We address the question of when a covering of the boundary of a surface F can be extended to a covering of the surface (equivalently: when is there a branched cover with a prescribedmonodromy ). If such an extension is possible, when can the total space be taken to be connected? When can the extension be taken to be regular? We give necessary and sufficient conditions for both finite and infini...

Let Σ be a surface whose interior admits a hyperbolic structure of finite volume. In this paper, we show that any infinite order mapping class acts with infinite order on the homology of some universal k–step nilpotent cover of Σ. We show that a Torelli mapping class either acts with infinite order on the homology of a finite abelian cover, or the suspension of the mapping class is a 3–manifold...

In this paper, we suggest a hybrid extragradient method for finding a common element of the set of fixed point sets of an infinite family of nonexpansive mappings and the solution set of the split feasibility problem (SFP) in real Hilbert spaces.

Strong convergence of a new iterative process based on the Shrinking projection method to a common element of the set of common fixed points of an infinite family of relatively quasi-nonexpansive multivalued mappings and the solution set of an equilibrium problem in a Banach space is established. Our results improved and extend the corresponding results announced by many others.

Multirelations model computations with both angelic and demonic non-determinism. We extend multirelations to represent finite and infinite computations independently. We derive an approximation order for multirelations assuming only that the endless loop is its least element and that the lattice operations are isotone. We use relations, relation algebra and RelView for representing and calculat...

We introduce an extension, indexed by a partially ordered set P and cardinal numbers κ, λ, denoted by (κ,<λ) ; P , of the classical relation (κ, n, λ) → ρ in infinite combinatorics. By definition, (κ, n, λ) → ρ holds if every map F : [κ] → [κ] has a ρ-element free set. For example, Kuratowski’s Free Set Theorem states that (κ, n, λ) → n + 1 holds iff κ ≥ λ+n, where λ+n denotes the n-th cardinal...

We extend the notion of a purely infinite simple C*-algebra to the context of unital rings, and we study its basic properties, specially those related to K-Theory. For instance, if R is a purely infinite simple ring, then K0(R) + = K0(R), the monoid of isomorphism classes of finitely generated projective R-modules is isomorphic to the monoid obtained from K0(R) by adjoining a new zero element, ...

In this paper, we introduce a general iterative scheme for finding a common element of the set of common fixed points of an infinite family of nonexpansive mappings and the set of solutions of variational inequalities for an inverse-strongly monotone mapping.

in this paper we consider the group algebra $r(c_2times‎ ‎d_infty)$‎. ‎it is shown that $r(c_2times d_infty)$ can be‎ ‎represented by a $4times 4$ block circulant matrix‎. ‎it is also‎ ‎shown that $mathcal{u}(mathbb{z}_2(c_2times d_infty))$ is‎ ‎infinitely generated‎.

‎linear semi-infinite programming problem is an important class of optimization problems which deals with infinite constraints‎. ‎in this paper‎, ‎to solve this problem‎, ‎we combine a discretization method and a neural network method‎. ‎by a simple discretization of the infinite constraints,we convert the linear semi-infinite programming problem into linear programming problem‎. ‎then‎, ‎we use...