On the jordan H-submodules of a simple superalgebra with superinvolution ∗

We prove that if A is a simple associative superalgebra with superinvolution ? and H = H(A, ?) is the hermitian superalgebra of symmetric elements then K(A, ?) is simple as a Jordan H-module. We also give a characterization of all Jordan H-submodules of A.     

On herstein's constructions relating jordan and associative superalgebras

We investigate the Jordan structure of a prime associative superalgebra and the Jordan structure of the symmetric elements of a *-prime associative superalgebra with superinvolution.     

Nested Cantor sets

We give sufficient conditions for two Cantor sets of the line to be nested for a positive set of translation parameters. This problem occurs in diophantine approximations. It also occurs as a toy model of the parameter selection for non-uniformly hyperbolic attractors of the plane. For natural Cantors sets, we show that this condition is optimal.     

Asymptotic Independence and Strong Approximation; A Survey

Strong approximation results are discussed for the partial sum process of i.i.d. sequences of vectors having dependent components, where the components of the approximating process are independent. Many applications are considered for additive functionals in one and two dimensions.     

Parallel communicating automata systems — A survey

A parallel communicating automata system is an accepting device based on the communication between more automata working in parallel. It consists of several automata working independently but communicating with each other by request. We survey several variants of parallel communicating automata systems with respect to their computational power. Other aspects like decidability and complexity matters are also briefly discussed. Some open problems and directions for future research are finally pointed out.