λ(s)δt = δst and ρ(s)δt = δts−1 for s, t ∈ Γ. The reduced group C∗-algebra C∗ λΓ is the C∗-algebra generated by λ, likewise for C∗ ρΓ; C∗ λΓ = λ(CΓ) ‖ ‖ ⊂ B(`2Γ) and C∗ ρΓ = ρ(CΓ) ‖ ‖ ⊂ B(`2Γ). The group von Neumann algebra LΓ is the von Neumann algebra generated by λ; LΓ = λ(CΓ)′′ = ρ(CΓ)′. We sometime use M instead of LΓ, and L2M instead of `2Γ. We denote by τ the canonical tracial state on L...

Zusammenfassung Es wurden zwei empirische Studien durchgeführt. In der einen Studie konnten Internetnutzer ihr Suchverhalten aus ihrer Sicht in einer Online Umfrage beschreiben. Die Fragen orientieren sich an den Ergebnissen früherer Studien und sind durch neue Fragestellungen bei der Online Suche erweitert worden. In der anderen Studie wurden vier weltweit Datensätze von Suchanfragen generiert...

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We give a new proof of a result of Ozawa showing that if a von Neumann subalgebra Q of a free group factor LFn, 2 ≤ n ≤ ∞ has relative commutant diffuse (i.e. without atoms), then Q is amenable.

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Let S be a finite nonabelian simple group, and let H be a subgroup of S . In this work, the dominion (in the sense of Isbell) of H in S in Var(S) is determined, generalizing an example of B.H. Neumann. A necessary and sufficient condition for H to be epimorphically embedded in S is obtained. These results are then extended to a variety generated by a family of finite nonabelian simple groups. S...

We continue the studies of the second author on regulated uniformly k-limited and regulated k-limited ET0L systems. We focus on the permitting and forbidding random context regulation. Especially, we establish some results on (regulated) propagating (uniformly) k-limited ET0L systems which were not solved in 2, 18, 21, 22]. Moreover, relations to recurrent programmed languages introduced by von...

We prove a generalization of the polarization identity linear algebra expressing inner product complex space in terms norm, where field scalars is extended to an associative equipped with involution, and viewed as averaging operation over compact multiplicative subgroup scalars. Using this we general form Jordan-von Neumann theorem on characterizing spaces among normed spaces, when are taken al...

This article describes the addition to the von Neumann cellular automaton of the Tom Thumb Algorithm, a mechanism developed for the self-replication of multi-processor systems. Except for the cell construction process, every functionality of the original CA has been preserved in our new system. Moreover, the Tom Thumb Algorithm now allows the replication of any structure within the von Neumann ...