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About duality and Killing tensors

Baleanu, Dumitru (2000)

Proceedings of the 19th Winter School "Geometry and Physics"

Summary: In this paper the isometries of the dual space were investigated. The dual structural equations of a Killing tensor of order two were found. The general results are applied to the case of the flat space.

Absolute Borel sets

Stone, A. H. (1971)

General Topology and Its Relations to Modern Analysis and Algebra

Adaptive finite element analysis based on perturbation arguments

Dai, Xiaoying, He, Lianhua, Zhou, Aihui (2012)

Applications of Mathematics 2012

We review some numerical analysis of an adaptive finite element method (AFEM) for a class of elliptic partial differential equations based on a perturbation argument. This argument makes use of the relationship between the general problem and a model problem, whose adaptive finite element analysis is existing, from which we get the convergence and the complexity of adaptive finite element methods for a nonsymmetric boundary value problem, an eigenvalue problem, a nonlinear boundary value problem...

Algebraic classification of the Weyl tensor

Pravdová, Alena (2012)

Applications of Mathematics 2012

Alignment classification of tensors on Lorentzian manifolds of arbitrary dimension is summarized. This classification scheme is then applied to the case of the Weyl tensor and it is shown that in four dimensions it is equivalent to the well known Petrov classification. The approaches using Bel-Debever criteria and principal null directions of the superenergy tensor are also discussed.

Algebraic classification of the Weyl tensor: selected applications

Pravda, Vojtěch (2012)

Applications of Mathematics 2012

Selected applications of the algebraic classification of tensors on Lorentzian manifolds of arbitrary dimension are discussed. We clarify some aspects of the relationship between invariants of tensors and their algebraic class, discuss generalization of Newman-Penrose and Geroch-Held-Penrose formalisms to arbitrary dimension and study an application of the algebraic classification to the case of quadratic gravity.

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