Results 11 to 20 of about 121,182 (204)
Abelian Hurwitz-Hodge integrals [PDF]
Michigan Mathematical Journal, 2011 25 pages, revised version.
Johnson, P. +2 more
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Efficient and Validated Numerical Evaluation of Abelian Integrals
ACM Transactions on Mathematical Software, 2022 Abelian integrals play a key role in the infinitesimal version of Hilbert’s 16th problem. Being able to evaluate such integrals—with guaranteed error bounds—is a fundamental step in computer-aided proofs aimed at this problem. Using interpolation by trigonometric polynomials and quasi-Newton-Kantorovitch validation, we develop a validated numerics ...
Florent Bréhard +3 more
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Abelian integrals in holomorphic foliations
Revista Matemática Iberoamericana, 2004 The aim of this paper is to introduce the theory of Abelian integrals for holomorphic foliations in a complex manifold of dimension two. We will show the importance of Picard-Lefschetz theory and the classification of relatively exact 1-forms in this theory.
Movasati, Hossein, Movasati, H.
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Sharp bounds of the number of zeros of Abelian integrals with parameters
Electronic Journal of Differential Equations, 2014 In this article, we study four Abelian integrals over compact level curves of four sixth-degree hyper-elliptic Hamiltonians with parameters. We prove that the sharp bound of the number of zeros for each Abelian integral is 2. The proofs rely mainly
Xianbo Sun, Junmin Yang
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Redundant Picard–Fuchs System for Abelian Integrals [PDF]
Journal of Differential Equations, 2001 We derive an explicit system of Picard-Fuchs differential equations satisfied by Abelian integrals of monomial forms and majorize its coefficients. A peculiar feature of this construction is that the system admitting such explicit majorants, appears only in dimension approximately two times greater than the standard Picard-Fuchs system.
Novikov, D., Yakovenko, S.
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$p$-groups with maximal elementary abelian subgroups of rank $2$ [PDF]
, 2010 Let p be an odd prime number and G a finite p-group. We prove that if the rank of G is greater than p, then G has no maximal elementary abelian subgroup of rank 2.
Mazza, Nadia, Glauberman, George
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Connected components of the category of elementary abelian $p$-subgroups. [PDF]
, 2008 We determine the maximal number of conjugacy classes of maximal elementary abelian subgroups of rank $2$ in a finite $p$-group $G$, for an odd prime $p$. Namely, it is $p$ if $G$ has rank at least $3$ and it is $p+1$ if $G$ has rank $2$.
Mazza, Nadia
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On the deformation of Abelian integrals [PDF]
Letters in Mathematical Physics, 1996 We consider the deformation of abelian integrals which arose from the study of SG form factors. Besides the known properties they are shown to satisfy Riemann bilinear identity. The deformation of intersection number of cycles on hyperelliptic curve is introduced.
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The monotonicity of the ratio of two Abelian integrals [PDF]
Transactions of the American Mathematical Society, 2013 In this paper, we study the monotonicity of the ratio of two Abelian integrals \[ I 0
Liu, Changjian, Xiao, Dongmei
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Lower bounds for the normalized height and non-dense subsets of varieties in an abelian variety [PDF]
, 2010 This work is the third part of a series of papers. In the first two we considered curves and varieties in a power of an elliptic curve. Here we deal with subvarieties of an abelian variety in general.
Viada, Evelina
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