On Young and Heinz inequalities for τ-measurable operators

The purpose of this article is to prove Young and Heinz inequalities for τ-measurable operators.     

Noncommutative algebras associated to complexes and graphs

A new class of noncommutative algebras associated to complexes and graphs is introduced. Algebras associated to one-dimensional complexes are studied.     

Multilinear Components of the Prime Subvarieties of the Variety Var(M2(F))

We describe the multilinear components of the prime subvarieties of the variety Var(M₂(F)) generated by the matrix algebra of order 2 over a field of characteristic p>0.     

Inverse closed ultradifferential subalgebras

In previous work we have shown that classical approximation theory provides methods for the systematic construction of inverse-closed smooth subalgebras. Now we extend this work to treat inverse-closed subalgebras of ultradifferentiable elements. In particular, Carleman classes and Dales–Davie algebras are treated. As an application the result of Demko, Smith and Moss, and Jaffard on the inverse of a matrix with exponential decay is obtained within the framework of a general theory of smoothness.     

A Class of Coquasitriangular Hopf Group Algebras

This article is devoted to constructing a class of coquasitriangular Hopf group algebras. First, we introduce the notion of group unified product. Then we prove the classification theorem for group unified products and discuss the sufficient and necessary conditions to make the group unified product to be a coquasitriangular Hopf group-algebra. Finally, some applications of the main results are considered.     

Generalized Digroups

The concept of digroup has been proposed as a generalization of continuous groups whose tangent space is a Leibniz algebra. We study a further generalization of the digroup structure in which we do not demand that the inverses are necessarily bilateral. We characterize a generalized digroup as a set and as a product. We show an analogous to the first isomorphism theorem. Additionally, we explore the concept of dialgebra digroup.     

Anti-control of Hopf Bifurcation in a Delayed Predator-prey Gompertz Model

A delayed predator-prey Gompertz model is investigated. The stability is ana- lyzed. Anti-control of Hopf bifurcation for the model is presented. Numerical simulations are performed to confirm that the new feedback controller using time delay is efficient in creating Hopf bifurcation. Finally, main conclusions are included.