For a distribution F on R(p) and a point x in R(p) the simplicial depth D(x), which is the probability that x be inside a random simplex whose vertices are p + 1 independent observations from F, is introduced. D(x) can be viewed as a measure of depth of the point x relative to F, and its empirical version gives rise to a natural ordering of the data points from the center outward. This ordering...

In this paper we establish a characterization of abelian compact Hausdorff semigroups with unique idempotent and ideal retraction property. We also introduce a function algebra on a semitopological semigroup whose associated semigroup compactification is universal withrespect to these properties.

We verify the Upper Bound Conjecture (UBC) for a class of odddimensional simplicial complexes that in particular includes all Eulerian simplicial complexes with isolated singularities. The proof relies on a new invariant of simplicial complexes — a short simplicial h-vector.

Let VR be a real vector space with an irreducible action of a finite reflection group W . We study the semi-algebraic geometry of the W-quotient affine variety V//W with the discriminant divisor DW in it and the τ -quotient affine variety V//W//τ with the bifurcation set BW in it, where τ is the Ga-action on V//W obtained by the integration of the primitive vector field D on V//W and BW is the ...

This paper is a part of a larger project devoted to the study of Floer cohomology in algebro-geometic context, as a natural cohomology theory defined on a certain class of ind-schemes. Among these ind-schemes are algebro-geometric models of the spaces of free loops. Let X be a complex projective variety. Heuristically, HQ(X), the quantum cohomology of X, is a version of the Floer cohomology of ...

The rank of a commutative cancellative semigroup S is the cardinality of a maximal independent subset of S. Commutative cancellative semigroups of finite rank are subarchimedean and thus admit a Tamura-like representation. We characterize these semigroups in several ways and provide structure theorems in terms of a construction akin to the one devised by T. Tamura for N-semigroups.

We derive the actions for type II Green-Schwarz strings up to second order in the fermions, for general bosonic backgrounds. We base our work on the so-called normal coordinate expansion. The resulting actions are κ-symmetric and, for the case of surviving background supersymmetries, supersymmetric. We first obtain the type IIa superstring action from the 11D supermembrane by double dimensional...

let s be a locally compact topological foundation semigroup with identity and ma(s) be its semigroup algebra. in this paper, we give necessary and sufficient conditions to have abounded approximate identity in closed codimension one ideals of the semigroup algebra $m_a(s)$ of a locally compact topological foundationsemigroup with identity.

We describe the structure of 0-simple countably compact topological inverse semigroups and the structure of congruence-free countably compact topological inverse semigroups. We follow the terminology of [3, 4, 8]. In this paper all topological spaces are Hausdorff. If S is a semigroup then we denote the subset of idempotents of S by E(S). A topological space S that is algebraically a semigroup ...

Let NA be the monoid generated byA = {a1, . . . ,an} ⊆ Z.We introduce the homogeneous catenary degree of NA as the smallest N ∈ N with the following property: for each a ∈ NA and any two factorizations u,v of a, there exists factorizations u = w1, . . . ,wt = v of a such that, for every k, d(wk,wk+1) ≤ N, where d is the usual distance between factorizations, and the length of wk, |wk|, is less ...