It was proved by Montaner and Zelmanov that up to classical twisting Lie bialgebra structures on g[u] fall into four classes. Here g is a simple complex finite-dimensional Lie algebra. It turns out that classical twists within one of these four classes are in a one-to-one correspondence with the so-called quasi-trigonometric solutions of the classical Yang-Baxter equation. In this paper we give...

We prove the equivalence between some intuitionistic theorems and the conjunction of a continuity principle and a compactness principle over Bishop’s Constructive Mathematics within the programme of Constructive Reverse Mathematics. To clarify our line of thought, we first point out the relation between quasi-equicontinuity, quasi-uniform convergence, and the continuity principle saying that th...

The main steps of the proof of the existence result for the quasi-static evolution of cracks in brittle materials, obtained in [7] in the vector case and for a general quasiconvex elastic energy, are presented here under the simplifying assumption that the minimizing sequences involved in the problem are uniformly bounded in L.

In this paper, we consider an iteration process for approximating common fixed points of two asymptotically quasinonexpansive mappings and we prove some strong and weak convergence theorems for such mappings in uniformly convex Banach spaces. Keywords—Asypmtotically quasi-nonexpansive mappings, Common fixed point, Strong and weak convergence, Iteration process.

This work presents a version of the Metropolis-Hastings algorithm using quasi-Monte Carlo inputs. We prove that the method yields consistent estimates in some problems with finite state spaces and completely uniformly distributed inputs. In some numerical examples, the proposed method is much more accurate than ordinary Metropolis-Hastings sampling.

Let X be a geodesic metric space with H1(X) uniformly generated. If X has asymptotic dimension one then X is quasi-isometric to an unbounded tree. As a corollary, we show that the asymptotic dimension of the curve graph of a compact, oriented surface with genus g ≥ 2 and one boundary component is at least two.

We introduce a new three-step iterative scheme with errors. Several convergence theorems of this scheme are established for common fixed points of nonself asymptotically quasi-non-expansive mappings in real uniformly convex Banach spaces. Our theorems improve and generalize recent known results in the literature.