A lattice L is coordinatizable, if it is isomorphic to the lattice L(R) of principal right ideals of some von Neumann regular ring R. This forces L to be complemented modular. All known sufficient conditions for coordinatizability, due first to J. von Neumann, then to B. Jónsson, are first-order. Nevertheless, we prove that coordinatizability of lattices is not first-order, by finding a non-coo...

We characterize by boundary conditions the Krein-von Neumann extension of a strictly positive minimal operator corresponding to regular even order quasi-differential expression Shin-Zettl type. The characterization is stated in terms specially chosen basis for kernel maximal and employs description Friedrichs due Möller Zettl.

The paper presents the dynamics of consumer preferences over two competing products acting in duopoly market. The model presented compared the majority and minority rules as well as the modified Snazjd model in the Von Neumann neighborhood. We showed how important advertising in marketing a product is. We show that advertising should also consider the social structure simultaneously with the co...

A subgraph of an edge-coloured graph is rainbow if all of its edges have different colours. For graphs G and H the anti-Ramsey number ar(G,H) is the maximum number of colours in an edge-colouring of G with no rainbow copy of H. The notion was introduced by Erdős, Simonovits and V. Sós and studied in case G = Kn. Afterwards exact values or bounds for anti-Ramsey numbers ar(Kn, H) were establishe...

In this paper we consider two von Neumann subalgebras B0 and B of a type II1 factor N . For a map φ on N , we define ‖φ‖∞,2 = sup{‖φ(x)‖2 : ‖x‖ ≤ 1}, and we measure the distance between B0 and B by the quantity ‖EB0 −EB‖∞,2. Under the hypothesis that the relative commutant in N of each algebra is equal to its center, we prove that close subalgebras have large compressions which are spatially is...

A complemented modular lattice L is coordinatizable, if it is isomorphic to the lattice L(R) of principal right ideals of some von Neumann regular ring R. All known sufficient conditions for coordinatizability, due first to J. von Neumann, then to B. Jónsson, are first-order. Nevertheless, we prove that coordinatizability of complemented modular lattices is not firstorder, even for countable 2-...

A new characteristic property of von Neumann regular rings is proposed in terms of annihilators of elements. An ELT fully idempotent ring is a regular ring whose simple left (or right) modules are either injective or projective. Artinian rings are characterized in terms of Noetherian rings. Strongly regular rings and rings whose two-sided ideals are generated by central idempotents are characte...

In diesem Beitrag wird die Berechnung von Differenzen zwischen Prozessmodellen betrachtet. Hierzu werden verschiedene Ansätze und Werkzeuge zur Berechnung von Differenzen beschrieben. Ausgehend von einem konkreten Anwendungsfall – einer EPK-zu-BPEL-Transformation – werden verschieden Testkriterien aufgestellt, die anschließend zur Evaluierung von zwei Differenzbildungswerkzeugen dienen. Abschli...

We introduce the notation Q(1) ∗ · · · ∗ Q(n) ∗L(Fr) for von Neumann algebra II1–factors where r is allowed to be negative. This notation is defined by rescalings of free products of II1–factors, and is proved to be consistent with known results and natural operations. We also give two statements which we prove are equivalent to isomorphism of free group factors.

The term von Neumann computer has two common meanings. Its strictest de nition refers to a speci c type of computer organization, or \architecture," in which instructions and data are stored together in a common memory. This type of architecture is distinguished from the \Harvard" architecture in which separate memories are used to store instructions and data. The term \von Neumann computer" al...