Various types of probabilistic proof systems have played a central role in the development of computer science in the last decade. In this exposition, we concentrate on three such proof systems — interactive proofs, zero-knowledge proofs, and probabilistic checkable proofs — stressing the essential role of randomness in each of them. This exposition is an expanded version of a survey written fo...

Man wolle dabei von der Arbeit, die Herr Dr. Hellinger zu erledigen hatte, nicht gering denken. Denn es ist auch so noch ein weiter Weg von der durch allerlei zufällige Umstände bedingten mündlichen Darlegung des Dozenten zu der schriftlichen, hinterher noch wesentlich abgeglichenen, lesbaren Darstellung. [One should not underestimate the work that Dr. Hellinger had to accomplish. It is a long ...

A systematic exposition is given of the theory of invariant differential operators on a not necessarily reductive homogeneous space. This exposition is modelled on Helgason’s treatment of the general reductive case and the special nonreductive case of the space of horocycles. As a final application the differential operators on (not a priori reductive) isotropic pseudo-Riemannian spaces are cha...

................................................................................................................... xxiii Kurzfassung ............................................................................................................... xxv Part A .............................................................................................................................. 1 1 Expositio...

by introducing two counterexamples, gettier claims that it is possible that a person s has true justified belief that p but fails to know that proposition. the proposition p in gettier’s first counterexample includes a “definite description”. we try, in this article, to refute gettier’s first counterexample by means of what russell, strawson and donnellan have said on the analysis of the propos...

The sonata form has been one of the most important large-scale musical structures used since the early Classical period. Typically, the first movements of symphonies and sonatas follow the sonata form, which (in its most basic form) starts with an exposition and a repetition thereof, continues with a development, and closes with a recapitulation. The recapitulation can be regarded as an altered...