منابع مشابه
Remarks on Affine Semigroups
A semigroup is a nonvoid Hausdorff space together with a continuous associative multiplication, denoted by juxtaposition. In what follows S will denote one such and it will be assumed that S is compact. I t thus entails no loss of generality to suppose that S is contained in a locally convex linear topological space 9C, but no particular imbedding is assumed. For general notions about semigroup...
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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 ...
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A general affine Markov semigroup is formulated as the convolution of a homogeneous one with a skew convolution semigroup. We provide some sufficient conditions for the regularities of the homogeneous affine semigroup and the skew convolution semigroup. The corresponding affine Markov process is constructed as the strong solution of a system of stochastic equations with non-Lipschitz coefficien...
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Let ∆ be a Euclidean n-simplex and let {∆j} denote a finite union of simplices which partition ∆. We assume that the partition is invariant under the affine symmetry group of ∆. A classical example of such a partition is the one obtained from barycentric subdivision, but there are plenty of other possibilities. (See §4.1, or else [Sp, p. 123], for a definition of barycentric subdivision.) Our p...
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S̄ = {x ∈ gp(S) | mx ∈ S for some m > 0}. One calls S normal if S = S̄. For simplicity we will often assume that gp(S) = Z; this is harmless because we can replace Z by gp(S) if necessary. The rank of S is the rank of gp(S). We will only be interested in the case in which S ∩ (−S) = 0; such affine semigroups will be called positive. The positivity of S is equivalent to the pointedness of the cone...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2013
ISSN: 0024-3795
DOI: 10.1016/j.laa.2013.06.005