The effect of distributed delays with strong kernel in the dynamics in three-neuron BAM neural network model is studied. Instead of destabilization phenomena this neural systems become asymptotically stable through Hopf bifurcation with the gradual increment of mean delay. Existence of Hopf bifurcation is studied in frequency domain. Direction and stability of Hopf bifurcating periodic solution...

Given a nite graded poset with labeled Hasse diagram, we construct a quasi-symmetric generating function for chains whose labels have xed descents. This is a common generalization of a generating function for the ag f-vector de-ned by Ehrenborg and of a symmetric function associated to certain edge-labeled posets which arose in the theory of Schubert polynomials. We show this construction gives...

Let A be a Hopf algebra in a braided rigid category B. In the case B admits a coend C, which is a Hopf algebra in B, we defined in 2008 the double D(A) = A⊗ A⊗C of A, which is a quasitriangular Hopf algebra in B whose category of modules is isomorphic to the center of the category of A-modules as a braided category. Here, quasitriangular means endowed with an R-matrix (our notion of R-matrix fo...

In this paper we study the limit cycles bifurcating from a nonisolated zero-Hopf equilibrium of a differential system in R3. The unfolding of the vector fields with a non-isolated zero-Hopf equilibrium is a family with at least three parameters. By using the averaging theory of the second order, explicit conditions are given for the existence of one or two limit cycles bifurcating from such a z...

It is shown that for any commutative unital ring R the category HopfR of R–Hopf algebras is locally presentable and a coreflective subcategory of the category BialgR of R–bialgebras, admitting cofree Hopf algebras over arbitrary R–algebras. The proofs are based on an explicit analysis of the construction of colimits of Hopf algebras, which generalizes an observation of Takeuchi. Essentially be ...

In the last lecture we have learned that the category of modules over a braided Hopf algebra H is a braided monoidal category. A braided Hopf algebra is a rather sophisticated algebraic object, it is not easy to give interesting nontrivial examples. In this text we develop a theory that will lead to a concrete recipe which produces a nontrivial braided Hopf algebra D(A) (called Drinfeld’s quant...

This thesis is concerned with the definition and the study of properties of homotopic Hopf-Galois extensions in the category Ch 0 k of chain complexes over a field k, equipped with its projective model structure. Given a differential graded k-Hopf algebra H of finite type, we define a homotopic H-Hopf-Galois extension to be a morphism ' : B ! A of augmented H-comodule dg-k-algebras, where B is ...

We determine necessary and sufficient conditions, in grouptheoretical terms, for a Hopf subalgebra in a cocycle deformation of a finite group to be normal.

– We classify pointed finite-dimensional complex Hopf algebras whose group of group-like elements is abelian of prime exponent p, p > 17. The Hopf algebras we find are members of a general family of pointed Hopf algebras we construct from Dynkin diagrams. As special cases of our construction we obtain all the Frobenius–Lusztig kernels of semisimple Lie algebras and their parabolic subalgebras. ...

The Multiplier Hopf Group Coalgebra was introduced by Hegazi in 2002 [] as a generalization of Hope group caolgebra, introduced by Turaev in 2000 [], in the non-unital case. We prove that the concepts introduced by A.Van Daele in constructing multiplier Hopf algebra [3] can be adapted to serve again in our construction. A multiplier Hopf group coalgebra is a family of algebras A = {A α } α∈π , ...