A bounded linear operator T on a Banach space X is called an (m, p)-isometry if it satisfies the equationIn this paper we study the structure which underlies the second parameter of (m, p)-isometric operators. We concentrate on determining when an (m, p)-isometry is a (µ, q)-isometry for some pair (µ, q). We also extend the definition of (m, p)-isometry, to include p = ∞ and study basic properties of these (m, ∞)-isometries.

Abstract. We study Colored Workflow nets [8], a model based on Workflow nets [14] enriched with data. Based on earlier work by Esparza and Desel on the negotiation model of concurrency [3,4], we present reduction rules for our model. Contrary to previous work, our rules preserve not only soundness, but also the data flow semantics. For free choice nets, the rules reduce all sound nets (and only them) to a net with one single transition and the same data flow semantics. We give an explicit algorithm that requires only a polynomial number of rule applications.

This article provides an overview of some of the mathematical principles of Automatic Differentiation (AD). In particular, we summarise different descriptions of the Forward Mode of AD, like the matrix-vector product based approach, the idea of lifting functions to the algebra of dual numbers, the method of Taylor series expansion on dual numbers and the application of the push-forward operator, and explain why they all reduce to the same actual chain of computations. We further give a short mathematical description of some methods of higher-order Forward AD and, at the end of this paper, briefly describe the Reverse Mode of Automatic Differentiation.

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Mathematics, Vol. 8, No. 2 (2015) * AbstractWe generalize the notion of m-isometric operator tuples on Hilbert spaces in a natural way to operator tuples on normed spaces. This is done by defining a tuple analogue of (m, p)-isometric operators, so-called (m, p)-isometric operator tuples. We then extend this definition further by introducing (m, ∞)-isometric operator tuples and study properties of and relations between these objects.