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Uniformly continuous composition operators in the space of functions of two variables of bounded φ-variation in the sense of Wiener

Guerrero J.A., Matkowski J., Merentes N.

Commentationes Mathematicae

2010

Vol. 50, [Z] 1

41-48

Assume that the generator of a Nemytskii composition operator is a function of three variables: the first two real and third in a closed convex subset of a normed space, with values in a real Banach space. We prove that if this operator maps a certain subset of the Banach space of functions of two real variables of bounded Wiener φ-variation into another Banach space of a similar type, and is uniformly continuous, then the one-sided regularizations of the generator are affine in the third variable.

Generalised composition operations for high-level Petri nets

Best E., Lavrov A.

Fundamenta Informaticae

1999

Vol. 40, Nr 2,3

125-163

We propose generic schemes for basic composition operations (sequential composition, choice, iteration, and refinement) for high-level Petri nets. They tolerate liberal combinations of place types (equal, disjoint, intersecting) and, owing to a parameterised scheme of type construction, allow for weak and strong versions of compositions. Properties such as associativity, commutativity, and coherence with respect to unfolding, are preserved.