In this note, we prove that the projective normality of (P(V )/G,L), the celebrated theorem of Erdös-Ginzburg-Ziv and normality of an affine semigroup are all equivalent, where V is a finite dimensional representation of a finite cyclic group G over C and L is the descent of the line bundle O(1)⊗|G|.

Given a non-negative integer k, we construct a lattice 3-simplex P with the following property: The affine semigroup QP associated to P is not normal, and every element q ∈ QP \ QP has lattice distance at least k above every facet of QP .

In this paper we introduce a digital architecture implementing the explicit solution of a switched model predictive control problem. Given a mixed-logic dynamical system, we derive an explicit controller in the form of a possibly discontinuous piecewise-affine function. This function is then approximated by resorting to piecewise-affine simplicial functions, which can be implemented on a circui...

The support of the tensor product decomposition integrable irreducible highest weight representations a symmetrizable Kac-Moody Lie algebra g <mml:annotation encoding="applic...

Let f ̸= 1, 3 be a positive integer. We prove that there exists a numerical semigroup S with embedding dimension three such that f is the Frobenius number of S. We also show that the same fact holds for affine semigroups in higher dimensional monoids.

The notion of "Semigroup compactification" which is in a sense, a generalization of the classical Bohr (almost periodic) compactlflcation of the usual additive reals R, has been studied by J.F. Berglund et. al. [2]. Their approach to the theory of semigroup compactification is based on the Gelfand-Naimark theory of commutative Calgebras, where the spectra of admissible C*-aigebras, are the semi...

The well-known theory of the “rational canonical form of an operator” describes the invariant factors, or equivalently, elementary divisors, as a complete set of invariants of a similarity class of an operator on a finite-dimensional vector space V over a given field F. A finer part of the theory is the contribution by Frobenius dealing with the structure of the centralizer of an operator. The ...

For any affine semigroup S, the set S∪{∞} has a natural structure; additionally, if S is endowed with discrete topology, then can be studied as one-point compactification of S. In this article, we study derivations on algebra C[S∪{∞}] in relation to C[S] considering metrizable topology induced by S∪{∞}.