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Affine Weyl groups and Langlands duality
No full textLet G be a compact connected semisimple Lie group. We show that, as well as the duality between K-theory and K-homology,
there is also a Langlands duality in the Baum-Connes correspondence for the (extended) affine Weyl group attached to G
Morita equivalence classes of 2-blocks of defect three
No full textWe give a complete description of the Morita equivalence classes of blocks with elementary abelian defect groups of order and of the derived equivalences between them. A consequence is the verification of Brou\'e's abelian defect group conjecture for these blocks. It also completes the classification of Morita and derived equivalence classes of -blocks of defect at most three defined over a suitable field
Statistical cluster analysis and visualisation for alarm management configuration
Get PDFThe effective performance of an alarm system is a key aspect of asset management for any industrial installation. However, it is not uncommon for alarm systems to be poorly configured, leading to large amounts of alarm noise and a potentially dangerous load on the operators. Here we present a novel method for the identification of redundant or bad actors in alarm systems through the application of statistical cluster analysis. This allows the system to be optimised to reduce the load on the operators through existing systems change management processes
Three-Dimensional Transient Electromagnetic Modeling Using Rational Krylov Methods
Get PDFA computational method is given for solving the forward modeling problem for transient electromagnetic exploration. Its key features are discretization of the quasi-static Maxwell's equations in space using the first-kind family of curl-conforming Nedelec elements combined with time integration using rational Krylov subspace methods. We show how rational Krylov subspace methods may be used to solve the same problem in the frequency domain followed by a synthesis of the transient solution using the fast Hankel transform, arguing that the pure time-domain is more efficient. We also propose a simple method for selecting the pole parameters of the rational Krylov subspace method which leads to convergence within an a priori determined number of iterations independent of mesh size and conductivity structure. These poles are repeated in a cyclic fashion, which, in combination with direct solvers for the discrete problem, results in significantly faster solution times than previously proposed schemes
Block Preconditioners for Linear Systems Arising from Multiscale Collocation with Compactly Supported RBFs
Get PDFSymmetric multiscale collocation methods with radial basis functions allow approximation of the solution of a partial differential equation, even if the right-hand side is only known at scattered data points, without needing to generate a grid. However, the benefit of a guaranteed symmetric positive definite block system comes at a high computational cost. In particular, the condition number and sparsity deteriorate with the number of data points. Therefore, we study certain block diagonal and triangular preconditioners. We investigate ideal preconditioners and determine the spectra of the preconditioned matrices before proposing more practical preconditioners based on a restricted additive Schwarz method with coarse grid correction (ARASM). Numerical results verify the effectiveness of the preconditioners
A Rational Krylov Toolbox for MATLAB
Get PDFThe Rational Krylov Toolbox contains MATLAB implementations of Ruhe's rational Krylov sequence method (and its block variants), algorithms for the implicit and explicit relocation of the poles of a rational Krylov space, an implementation of RKFIT, a robust algorithm for rational least squares fitting, and the RKFUN/RKFUNM/RKFUNB classes for numerical computations with rational functions
Second Order Inductive Logic and Wilmers' Principle
Get PDFWe extend the framework of Inductive Logic to Second Order languages and introduce Wilmers' Principle, a rational principle for probability functions on Second Order languages. We derive a representation theorem for functions satisfying this principle and investigate its relationship to the first order principles of Regularity and Super Regularity
Unsolved problems in group theory. The Kourovka notebook. No. 18
No full textThis is a collection of open problems in Group Theory proposed by more than 300 mathematicians from all over the world. It has been published every 2-4 years in Novosibirsk since 1965, now also in English. This is the 18th edition, which contains 120 new problems and a number of comments on about 1000 problems from the previous editions
Strongly damped quadratic matrix polynomials
No full textWe study the eigenvalues and eigenspaces of the quadratic matrix polynomial \allowbreak as , where and are symmetric positive definite and is symmetric positive semi-definite. The work is motivated by its application to modal analysis of finite element models with strong linear damping. Our results yield a mathematical explanation of why too strong damping may lead to practically undamped
modes such that all nodes in the model vibrate essentially in phase
Tail behavior of the generalized Maxwell distribution
No full textIn this paper, we investigate the tail properties of the generalized Maxwell distribution and gain an asymptotic
behavior of Mills-type ratio. Meanwhile, We show two applications. The first application thinks about the asymptotic property of the ratio of density functions and the ratio of the tails of the generalized Maxwell and classical Maxwell distributions. Another application obtains the asymptotic distribution of the partial maximum of an independent and identically distributed sequence from
the distribution