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The proof of the theorem heavily depends on the fact that group schemes of type F 4 with trivial g 3 invariant are split by an ´etale quadratic extension of the ground ring R.. This
In this paper, we show that the set of translation-invariant monotone couplings of Poisson processes X and Y with rates λ1 > λ2 includes the special class of
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,
We prove that for symmetric Markov processes of diffusion type admitting a “carré du champ”, the Poincaré inequality is equivalent to the exponential convergence of the
For the plane, sphere, and hyperbolic plane we consider the canonical invariant determinan- tal point processes Z ρ with intensity ρdν, where ν is the corresponding invariant
In this paper a method for proving homogenization of divergence form elliptic equations is extended to the non-divergence case.. A new proof of homogenization is given when the
The main step in the proof of Theorem 1 (ii) will be Theorem 10 below, which states that within a cube of appropriate size, the final configuration of the model resembles
In this section we prove a fixed point theorem in a complete metric space by employing notion of generalized w-distance.. The following Lemma is crucial in the proof of
