منابع مشابه
Factorization Invariants in half-Factorial Affine Semigroups
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 ...
متن کاملA New Characterization of Half-factorial Krull Monoids
Let M be a Krull monoid. Then every element of M may be written as a finite product of irreducible elements. If for every a ∈ M , each two factorizations of a have the same number of irreducible elements, then M is called half-factorial. Using a property of element exponentiation, we provide a new characterization of half-factoriality, valid for all Krull monoids whose class group has torsion-f...
متن کاملQuasi-half-factorial Subsets of Abelian Torsion Groups
If G is an abelian torsion group with generating subset G0, then by a classical result in the theory of non-unique factorizations, the block monoid B(G0) is a half-factorial monoid if each of its atoms has cross number 1. In this case, G0 is called a half-factorial set. In this note, we introduce the notion of a k-quasihalf-factorial set and show for many abelian torsion groups that G0 k-quasi-...
متن کاملGlobal Heat Kernel Estimates for ∆+∆ in Half-space-like Domains
Suppose that d ≥ 1 and α ∈ (0, 2). In this paper, we establish by using probabilistic methods sharp two-sided pointwise estimates for the Dirichlet heat kernels of {∆+ a∆; a ∈ (0, 1]} on half-space-like C domains for all time t > 0. The large time estimates for half-spacelike domains are very different from those for bounded domains. Our estimates are uniform in a ∈ (0, 1] in the sense that the...
متن کاملHalf-Dirichlet problems for Dirac operators in Lipschitz domains
Recall that in the case of the Dirichlet problem for the Laplace operator ∂2 x +∂ 2 y in Ω ⊆ R2, one prescribes the whole trace of a harmonic function in, say, L2(∂Ω). On the other hand, for the Cauchy-Riemann operator ∂x + i∂y, natural boundary problems are obtained by prescribing “half” of the trace of the analytic function in L2(∂Ω). Such half-Dirichlet problems arise when, for example, one ...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1976
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1976-14130-4