We present the results for two-loop massive kite master integrals with elliptics in terms of iterated algebraic kernels. The key ingredients are new integral representations sunset subgraphs d=4?2? and d=2?2? dimensions together differential equations considered A+B? form. obtained can be easily generalized to all orders ?-expansion show that class functions defined as kernels may large enough ...

The relationship between Feynman diagrams and hypergeometric functions is discussed. Special attention devoted to existing techniques for the construction of ?-expansion. As an example, we present a detailed discussion ?-expansion Appell function F3 around rational values parameters via iterative solution differential equations. by-product, have found that one-loop massless pentagon diagram in ...

Abstract We present an algorithm that, given finite diagrams of simplicial sets X , A Y i.e., functors $${\mathcal {I}}^\textrm{op}\rightarrow {\textsf {s}} {Set}}$$ I op → s Set such that (...

Design patterns are patterns of classes and objects that represent solutions to recurring design problems. They are usually described using class diagrams. Class diagrams, however, often intertwine the actual solution with efficient ways of implementing it. This paper uses role diagrams to describe and compose patterns. Role diagrams help designers focus on the collaborations and distribution o...