In this paper we prove existence and uniqueness of matings of a large class of renormalizable cubic polynomials with one fixed critical point and the other cubic polynomial having two fixed critical points. The resulting mating is a Newton map. Our result is the first part towards a conjecture by Tan Lei, stating that all (cubic) Newton maps can be described as matings or captures.

We prove that the Beta random walk, introduced in [BC17] 2017, has cubic fluctuations from large deviation principle of GUE Tracy-Widom type for arbitrary values ?>0 and ?>0 parameters distribution, removing previous restrictions on their values. Furthermore, we still hold intermediate disorder regime. also show any walk space-time environment matches certain moments with As a corollary emergen...

Recently, a large amount of studies have been related to nonlinear systems with multi-degrees of freedom as well as continuous systems. The purpose of this paper is to optimize passive vibration absorbers in linear and nonlinear states for an Euler-Bernoulli beam with a nonlinear vibratory behavior under concentrated moving load. The goal parameter in the optimization is maximum deflection of t...

The domination number γ(G) and the total domination number γt(G) of a graph G without an isolated vertex are among the most well studied parameters in graph theory. While the inequality γt(G) ≤ 2γ(G) is an almost immediate consequence of the definition, the extremal graphs for this inequality are not well understood. Furthermore, even very strong additional assumptions do not allow to improve t...

Let m be a positive integer and let G be a cubic graph of order 2n. We consider the problem of covering the edge-set of G with the minimum number of matchings of size m. This number is called the excessive [m]-index of G in the literature. The case m = n, that is, a covering with perfect matchings, is known to be strictly related to an outstanding conjecture of Berge and Fulkerson. In this pape...