We discuss regularization by noise of the spectrum of large random non-normal matrices. Under suitable conditions, we show that the regularization of a sequence of matrices that converges in ∗-moments to a regular element a by the addition of a polynomially vanishing Gaussian Ginibre matrix forces the empirical measure of eigenvalues to converge to the Brown measure of a.

Non-orthogonal spline wavelets are developed for Galerkin BEM. The proposed wavelets have compact supports and closed-form expressions. Besides of it, one can choose arbitrarily the order of vanishing moments of the wavelets independently of order of B-splines. Sparse coefficient matrices are obtained by truncating the small elements a priori. The memory requirement and computational time can b...

Let p be prime, K a field of characteristic 0. Let (x1, . . . , xn) ∈ Kn such that xi 6= 0 for all i and xi/xj is not a root of unity for all i 6= j. We prove that there exist integers 0 < e1 < e2 < · · · < en such that det (x ei j ) 6= 0. The proof uses p-adic arguments. As corollaries, we derive the linear independence of certain Witt vectors and study the result of applying the Witt functor ...

Let V be a q-dimensional vector space. Fix a set B of q(q − 1) monomials in S(V ) of the form x where ik > 0 for all k. The generic element of S(V ) is conjugate under a suitable linear transformation to an element with support off of B. We prove this by showing the existence of a perfect matching with a unique weight in a certain weighted bipartite graph. Such a perfect matching corresponds to...

It is a well known fact that a supersolvable lattice is ELoshellable. Hence a supersolvable lattice (resp., its Stanley-Reisner ring) is Cohen-Macaulay. We prove that if L is a supersolvable lattice such that all intervals have non-vanishing Mt~bius number, then for an arbitrary element x e L the poser L {x} is also Cohen-Macaulay. Posets with this property are called 2-Cohen-Macaulay posets. I...