zelinsky9. 227KB Jun 04 2011 12:09:43 AM
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Notice that by Theorem 2.1 all prime factors of Fermat numbers are anti-elites with L = 1, such that the Table contains all possible prime factors p of Fermat numbers that fulfill
This new proof, however, is elementary in that it does not use the Kummer- Dedekind, nor the Kronecker Density Theorems; the proof actually shows that our sets of primes have a
Although we do not know the minimum spectral norm for all cases where n = 2 m , we will prove in Theorem 3.5 that any tournament matrix of even order that attains the minimum
The weak interlacing theorem enables us to bound the average number of leaves in a dense expander graph.. In this paper we proved a weak interlacing theorem for the
One reason for this is that the Bahadur-Rao theorem, used to get the exponential form of the density in the proof of Theorem 1, takes a different form for lattice laws (see e.g.
Hence, we can define the marked Gromov-weak topology based on weak convergence of marked distance matrix distributions, which turns ▼ I into a Polish space (Theorem
Using a certain renewal structure, Sznitman and Zerner (see [2] and [3, Theorem 3.2.2]) proved the following law of large numbers..
We now show how the uniform law of large numbers in Theorem 1.1 can be used to prove the hydrodynamic limits for the system of RWRE as stated in Theorem 1.4.. Proof of Theorem 1.4:
