Computational complexity. On the geometry of polynomials and a theory of cost. I

13 In [9, Theorem 2], by considering the distribution of the zeros of a polynomial g(z) relative to an annulus, 1 obtained the best possible results for the

The second step in the proof of Theorem 6.11 is to extend Lemma 6.8 from one trajectory to a fixed number, say G, of independent random walk trajectories.. First, consider G

We develop a new method that allows us to give a new proof of the main theorem of Male in [19], and thus a new proof of the result of Haagerup and Thorbjørnsen.. Our approach

Although by Theorem 3.1 we know that the Identity Theorem holds for bicomplex holomorphic functions, the proof of Theorem 3.5 offers an inspiration for a different proof of the

Very recently, the author provided a simultaneously simple proof of Birkhoff ergodic theorem and Bourgain homogeneous ergodic bilinear theorem with an extension to polynomials

As in the ergodic theoretical proof of Szemer´edi’s theorem (as well as its extension to polynomial progressions), the analogy between sets of integers with positive upper

Our goal is to simplify the proof given in [7] of the stability of a single peakon for the DP equation.. Recall that the proof of the stability for the Camassa-Holm equation (CH) in

Section 3 is practically a short survey of what’s known about regular contact manifolds, but it contains some new results: (1) the proof of Theorem 1.1; (2) the proof that