Quantum Sufficiency in the Operator Algebra Framework

The paper is devoted to the investigation of the notion of sufficiency in quantum statistics. Three kinds of this notion are considered: plain sufficiency (called simply: sufficiency), Petz’s sufficiency, and Umegaki’s sufficiency. The problem of the existence and structure of the minimal sufficient subalgebra is analyzed in some detail, conditions yielding equivalence of the three modes of sufficiency are considered, and quantum Basu’s theorem is obtained. Moreover, it is shown that an interesting “factorization theorem” of Jenčová and Petz needs some corrections to hold true

Vegetation of the Paprotnia range in the Wzniesienia Łódzkie Landscape Park

In the paper there are presented results of researches on flora and plant communities of the Paprotnia Range. These researches were carried out in the years 1993-1994. The following forest communities were distinguished in the range: Circaeo-Alnetum, Luzulo pilosae-Fagetum - the poor variant and variant with Anemone nemorosa, Tilio-Carpinetum typicum, T.-C. stachyetosum, the pine-oak community in the habitat of Luzulo pilosae-Fagetum, the pine community in the habitat of an oak-hornbeam forest. The paper contains also the map of real vegetation of the Range and the list of 265 species of bryophyta and vascular plants.Zadanie pt. Digitalizacja i udostępnienie w Cyfrowym Repozytorium Uniwersytetu Łódzkiego kolekcji czasopism naukowych wydawanych przez Uniwersytet Łódzki nr 885/P-DUN/2014 zostało dofinansowane ze środków MNiSW w ramach działalności upowszechniającej naukę

Cloning by positive maps in von Neumann algebras

We investigate cloning in the general operator algebra framework in arbitrary dimension assuming only positivity instead of strong positivity of the cloning operation, generalizing thus results obtained so far under that stronger assumption. The weaker positivity assumption turns out quite natural when considering cloning in the general C∗-algebra framework