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Quantum groupoids of the finite type and quantization on orbit spaces

Heller M., Odrzygóźdź Z., Pysiak L., Sasin W.

Demonstratio Mathematica

2004

Vol. 37, nr 3

671--678

We show that the Hopf algebra on a transformation groupoid F = E x G where G is a finite group acting on the total space of a principal fibre boundle over M = E/G, is the cross product of the algebras C°°(E) and CG. We study duality properties of this algebra, and consider quantization on orbit spaces program in this context.

On characterization of distributions by expectations of transformed generalized order statistics

Pawlas P., Rychlik T., Szynal D.

Demonstratio Mathematica

2003

Vol. 36, nr 1

239--245

We generalize results of Swanepoel [10] on the characterization of distributions by expectations of transformed order statistics using lower generalized order statistics. In particular we characterize continuous distributions via expectations of kth lower record values.