After some earlier work on single operators, von Neumann turned to families of operators in [1]. He initiated the study of rings of operators which are commonly called von Neumann algebras today. The papers which constitute the series “Rings of operators” opened a new field in mathematics and influenced research for half a century (or even longer). In the standard theory of modern operator alge...

In der industriellen Fertigung wird ein Bauteil im Laufe des Herstellungsprozesses immer wertvoller, so dass Störungen um Produktionsablauf oder Fertigungsfehler möglichst frühzeitig erkannt werden müssen. Im Zeichen von Industrie 4.0 geschieht dies mittels unterschiedlicher Sensoren, die automatisch ausgelesen werden oder selbst aktiv ihre Werte kommunizieren. Die Daten müssen analysiert und m...

By the Von Neumann regular graph of R, we mean the graph that its vertices are all elements of R such that there is an edge between vertices x,y if and only if x+y is a von Neumann regular element of R, denoted by G_Vnr (R). For a commutative ring R with unity, x in R is called Von Neumann regular if there exists x in R such that a=a2 x. We denote the set of Von Neumann regular elements by V nr...

A correct understanding of the law of diminishing returns both as to its application, as well as to its statement as a principle, is fundamental in any study designed to measure the effect of increasing units of an input factor upon the output whether this output be in the form of plant growth or animal production. Immediately following Von Liebig's emphasis of the need by plants of various min...

die direktreduktion von eisenerzen zu eisenschwamm mittels erdgas wird iiberall dort verwendet wo einmal die notwendtigen rohstoffe und besonders der metallurgische koks zu wirtschaftlischen bedingungen fehlen. andereseirs wiederum miissen erdgasrerven in geniigenden mengen und qualitat zu verfugung stehen, urn die direktredution mit gutem wirkungsgrad durchfuhren zu konnen. in dieser arbeit wi...

Von Neumann entropy rate for open quantum systems is, in general, written terms of production and flow rates, encompassing the second law thermodynamics. When open-quantum-system evolution corresponds to a dynamical semigroup, we find decomposition infinitesimal generator dynamics, that allows relate von with divergence-based Fisher information, at any time. Applied Gaussian channels are semigr...

PURPOSE OF REVIEW This review focuses on recent advances in the use of immune-based therapy to treat patients with refractory and relapsing acquired thrombotic thrombocytopenic purpura. RECENT FINDINGS Advances in understanding of the pathophysiology of idiopathic thrombotic thrombocytopenic purpura have provided the rationale for immune-based treatment approaches to refractory and relapsing ...

Monotonicity under coarse-graining is a crucial property of the quantum relative entropy. The aim of this paper is to investigate the condition of equality in the monotonicity theorem and in its consequences as the strong sub-additivity of von Neumann entropy, the Golden-Thompson trace inequality and the monotonicity of the Holevo quantitity. The relation to quantum Markov states is briefly ind...

We study some of the possibilities for formulating the Heisenberg relation of quantum mechanics in mathematical terms. In particular, we examine the framework discussed by Murray and von Neumann, the family (algebra) of operators affiliated with a finite factor (of infinite linear dimension).