getdoc0d72. 406KB Jun 04 2011 12:04:05 AM
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We generalize the construction of canonical algebraic curvature tensors by self- adjoint endomorphisms of a vector space to arbitrary endomorphisms.. Provided certain basic
On checking the history of the basic ideas, we find that the companion matrix itself plays an important role in the “rational canonical form” of a matrix under similarity (over
Proof : The only problem is to prove formula (4), that is to prove that u is the sum of its Taylor expansion with respect to λ. In the case where A is a complex Banach algebra,
To prove those results, we use the fact that the ISE has the same distribution (up to a constant scaling) as the total mass of an excursion of the Brownian snake conditioned to have
We conjecture that the Parisi functional in the Sherrington-Kirkpatrick model is convex in the functional order parameter.. We prove a partial result that shows the convexity
We derive a simple integral representation for the distribution of the maximum of Brownian motion minus a parabola, which can be used for computing the density and moments of
We prove the moderate deviation principle for subgraph count statistics of Erd˝ os-Rényi random graphs.. This is equivalent in showing the moderate deviation principle for the trace
We prove that for almost all values of the index α – except for a dense set of Lebesgue measure zero – the asymptotic series which were obtained in [13] are in fact
