We study the relation between zero loci of Bernstein-Sato ideals and roots b-functions obtain a criterion to guarantee that reducible polynomial are determined by locus associated ideal. Applying together with result Maisonobe we prove set b-function free hyperplane arrangement is its intersection lattice. also relative characteristic cycles for arbitrary central arrangements. multivariable n/d...

A topological hyperplane is a subspace of R (or a homeomorph of it) that is topologically equivalent to an ordinary straight hyperplane. An arrangement of topological hyperplanes in R is a finite set H such that for any nonvoid intersection Y of topological hyperplanes in H and any H ∈ H that intersects but does not contain Y , the intersection is a topological hyperplane in Y . (We also assume...

Let μ1, . . . , μn be continuous probability measures on Rn and α1, . . . , αn ∈ [0, 1]. When does there exist an oriented hyperplane H such that the positive half-space H+ has μi(H) = αi for all i ∈ [n]? It is well known that such a hyperplane does not exist in general. The famous ham sandwich theorem states that if αi = 2 for all i, then such a hyperplane always exists. In this paper we give ...

Due to the importance that verbs have in language an identification of their actants (obligatory complements) is important for understanding of the meaning of sentences. Usually, the solution of this problem in natural language processing is based on machine learning approaches, which are trained on large sets of tagged texts. We show that it is possible to work with other kind of sources, i.e....