INTEGRATION BY PARTS FOR THE PERRON INTEGRAL

1990 ◽  
Vol 16 (2) ◽  
pp. 546
Author(s):  
Cross
Keyword(s):  
Integration By Parts ◽  
Perron Integral

scholarly journals A wide Perron integral

1986 ◽  
Vol 34 (2) ◽  
pp. 233-251
Author(s):  
D. N. Sarkhel
Keyword(s):  
Decomposition Theorem ◽  
Mean Value ◽  
Lebesgue Decomposition ◽  
Integration By Parts ◽  
Mean Value Theorems ◽  
Limit Process ◽  
Real Functions ◽  
Marcinkiewicz Theorem ◽  
Perron Integral ◽  
Interesting Generalization

In terms of an arbitrary limit process T, defined abstractly for real functions, we define in a novel way a T-continuous integral of Perron type, admitting mean value theorems, integration by parts and the analogue of the Marcinkiewicz theorem for the ordinary Perron integral. The integral is shown to include, as particular cases, the various known continuous, approximately continuous, cesàro-continuous, mean-continuous and proximally Cesàro-continuous integrals of Perron and Denjoy types. An interesting generalization of the classical Lebesgue decomposition theorem is also obtained.

scholarly journals A survey of intergration by parts for Perron integrals

1986 ◽  
Vol 40 (3) ◽  
pp. 343-363 ◽  
Author(s):  
P. S. Bullen
Keyword(s):  
Integration By Parts ◽  
Integration By Parts Formula ◽  
History Of ◽  
Perron Integral

AbstractThe history of the proof of the integration by parts formula for the Perron integral, and for the SCP-integral of Burkill, is discussed.

A Simple Proof of Integration by Parts for the Perron Integral

1985 ◽  
Vol 28 (2) ◽  
pp. 195-199 ◽  
Author(s):  
P. S. Bullen
Keyword(s):  
Simple Proof ◽  
Integration By Parts ◽  
Integration By Parts Formula ◽  
Perron Integral

AbstractThis note presents a very simple proof for the integration by parts formula for the Perron integral.

scholarly journals (PVB) functions and integration

1984 ◽  
Vol 36 (3) ◽  
pp. 335-353 ◽  
Author(s):  
D. N. Sarkhel ◽  
A. B. Kar
Keyword(s):  
Real Line ◽  
Mean Value ◽  
Integration By Parts ◽  
The Real ◽  
Mean Value Theorems ◽  
Marcinkiewicz Theorem ◽  
Perron Integral

AbstractWe introduce the notion of functions of bounded proximal variation and the notion of orderly connected topology on the real line. Using these notions, we define in a novel way an integral of Perron type, including virtually all the known integrals of Perron and Denjoy types and admitting mean value theorems and integration by parts and the analog of Marcinkiewicz theorem for the ordinary Perron integral.

Integration by Parts in the SCP Integral

1990 ◽  
Vol 16 (1) ◽  
pp. 34
Author(s):  
Henstock
Keyword(s):  
Integration By Parts

scholarly journals On the sub–diffusion fractional initial value problem with time variable order

2021 ◽  
Vol 10 (1) ◽  
pp. 1301-1315
Author(s):  
Eduardo Cuesta ◽  
Mokhtar Kirane ◽  
Ahmed Alsaedi ◽  
Bashir Ahmad
Keyword(s):  
Asymptotic Behavior ◽  
Fractional Derivative ◽  
Initial Value Problem ◽  
Regularity Result ◽  
Time Variable ◽  
Variable Order ◽  
Initial Value ◽  
Integration By Parts ◽  
Integration By Parts Formula ◽  
Variable Order Fractional Derivative

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.

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

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.

scholarly journals Construction of a surface integral under local Malliavin assumptions, and related integration by parts formulas

2018 ◽  
Vol 18 (2) ◽  
pp. 871-897 ◽  
Author(s):  
Stefano Bonaccorsi ◽  
Giuseppe Da Prato ◽  
Luciano Tubaro
Keyword(s):  
Surface Integral ◽  
Integration By Parts
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