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The purpose of this article is to prove the relative consistency of certain statements about open colorings with 2ℵ0 < 2ℵ1. In particular both OCA and the statement that every 1-1 function...
DIAMOND AGGREGATION
DIAMOND AGGREGATION
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2015/8/14
Internal diffusion-limited aggregation is a growth model based on random walk in Zd. We study how the shape of the aggregate depends on the law of the underlying walk, focusing on a family of walks in...
Composition-Diamond Lemma for Non-associative Algebras over a Commutative Algebra
Gr¨obner-Shirshov basis non-associative algebra commutative algebra
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2010/11/26
We establish the Composition-Diamond lemma for non-associative algebras over a free commutative algebra. As an application, we prove that every countably generated non-associative algebra over an arbi...
Some results on the diamond-$\alpha$ dynamic derivative on time scales
Dynamic derivatives Combined formula Linear combination
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2010/9/14
Various dynamic derivative formulae have been proposed in the development of a time scales calculus, with the goal of unifying continuous and discrete analysis. Recent discussion of combined dynamic d...
Quantum Co-Adjoint Orbits of the Real Diamond Group
Quantum Co-Adjoint Orbits Real Diamond Group
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2010/10/29
We present explicit formulas for deformation quantization on the co-adjoint orbits of the real diamond Lie group. From this we obtain quantum half-plans, quantum hyperbolic cylinders, quantum hyperbol...