getdoc320f. 136KB Jun 04 2011 12:04:13 AM
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We formulate these systems by cluster algebras, which turn out to be of finite type, and prove their periodicities and the associated dilogarithm identities which have been
The above theorem obviously has a natural counterpart, consisting of two series of minimax and maximin identities, for µ k’s. We omit stating and proving those, since it can easily
hand the auxiliary results leading to Theorem 2.1 can be employed to obtain results on the optimal speed of the random walk under the random potential ξ (see Corollary 2.3
We will show how the potential theoretic approach can be used to prove sharp estimates on capacities and metastable exit times also in the case when the distribution of the random
The maximal inequalities can be used to obtain the invariance principles for random elements associated to partial sums of weakly dependent random variables by using Theorem (8.3)
By the way, we also prove that the Häggström-Pemantle non-coexistence result "except perhaps for a denumerable set" can be extended to families of stochastically
As any feature selection, the Weka subset evaluation is going to try to evaluate the attributes, arrange them in the order of their importance, and tell the user, which are the
We expect that our methods extend to other situations with similar applications to automorphic representations; and we hope the point of view introduced here also will help
