Weak Derivatives and Integration by Parts

Abstract We consider a fractional derivative with order varying in time. Then, we derive for it a Leibniz' inequality and an integration by parts formula. We also study an initial value problem with our time variable order fractional derivative and present a regularity result for it, and a study on the asymptotic behavior.

Download Full-text

Weak Derivatives

Universitext - Distributions, Partial Differential Equations, and Harmonic Analysis ◽

10.1007/978-3-030-03296-8_1 ◽

2018 ◽

pp. 1-16

Author(s):

Dorina Mitrea

Keyword(s):

Weak Derivatives

Download Full-text

A new algorithm for the generation of unitarity-compatible integration by parts relations

Journal of High Energy Physics ◽

10.1007/jhep01(2012)077 ◽

2012 ◽

Vol 2012 (1) ◽

Cited By ~ 40

Author(s):

Robert M. Schabinger

Keyword(s):

Integration By Parts

Download Full-text

Two-loop leading colour QCD corrections to $$ q\overline{q} $$ → γγg and qg → γγq

Journal of High Energy Physics ◽

10.1007/jhep04(2021)201 ◽

2021 ◽

Vol 2021 (4) ◽

Author(s):

Bakul Agarwal ◽

Federico Buccioni ◽

Andreas von Manteuffel ◽

Lorenzo Tancredi

Keyword(s):

Numerical Code ◽

Tree Level ◽

Partial Fraction ◽

Integration By Parts ◽

Analytic Expressions ◽

Partial Fraction Decomposition ◽

Loop Amplitudes

Abstract We present the leading colour and light fermionic planar two-loop corrections for the production of two photons and a jet in the quark-antiquark and quark-gluon channels. In particular, we compute the interference of the two-loop amplitudes with the corresponding tree level ones, summed over colours and polarisations. Our calculation uses the latest advancements in the algorithms for integration-by-parts reduction and multivariate partial fraction decomposition to produce compact and easy-to-use results. We have implemented our results in an efficient C++ numerical code. We also provide their analytic expressions in Mathematica format.

Download Full-text