We establish an integration by parts formula in bounded domains for the higher order fractional Laplacian (−∆) with s > 1. We also obtain the Pohozaev identity for this operator. Both identities involve local boundary terms, and they extend the identities obtained by the authors in the case s ∈ (0, 1). As an immediate consequence of these results, we obtain a unique continuation property for th...

Some versions of the formula of integration by parts with respect to the Henstock-Kurzweil and the Henstock-Stieltjes integrals in Riesz spaces are given.

It is shown how strictly four-dimensional integration by parts combined with differential renormalization and its infrared analogue can be applied for calculation of Feynman diagrams. submitted to Teor. Mat. Fiz. E-mail: [email protected] 1. Integration by parts (IBP) [1] within dimensional regularization [2] turned out to be one of the most powerful methods of calculation of Feynman di...

This paper is devoted to the study of four integral operators that are basic generalizations and modifications of fractional integrals of Hadamard, in the space X c of Lebesgue measurable functions f on R+ = (0,∞) such that ∞ ∫ 0 ∣∣ucf (u)∣∣p du u <∞ (1 p <∞), ess sup u>0 [ u ∣∣f (u)∣∣]<∞ (p =∞), for c ∈ R = (−∞,∞), in particular in the space Lp(0,∞) (1 p ∞). Formulas for the Mellin transforms ...

It is shown that for every problem within dimensional regularization, using the Integration-By-Parts method, one is able to construct a set of master integrals such that each corresponding coefficient function is finite in the limit of dimension equal to four. We argue that the use of such a basis simplifies and stabilizes the numerical evaluation of the master integrals. As an example we expli...

Binocular rivalry occurs when the images presented to the two eyes do not match. Instead of fusing into a stable percept, perception during rivalry alternates between images over time. However, during rivalry, perception can also resemble a patchwork of parts of both eyes' images. Such integration of image parts across eyes is relatively rare compared to integration of image parts presented to ...