The accurate evaluation of nearly singular boundary integrals is an important issue in BEM. Several techniques have been developed in recent years, with various degree of success, but it should be stressed that the boundary geometry is depicted essentially by using lower-order elements in those approaches. However, a high level of the geometry approximation in BEM is desired in many application...

In this work we present a formal generalization of the Hamilton-Jacobi formalism, recently developed for singular systems, to include the case of Lagrangians containing variables which are elements of Berezin algebra. We derive the HamiltonJacobi equation for such systems, analizing the singular case in order to obtain the equations of motion as total differential equations and study the integr...

• First, the lower bidiagonal matrix A11 with nonzero bidiagonal elements has full column rank and its singular values are simple. Consequently, any zero singular values or repeats that A has must appear in A22. • Second, A11 has minimal dimensions, and A22 has maximal dimensions, over all orthogonal transformations giving the block structure in (2), without any additional assumptions on the st...

We obtain a presentation for the singular part of the Brauer monoid with respect to an irreducible system of generators, consisting of idempotents. As an application of this result we get a new construction of the symmetric group via connected sequences of subsets. Another application describes the lengths of elements in the singular part of the Brauer monoid with respect to the system of gener...

Consider the space Hom(Z n , G) of pairwise commuting n-tuples of elements in a compact Lie group G. This forms a real algebraic variety, which is generally singular. In this paper, we construct a desingulariza-tion of the generic component of Hom(Z n , G), which allows us to derive formulas for its singular and equivariant cohomology in terms of the Lie algebra of a maximal torus in G and the ...

‎this paper presents two main results that the singular values of the hadamard product of normal matrices $a_i$ are weakly log-majorized by the singular values of the hadamard product of $|a_{i}|$ and the singular values of the sum of normal matrices $a_i$ are weakly log-majorized by the singular values of the sum of $|a_{i}|$‎. ‎some applications to these inequalities are also given‎. ‎in addi...