This paper discusses the problem of whether it is possible to annihilate elements of local cohomology modules by elements of arbitrarily small order under a fixed valuation. We first discuss the general problem and its relationship to the Direct Summand Conjecture, and next present two concrete examples where annihilators with small order are shown to exist. We then prove a more general theorem...

We establish many previously unknown properties of zero-divisors in Cayley-Dickson algebras. The basic approach is to use a certain splitting that simplifies computations surprisingly.

Seismic data are commonly modeled by a linearization around a smooth background medium in combination with a high frequency approximation. The perturbation of the medium coefficient is assumed to contain the discontinuities. This leads to two inverse problems, first the linearized inverse problem for the perturbation, and second the estimation of the background, which is a priori unknown (veloc...

We present several examples where moments of creators and annihilators on an interacting Fock space may be realized as moments of creators and annihilators on a full Fock module. Motivated by this experience we answer the question, whether such a possibility exists for arbitrary interacting Fock spaces, in the affirmative sense. We treat the problem in full algebraic generality. As a by-product...

In Part I of this thesis, we locate a (conjecturally complete) set of unitary representations in the admissible dual of U(p, q). In a little more detail, Barbasch and Vogan have used the theory of Kazhdan-Lusztig cells to parametrize the irreducible Harish-Chandra modules with integral infinitesimal character in terms of their annihilators and associated varieties. Vogan has conjectured that th...

In this paper, we introduce the notion of co-annihilator of a subsetin a triangle algebra. It is shown that the co-annihilator of asubset is an interval valued residuated lattice (IVRL)-filter. Also, aspecial set of a triangle algebra is defined and the relationshipbetween this set and co-annihilator of a subset in triangle algebrais considered. Finally, co-annihilators preserving congruencerel...

We consider finite sequences s ∈ D n where D is a commutative, unital, integral domain. We prove three sets of identities (possibly with repetitions), each involving 2n polynomials associated to s. The right-hand side of these identities is a recursively-defined (non-zero) 'product-of-discrepancies'. There are implied iterative algorithms (of quadratic complexity) for the left-hand side coeffic...