A limit theorem for projections

The main purpose of this paper is to establish a limit theorem for convex combinations of linear projections. We also include nonlinear extensions as well as several applications.     

Über die globale Lösung der Schröderschen Funktionalgleichung für holomorphe Abbildungen mit anziehendem Fixpunkt

Ohne Zusammenfassung     

Quantitative determination of beta-asarone in calamus by high-performance thin-layer chromatography

A quantitative high-performance thin-layer chromatographic method for determination of beta-asarone in Calamus rhizome was developed and validated. The method is suitable for proper identification of Acorus calamus. Through the use of caffeine-modified silica gel as the stationary phase and toluene-ethyl acetate (93 + 7, v/v) as the mobile phase, beta-asarone is baseline separated from its isomer alpha-asarone. Scanning densitometry with absorption measurement at 313 nm allows specific, accurate, and precise quantification of beta-asarone. The working range of 40 to 200 ng absolute of the target substance is sufficient to establish whether a given sample passes the limit test of 0.5% maximum as required by the Swiss Pharmacopoeia.     

ParaHermitian and paraquaternionic manifolds

A set of canonical paraHermitian connections on an almost paraHermitian manifold is defined. ParaHermitian version of the Apostolov-Gauduchon generalization of the Goldberg-Sachs theorem in General Relativity is given. It is proved that the Nijenhuis tensor of a Nearly paraKähler manifolds is parallel with respect to the canonical connection. Salamon's twistor construction on quaternionic manifold is adapted to the paraquaternionic case. A hyper-paracomplex structure is constructed on Kodaira-Thurston (properly elliptic) surfaces as well as on the Inoe surfaces modeled on . A locally conformally flat hyper-paraKähler (hypersymplectic) structure with parallel Lee form on Kodaira-Thurston surfaces is obtained. Anti-self-dual non-Weyl flat neutral metric on Inoe surfaces modeled on is presented. An example of anti-self-dual neutral metric which is not locally conformally hyper-paraKähler is constructed.