We define an analog of Voiculescu’s free entropy for n-tuples of unitaries u1, . . . , un in a tracial von Neumann algebra M which normalize a unital subalgebra L[0, 1] = B ⊂ M. Using this quantity, we define the free dimension δ0(u1, . . . , un G B). This number depends on u1, . . . , un only up to orbit equivalence over B. In particular, if R is a measurable equivalence relation on [0, 1] gen...

Zusammenfassung. Im folgenden wird ein Verfahren zur Segmentierung von medizinischen Volumendaten vorgestellt. Ausgehend von einem Punkt innerhalb eines zu segmentierenden Objektes wird radial nach Kanten gesucht, welche das Objekt begrenzen. Durch eine Oberflächenfilterung werden Punkte die nicht auf eine Objektkante treffen (Ausreißer) eliminiert. Die so gefundenen Begrenzungspunkte werden an...

‎Let $lambda_1,dots,lambda_n$  be positive real numbers such that $sum_{k=1}^n lambda_k=1$. In this paper, we prove that for any positive operators $a_1,a_2,ldots, a_n$ in semifinite von Neumann algebra $M$ with faithful normal trace that $t(1)

The aim of this note is to study the submajorization inequalities for $tau$-measurable operators in a semi-finite von Neumann algebra on a Hilbert space with a normal faithful semi-finite trace $tau$. The submajorization inequalities generalize some results due to Zhang, Furuichi and Lin, etc..

In this paper we characterize the left Jordan derivations on Banach algebras. Also, it is shown that every bounded linear map $d:mathcal Ato mathcal M$ from a von Neumann algebra $mathcal A$ into a Banach $mathcal A-$module $mathcal M$ with property that $d(p^2)=2pd(p)$ for every projection $p$ in $mathcal A$ is a left Jordan derivation.

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...