Experience in Engineers Training on Multiple Integrals in the Nomotex DLS [PDF]
ITM Web of Conferences, 2020 The paper discusses a new approach to teaching the discipline “Multiple and curvilinear integrals, series” for engineers, using a new digital information and educational environment “NOMOTEX”, developed at the Department of Computational Mathematics and ...
Dimitrienko Yury I. +6 more
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Constructing canonical Feynman integrals with intersection theory
Physics Letters B, 2021 Canonical Feynman integrals are of great interest in the study of scattering amplitudes at the multi-loop level. We propose to construct dlog-form integrals of the hypergeometric type, treat them as a representation of Feynman integrals, and project them
Jiaqi Chen +3 more
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A symbol and coaction for higher-loop sunrise integrals
SciPost Physics Core, 2023 We construct a symbol and coaction for the $l$-loop sunrise family of integrals, both for equal-mass and generic-mass cases. These constitute the first concrete examples of symbols and coactions for integrals involving Calabi-Yau threefolds and higher ...
Andreas Forum, Matt von Hippel
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Analytic two-loop master integrals for tW production at hadron colliders. Part II
Journal of High Energy Physics, 2023 We present analytic results of the two-loop master integrals for hadronic tW production that contain two massive propagators. For the planar integral family, we succeed in constructing the canonical basis, so the results are written in terms of multiple ...
Jian Wang, Yefan Wang
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Enumeration of shifting U-shaped standard Young tableaux
Nantong Daxue xuebao. Ziran kexue ban, 2023 This paper studies the enumeration problem of the standard Young tableaux in the shifted U-shaped semiclosed model, which is obtained by folding the first cell of the U-shaped in the southwest corner to the northeast corner.
FU Yao; SUN Ping; JIANG Songshui
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Analytic results for two-loop planar master integrals for Bhabha scattering
Journal of High Energy Physics, 2021 We analytically evaluate the master integrals for the second type of planar contributions to the massive two-loop Bhabha scattering in QED using differential equations with canonical bases.
Claude Duhr +2 more
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Generalizations of Shannon type inequalities via diamond integrals on time scales
Journal of Inequalities and Applications, 2023 The paper generalizes Shannon-type inequalities for diamond integrals. It includes two-dimensional Hölder’s inequality and Cauchy–Schwartz’s inequality, which help to prove weighted Grüss’s inequality for diamond integrals.
Muhammad Bilal +3 more
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A study of Feynman integrals with uniform transcendental weights and their symbology
Journal of High Energy Physics, 2022 Multi-loop Feynman integrals are key objects for the high-order correction computations in high energy phenomenology. These integrals with multiple scales may have complicated symbol structures, and we show that twistor geometries of closely related dual
Song He +5 more
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Optimization of the mean-square approximation procedures for iterated Stratonovich stochastic integrals of multiplicities 1 to 3 with respect to components of the multi-dimensional Wiener process based on Multiple Fourier–Legendre series [PDF]
MATEC Web of Conferences, 2022 The article is devoted to approximation of iterated Ito and Stratonovich stochastic integrals of multiplicities 1 to 3 by the method of multiple Fourier–Legendre series.
Kuznetsov Dmitriy, Kuznetsov Mikhail
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On the multiplicity of hyperelliptic integrals [PDF]
Nonlinearity, 2004 Let $I(t)= \oint_{δ(t)} ω$ be an Abelian integral, where $H=y^2-x^{n+1}+P(x)$ is a hyperelliptic polynomial of Morse type, $δ(t)$ a horizontal family of cycles in the curves $\{H=t\}$, and $ω$ a polynomial 1-form in the variables $x$ and $y$. We provide an upper bound on the multiplicity of $I(t)$, away from the critical values of $H$.
openaire +2 more sources