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Although there are known different methods to obtain stability properties for functional equations, almost all proofs used the direct method, discovered by Hyers ( see [13], [1],
However, our congruence is more versatile, and we exploit it in the final section together with The- orem 1.1 to prove the congruences involving Bernoulli numbers stated in
This fact, together with the construction of canonical systems in [1] by similarity permutation, motivates us to consider a special similarity concept for positive systems (in [8]
Moreover we proved the existence of certain plane algebraic curves with points such that the corresponding self-similar measures get singular and have Hausdorff dimension less than
The purpose of this note is to prove the existence of a non-trivial critical point for the existence of a type of open Lipschitz surface within site percolation on Z d with d ≥ 2..
Using the Lyapunov function approach we prove that such measures satisfy different kind of functional inequalities such as weak Poincaré and weak Cheeger, weighted Poincaré and
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
The key point is to exploit the strong parallel between the new technique introduced by Bass and Perkins [2] to prove uniqueness of the martingale problem in the framework
