In the last chapter we have shown that the problem of determining the counterterms in φ 4-theory can be reduced completely to the calculation of massless Feynman integrals in momentum space. Among these, the massless propagator-type integrals generated by the technique of infrared rearrangement in Section 12.2 can be calculated most easily by algebraic methods. The result of a successive applic...

Abstract In this study, fractional versions of Milne-type inequalities are investigated for differentiable convex functions. We present bounded functions, Lipschitz functions variation, etc., found in the literature. New results established area inequalities. This article is first to study integrals.

The problem of constructing semi-discrete integrable analogues the Liouville type PDE is discussed. We call equation a discretization if these two equations have common integral. For from well-known Goursat list for which integrals minimal order are less than or equal to we presented corresponding versions. contains new examples non-autonomous Darboux chains.