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 ...

There was an elegant expression for the volume of hypercube [0, 1] clipped by a hyperplane. We generalize the formula to the case of more than one hyperplane. Furthermore we derive several combinatorial identities from the volume expressions of clipped hypercubes.