We discuss the (conjugated) Bubnov–Galerkin and Petrov–Galerkin infinite element (IE) discretizations to Helmholtz equation including the use of elements of locally variable order, optimal choice of IE shape functions, calculation of Echo Area (EA), and automatic hp-adaptivity. The discussion is illustrated with 2D numerical experiments. 2005 Elsevier B.V. All rights reserved. MSC classificatio...

Projecting a non-Abelian SU(2) vacuum gauge field – a pure gauge constructed from the group element U – onto a fixed (electromagnetic) direction in isospace gives rise to a nontrivial magnetic field, with nonvanishing magnetic helicity, which coincides with the winding number of U . Although the helicity is not conserved under Maxwell (vacuum) evolution, it retains one-half its initial value at...

We propose several algorithms to obtain bounds based on Censored Markov Chains to analyze partially generated discrete time Markov chains. The main idea is to avoid the generation of a huge (or even infinite) state space and to truncate the state space during the visit. The approach is purely algebraic and provides element-wise and stochastic bounds for the CMC.

B → πlν decay is studied in the effective theory of heavy quark with infinite mass limit. The leading order heavy flavor-spin independent universal wave functions which parameterize the relevant matrix elements are evaluated via light cone sum rule method in the effective theory. The important quark mixing matrix element |V ub | is then extracted via B → πlν decay mode.

Let p be a prime greater than three. In the p–local stable homotopy groups of spheres, R L Cohen constructed the infinite –element n 1 2 2pnC1 2pnC2p 5.S/ of order p . In the stable homotopy group 2pnC1 2pnC2p2 3.V .1// of the Smith– Toda spectrum V .1/ , X Liu constructed an essential element $k for k 3 . Let ˇ s D j0j1ˇ s 2 ŒV .1/;S 2sp2 2s 2p denote the Spanier–Whitehead dual of the generat...

We study representations of the simple Lie antialgebra asl 2 introduced in [4]. We show that representations of asl 2 are closely related to the famous ghost Casimir element of the universal enveloping algebra osp(1|2). We prove that asl 2 has no non-trivial finite-dimensional representations; we define and classify some particular infinite-dimensional representations that we call weighted repr...

In this paper, we prove the following result: Let A be an infinite set of positive integers. For all positive integer n, let τn denote the smallest element of A which doesn’t divide n. Then we have lim N→+∞ 1 N N ∑

We explore representing the compact subsets of a given represented space by infinite sequences over Plotkin's T. We show that compact Hausdorff spaces with a proper dyadic subbase admit representations of their compact subsets in such a way that compact sets are essentially underspecified points. We can even ensure that a name of an n-element compact set contains at most n occurrences of ⊥.

In a finite graph, an edge set Z is an element of the cycle space if and only if every vertex has even degree in Z. We extend this basic result to the topological cycle space, which allows infinite circuits, of locally finite graphs. In order to do so, it becomes necessary to attribute a parity to the ends of the graph.

A homogeneous family of subsets over a given set is one with a very “rich” automorphism group. We prove the existence of a bi-universal element in the class of homogeneous families over a given infinite set and give an explicit construction of 2 א0 isomorphism types of homogeneous families over a countable set.