Results 11 to 20 of about 697,316 (261)
Intersection numbers from higher-order partial differential equations
Journal of High Energy Physics, 2023 We propose a new method for the evaluation of intersection numbers for twisted meromorphic n-forms, through Stokes’ theorem in n dimensions. It is based on the solution of an n-th order partial differential equation and on the evaluation of multivariate ...
Vsevolod Chestnov +4 more
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Decomposition of Feynman integrals by multivariate intersection numbers
Journal of High Energy Physics, 2021 We present a detailed description of the recent idea for a direct decomposition of Feynman integrals onto a basis of master integrals by projections, as well as a direct derivation of the differential equations satisfied by the master integrals ...
Hjalte Frellesvig +6 more
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On Kelley’s intersection numbers [PDF]
Proceedings of the American Mathematical Society, 2000 We introduce a notion of weak intersection number of a collection of sets, modifying the notion of intersection number due to J.L. Kelley, and obtain an analogue of Kelley’s characterization of Boolean algebras which support a finitely additive strictly positive measure.
Galvin, Fred, Prikry, Karel
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Center of circles intersection, a new defuzzification method for fuzzy numbers [PDF]
Bulletin of the Polish Academy of Sciences: Technical Sciences, 2020 The article introduces a new proposal of a defuzzification method, which can be implemented in fuzzy controllers. The first chapter refers to the origin of fuzzy sets.
H. Zarzycki +3 more
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Vector weighted Stirling numbers and an application in graph theory
Electronic Journal of Graph Theory and Applications, 2021 We introduce \textit{vector weighted Stirling numbers}, which are a generalization of ordinary Stirling numbers and restricted Stirling numbers. Some relations between vector weighted Stirling numbers and ordinary Stirling numbers and some of their ...
Fahimeh Esmaeeli +2 more
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On affine coordinates of the tau-function for open intersection numbers
Nuclear Physics B, 2021 In Alexandrov's work [4,5] it has been shown that the extended partition function exp(Fo,ext+Fc) introduced by Buryak in [14,15] is a tau-function of the KP hierarchy.
Zhiyuan Wang
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Macaulay matrix for Feynman integrals: linear relations and intersection numbers
Journal of High Energy Physics, 2022 We elaborate on the connection between Gel’fand-Kapranov-Zelevinsky systems, de Rham theory for twisted cohomology groups, and Pfaffian equations for Feynman Integrals.
Vsevolod Chestnov +6 more
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Reduction to master integrals via intersection numbers and polynomial expansions
Journal of High Energy Physics, 2023 Intersection numbers are rational scalar products among functions that admit suitable integral representations, such as Feynman integrals. Using these scalar products, the decomposition of Feynman integrals into a basis of linearly independent master ...
Gaia Fontana, Tiziano Peraro
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Intersection numbers of special cycles [PDF]
Journal of the American Mathematical Society, 1993 Bei der näheren Beschreibung von Quotientenräumen symmetrischer Gebiete nach arithmetischen Gruppen spielen ``spezielle Zykeln'' und ihre Schnitte ein große Rolle, z.B. die Hirzebruch-Zagier-Zykeln auf Hilbertschen Modulflächen. Diese Zykeln kann man einerseits als Quotienten von Fixmannigfaltigkeiten für Involutionen beschreiben, andererseits durch ...
Rohlfs, Jürgen, Schwermer, Joachim
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Intersection Numbers on Fibrations and Catalan Numbers
Experimental Mathematics, 2023 On an elliptic surface or threefold, Catalan numbers appear when one tries to compute the autoequivalence group action on the Bridgeland stability manifold. We explain why this happens by identifying a class of equations in the Chow ring of a fibration, where the solutions always involve Catalan numbers.
Rimma Hämäläinen +2 more
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