Let $mathcal M$ be a factor von Neumann algebra. It is shown that every nonlinear $*$-Lie higher derivation$D={phi_{n}}_{ninmathbb{N}}$ on $mathcal M$ is additive. In particular, if $mathcal M$ is infinite type $I$factor, a concrete characterization of $D$ is given.

When the computer scientist seeks to model natural phenomena, he or she may select from two paths. Modeling may be by representation or by realization. This distinction is clarified by means of a simple physical example: an adiabatic pressure vessel. A representational model will in no way involve the operation of such a vessel even as a real gas law is observed (like van der Waals’ gas law), w...

“The von Neumann vicious circle” means that non-von Neumann computer architectures cannot be developed because of the lack of widely available and effective non-von Neumann languages. New languages cannot be created because of lack of conceptual foundations for non-von Neumann architectures. The reason is that programming languages are high-level abstract isomorphic copies of von Neumann comput...

We develop the argument that the Gibbs-von Neumann entropy is the appropriate statistical mechanical generalisation of the thermodynamic entropy, for macroscopic and microscopic systems , whether in thermal equilibrium or not, as a consequence of Hamiltonian dynamics. The mathematical treatment utilises well known results [Gib02, Tol38, Weh78, Par89], but most importantly, incorporates a variet...

A ternary ring of operators is an “off-diagonal corner” of a C∗-algebra and the predual of a ternary ring of operators (if it exists) is of the form pR∗q for some von Neumann algebra R and projections p and q in R. In this paper, we prove that a subspace of the predual of a ternary ring of operators is completely 1-complemented if and only if it is completely isometrically isomorphic to the pre...

Suppose M is a compact manifold with boundary ∂M . Let M̃ be a normal covering of M . Suppose (A, T ) is an elliptic differential boundary value problem on M with lift (Ã, T̃ ) to M̃ . Then the von Neumann dimension of kernel and cokernel of this lift are defined. The main result of this paper is: These numbers are finite, and their difference, by definition the von Neumann index of (Ã, T̃ ), equal...

Regionale und lokale Zeitungen sind durch besondere Qualitätsmerkmale gekennzeichnet, die im vorliegenden Beitrag diskutiert werden. Ausgehend von dem Konstanzer Ansatz zur Bewertung von Informationsdienstleistungen werden zeitungsspezifische Kriterien eingearbeitet und den fünf Hauptkennzahlen Information, Präsentation, Interaktion und Kommunikation, Technik und Methodik sowie Organisatorische...

Given a Coxeter system .W;S/ and a positive real multiparameter q , we study the “weighted L–cohomology groups,” of a certain simplicial complex † associated to .W;S/ . These cohomology groups are Hilbert spaces, as well as modules over the Hecke algebra associated to .W;S/ and the multiparameter q . They have a “von Neumann dimension” with respect to the associated “Hecke–von Neumann algebra” ...

We generalize to an arbitrary variety the von Neumann axiom for a ring. We study its implications on the purity of monomorphisms and the flatness of algebras.