We study representations of the simple Lie antialgebra asl 2 introduced in [5]. We show that representations of asl 2 are closely related to the famous ghost Casimir element of the universal enveloping algebra osp(1|2). We prove that asl 2 has no non-trivial finite-dimensional representations; we define and classify some particular infinite-dimensional representations that we call weighted repr...

The goal of this paper is to construct infinite dimensional Lie algebras using infinite product identities, and to use these Lie algebras to reduce the generalized moonshine conjecture to a pair of hypotheses about group actions on vertex algebras and Lie algebras. The Lie algebras that we construct conjecturally appear in an orbifold conformal field theory with symmetries given by the monster ...

The purpose of this paper is to introduce a general iterative process for the problem of finding a common element in the set of common fixed points of an infinite family of nonexpansive mappings and in the set of solutions of variational inequalities for inverse-strongly monotone mappings.

In this paper we investigated some operations on fuzzy h-ideals. Among all the results, we show that the set of all fuzzy left h-ideals of a Γ−hemiring S is zerosumfree hemiring having infinite element 1 under the operations of sum and composition of fuzzy left h-ideals of S. Mathematics Subject Classification: 08A72,16Y99

In this paper, the artificial boundary method for Poisson problem in an infinite domain with a concave angle is investigated. The exact and approximate elliptical arc artificial boundary conditions are given. The finite element approximation is formulated in a bounded domain using the approximate artificial boundary condition and error estimates are obtained. Finally, some numerical examples sh...

In this survey we will define the Grigorchuk group and prove some of its properties. We will show that the Grigorchuk group is finitely generated but infinite. We will also show that the Grigorchuk group is a 2-group, meaning that every element has finite order a power of two. This, along with Burnside’s Theorem, gives that the Grigorchuk group is not linear.

Spectral and pseudo spectral methods for advection equations are investigated. A basic framework is given which allows the application of techniques used in finite element analysis to spectral methods with trigonometric polynomials. Error estimates for semidiscrete spectral and pseudo spectral as well as fully discrete explicit pseudo spectral methods are given. The approximation schemes are sh...

Let A be an excellent ring. We show that if the real dimension of A is at least three then A has infinite Pythagoras number, and there exists a positive semidefinite element in A which is not a sum of squares in A.

We introduce a new iterative scheme by hybrid method for finding a common element of the set of common fixed points of infinite family of k-strictly pseudocontractive mappings and the set of common solutions to a system of generalized mixed equilibrium problems and the set of solutions to a variational inequality problem in a real Hilbert space. We then prove strong convergence of the scheme to...

We introduce a new iterative scheme by hybrid method for finding a common element of the set of common fixed points of infinite family of nonexpansive mappings, the set of common solutions to a system of generalized mixed equilibrium problems, and the set of solutions to a variational inequality problem in a real Hilbert space. We then prove strong convergence of the scheme to a common element ...