Active scalars and the Euler equations
Adaptive finite element analysis based on perturbation arguments
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...
Adaptive frame methods with cubic spline-wavelet bases
Algebraic characterization of the dimension of differential spaces
Algebraic classification of the Weyl tensor
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
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.
Algebraic generalization of the topological theorems of Bolzano and Weierstrass
Algebraic properties of function spaces
Algebraic properties of the 3-state vector Potts model
Algebras of germs of Fourier transforms
Algorithm for construction of explicit -order Runge-Kutta formulas for the systems of differential equations of the 1st order
Algorithmic computations of Lie algebras cohomologies
From the text: The aim of this work is to advertise an algorithmic treatment of the computation of the cohomologies of semisimple Lie algebras. The base is Kostant’s result which describes the representation of the proper reductive subalgebra on the cohomologies space. We show how to (algorithmically) compute the highest weights of irreducible components of this representation using the Dynkin diagrams. The software package offers the data structures and corresponding procedures for computing...
ALIO/EURO V conference on combinatorial optimization
ALIO/EURO V Conference on Combinatorial Optimization (ENST, Paris, 26–28 October 2005)
All natural concomitants of vector valued differential forms
Almost continuous functions with closed graphs
An adaptive -discontinuous Galerkin approach for nonlinear convection-diffusion problems
We deal with a numerical solution of nonlinear convection-diffusion equations with the aid of the discontinuous Galerkin method (DGM). We propose a new -adaptation technique, which is based on a combination of a residuum estimator and a regularity indicator. The residuum estimator as well as the regularity indicator are easily evaluated quantities without the necessity to solve any local problem and/or any reconstruction of the approximate solution. The performance of the proposed -DGM is demonstrated....
An application of principal bundles to coloring of graphs and hypergraphs
An interesting connection between the chromatic number of a graph and the connectivity of an associated simplicial complex , its “neighborhood complex”, was found by Lovász in 1978 (cf. L. Lovász [J. Comb. Theory, Ser. A 25, 319-324 (1978; Zbl 0418.05028)]). In 1986 a generalization to the chromatic number of a -uniform hypergraph , for an odd prime, using an associated simplicial complex , was found ([N. Alon, P. Frankl and L. Lovász, Trans. Am. Math. Soc. 298, 359-370 (1986; Zbl 0605.05033)],...
An application of quaternionic analysis to the solution of time-independent Maxwell equations and of Stokes’ equation
An application of the averaged gradient technique