Introduction: In radiation therapy, the accuracy of dose calculations by a treatment planning system (TPS) is important to achieve tumor control and to spare normal tissue. Treatment planning system calculations in the heterogeneous situation may present significant inaccuracies. In this study, three different dose calculation algorithms, pencil beam (PB), collapsed cone (CC), ...

We study numerically the regularity of Arnold tongues corresponding to Diophantine rotation numbers of circle maps at the edge of validity of KAM theorem. This serves as a good test for the numerical stability of two different algorithms. We conclude that Arnold tongues are only finitely differentiable and we also provide a renormalization group explanation of the borderline regularity. Further...

We study preservation of distance regularity when taking strong sums and strong products of distance-regular graphs. MSC 2000 Classification: 05C12

Abstract. Malliavin Calculus is about Sobolev-type regularity of functionals on Wiener space, the main example being the Itô map obtained by solving stochastic differential equations. Rough path analysis is about strong regularity of solution to (possibly stochastic) differential equations. We combine arguments of both theories and discuss existence of a density for solutions to stochastic diff...

The paper investigates stationarity and regularity concepts for set systems in a normed space. Several primal and dual constants characterizing these properties are introduced and the relations between the constants are established. The equivalence between the regularity property and the strong metric inequality is established. The extended extremal principle is formulated. keywords: nonsmooth ...

Bounded linear regularity, the strong conical hull intersection property (strong CHIP), and the conical hull intersection property (CHIP) are properties of a collection of finitely many closed convex intersecting sets in Euclidean space. It was shown recently that these properties are fundamental in several branches of convex optimization, including convex feasibility problems, error bounds, Fe...