditionerLaplace operatorJournal of Computational Physics
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A damping preconditioner for time-harmonic wave equations in fluid and elastic material

2009

A physical damping is considered as a preconditioning technique for acoustic and elastic wave scattering. The earlier preconditioners for the Helmholtz equation are generalized for elastic materials and three-dimensional domains. An algebraic multigrid method is used in approximating the inverse of damped operators. Several numerical experiments demonstrate the behavior of the method in complicated two-dimensional and three-dimensional domains. peerReviewed

Algebraic multigrid methodPhysics and Astronomy (miscellaneous)Helmholtz equationGMRESNavier equationMathematics::Numerical AnalysisMultigrid methodHelmholtz equationäärellisten elementtien menetelmäMathematicsElastic scatteringNumerical AnalysisNavierin yhtälöPreconditionerApplied MathematicsMathematical analysispohjustinAcoustic waveWave equationAlgebrallinen multigrid-menetelmäHelmholzin yhtälöGeneralized minimal residual methodComputer Science::Numerical AnalysisFinite element methodComputer Science ApplicationselementtimenetelmäComputational MathematicsClassical mechanicsModeling and SimulationPreconditioner
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Electronic excitations of 1,4-disilyl-substituted 1,4-disilabicycloalkanes: a MS-CASPT2 study of the influence of cage size.

2007

We present a multistate complete active space second-order perturbation theory computational study aimed to predict the low-lying electronic excitations of four compounds that can be viewed as two disilane units connected through alkane bridges in a bicyclic cage. The analysis has focused on 1,4-disilyl-1,4-disilabicyclo[2.2.1]heptane (1a), 1,4-bis(trimethylsilyl)-1,4-disilabicyclo[2.2.1]heptane (1b), 1,4-disilyl-1,4-disilabicyclo[2.1.1]hexane (2a), and 1,4-bis(trimethylsilyl)-1,4-disilabicyclo[2.1.1]hexane (2b). The aim has been to find out the nature of the lowest excitations with significant oscillator strengths and to investigate how the cage size affects the excitation energies and the…

Alkanechemistry.chemical_classificationHeptaneBicyclic moleculeTrimethylsilylMolecular StructureElectronsHexanechemistry.chemical_compoundchemistryModels ChemicalComputational chemistryPhysical chemistryQuantum TheoryOrganosilicon CompoundsComplete active spaceDisilanePhysical and Theoretical ChemistryExcitationThe journal of physical chemistry. A
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