Let S be a set of n intervals in R, and let (S,+) be any commutative semigroup. We assign a weight ω(s) ∈ S to each interval in S. For a point x ∈ R, let S(x) ⊆ S be the set of intervals that contain x. Given a point q ∈ R, the stabbing-semigroup query asks for computing

The Graham-Rothschild Parameter Sets Theorem is one of the most powerful results of Ramsey Theory. (The Hales-Jewett Theorem is its most trivial instance.) Using the algebra of βS, the Stone-Čech compactification of a discrete semigroup, we derive an infinitary extension of the GrahamRothschild Parameter Sets Theorem. Even the simplest finite instance of this extension is a significant extensio...

in the present paper, we consider biflatness of certain classes of semigroupalgebras. indeed, we give a necessary condition for a band semigroup algebra to bebiflat and show that this condition is not sufficient. also, for a certain class of inversesemigroups s, we show that the biflatness of ell^{1}(s)^{primeprime} is equivalent to the biprojectivity of ell^{1}(s).

The main objects of this paper are the graded automorphisms of w x polytopal semigroup rings, i.e., semigroup rings k S where k is a field P Ž and S is the semigroup associated with a lattice polytope P Bruns, P w x. w x Gubeladze, and Trung BGT . The generators of k S correspond bijecP tively to the lattice points in P, and their relations are the binomials representing the affine dependencies...

An invariant Q of a tree T under a k-state Markov model, where a generalized time parameter is identified with the E edges of T, allows us to recognize whether data on N observed species (usually, N DNA sequences, one from each species) can be associated with the N leaves of T in the sense of having been generated on T rather than on any other N-leaf tree. The form of the generalized time param...

This paper is concerned with the initial value problem for a strictly hyperbolic n n system of conservation laws in one space dimension: u t + F(u) x = 0; u(0; x) = u(x): () Each characteristic eld is assumed to be either linearly degenerate or genuinely nonlinear. We prove that there exists a domain D L 1 , containing all functions with suuciently small total variation, and a uniformly Lipschi...

The main purpose of this paper is to establish a relation between universality of certain P-compactifications of a semitopological semigroup and their corresponding enveloping semigroups. In particular, we show that if we take P to be the property that the enveloping semigroup of a compactification of a semitopological semigroup s is left simple, a group, or the trivial singleton semigroup, t...

We analyze cohomological properties of the Krichever map and use the results to study Weierstrass cycles in moduli spaces and the tautological ring. Let us consider a point p on a smooth projective connected curve C over C of genus g. We say that a natural number n is a non-gap if there exists a function that is holomorphic on C \p and has a pole of order n at the point p (in other words h0(O(n...

There is a well-known combinatorial definition, based on ordered set partitions, of the semigroup of faces of the braid arrangement. We generalize this definition to obtain a semigroup ΣGn associated with G ≀ Sn, the wreath product of the symmetric group Sn with an arbitrary group G. Techniques of Bidigare and Brown are adapted to construct an anti-homomorphism from the Sn-invariant subalgebra ...

Soft set theory is a general mathematical tool for dealing with uncertain, fuzzy, not clearly defined objects. In this paper we introduced soft neutrosophic semigroup,soft neutosophic bisemigroup, soft neutrosophic N -semigroup with the discuissionf of some of their characteristics. We also introduced a new type of soft neutrophic semigroup, the so called soft strong neutrosophic semigoup which...