A classification scheme for axioms weaker than
G. Ervynck (1991)
Matematički Vesnik
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G. Ervynck (1991)
Matematički Vesnik
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Abdulatif Badenjki, Gerald G. Warnecke (2019)
Applications of Mathematics
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We give a proof of the existence of a solution of reconstruction operators used in the DG schemes in one space dimension. Some properties and error estimates of the projection and reconstruction operators are presented. Then, by applying the DG schemes to the linear advection equation, we study their stability obtaining maximal limits of the Courant numbers for several DG schemes mostly experimentally. A numerical study explains how the stencils used in the reconstruction affect...
Satoshi Takagi (2012)
Rendiconti del Seminario Matematico della Università di Padova
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David Ben-Zvi, Thomas Nevins (2011)
Journal of the European Mathematical Society
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We study the geometry of -bundles—locally projective -modules—on algebraic curves, and apply them to the study of integrable hierarchies, specifically the multicomponent Kadomtsev–Petviashvili (KP) and spin Calogero–Moser (CM) hierarchies. We show that KP hierarchies have a geometric description as flows on moduli spaces of -bundles; in particular, we prove that the local structure of -bundles is captured by the full Sato Grassmannian. The rational, trigonometric, and elliptic solutions...
Dobeš, Jiří, Deconinck, Herman
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A space-time formulation for unsteady inviscid compressible flow computations in 2D moving geometries is presented. The governing equations in Arbitrary Lagrangian-Eulerian formulation (ALE) are discretized on two layers of space-time finite elements connecting levels , and . The solution is approximated with linear variation in space (P1 triangle) combined with linear variation in time. The space-time residual from the lower layer of elements is distributed to the nodes at level...
Jeffrey Giansiracusa, Noah Giansiracusa (2022)
Kybernetika
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Given an integral scheme over a non-archimedean valued field , we construct a universal closed embedding of into a -scheme equipped with a model over the field with one element (a generalization of a toric variety). An embedding into such an ambient space determines a tropicalization of by previous work of the authors, and we show that the set-theoretic tropicalization of with respect to this universal embedding is the Berkovich analytification . Moreover, using the scheme-theoretic...
A. Mézard, M. Romagny, D. Tossici (2013)
Annales de l’institut Fourier
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Let be a discrete valuation ring of mixed characteristics , with residue field . Using work of Sekiguchi and Suwa, we construct some finite flat -models of the group scheme of -th roots of unity, which we call . We carefully set out the general framework and algebraic properties of this construction. When is perfect and is a complete totally ramified extension of the ring of Witt vectors , we provide a parallel study of the Breuil-Kisin modules of finite flat models of ,...
Oriol Farràs (2020)
Kybernetika
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A secret sharing scheme is ideal if the size of each share is equal to the size of the secret. Brickell and Davenport showed that the access structure of an ideal secret sharing scheme is determined by a matroid. Namely, the minimal authorized subsets of an ideal secret sharing scheme are in correspondence with the circuits of a matroid containing a fixed point. In this case, we say that the access structure is a matroid port. It is known that, for an access structure, being a matroid...
Ilya Tyomkin (2013)
Journal of the European Mathematical Society
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In the current paper we show that the dimension of a family of irreducible reduced curves in a given ample linear system on a toric surface over an algebraically closed field is bounded from above by , where denotes a general curve in the family. This result generalizes a famous theorem of Zariski to the case of positive characteristic. We also explore new phenomena that occur in positive characteristic: We show that the equality does not imply the nodality of even if belongs...
Amir Akbary, Adam Tyler Felix (2015)
Acta Arithmetica
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We prove several results regarding some invariants of elliptic curves on average over the family of all elliptic curves inside a box of sides A and B. As an example, let E be an elliptic curve defined over ℚ and p be a prime of good reduction for E. Let be the exponent of the group of rational points of the reduction modulo p of E over the finite field . Let be the family of elliptic curves , where |a| ≤ A and |b| ≤ B. We prove that, for any c > 1 and k∈ ℕ, )as x → ∞, as long...
David Masser, Umberto Zannier (2015)
Journal of the European Mathematical Society
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In recent papers we proved a special case of a variant of Pink’s Conjecture for a variety inside a semiabelian scheme: namely for any curve inside anything isogenous to a product of two elliptic schemes. Here we go beyond the elliptic situation by settling the crucial case of any simple abelian surface scheme defined over the field of algebraic numbers, thus confirming an earlier conjecture of Shou-Wu Zhang. This is of particular relevance in the topic, also in view of very recent counterexamples...
Herbert Lange, Christian Pauly (2009)
Journal of the European Mathematical Society
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Let be a Galois covering of smooth projective curves with Galois group the Weyl group of a simple and simply connected Lie group . For any dominant weight consider the curve . The Kanev correspondence defines an abelian subvariety of the Jacobian of . We compute the type of the polarization of the restriction of the canonical principal polarization of to in some cases. In particular, in the case of the group we obtain families of Prym-Tyurin varieties. The main idea is...
Margarida Mendes Lopes, Rita Pardini, Pietro Pirola (2014)
Journal of the European Mathematical Society
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We take up the study of the Brill-Noether loci , where is a smooth projective variety of dimension , , and is an integer. By studying the infinitesimal structure of these loci and the Petri map (defined in analogy with the case of curves), we obtain lower bounds for , where is a divisor that moves linearly on a smooth projective variety of maximal Albanese dimension. In this way we sharpen the results of [Xi] and we generalize them to dimension . In the -dimensional case...
Vikram B. Mehta, Christian Pauly (2007)
Bulletin de la Société Mathématique de France
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Let be a smooth projective curve of genus defined over an algebraically closed field of characteristic . Given a semistable vector bundle over , we show that its direct image under the Frobenius map of is again semistable. We deduce a numerical characterization of the stable rank- vector bundles , where is a line bundle over .
Gilberto Bini, John Harer (2011)
Journal of the European Mathematical Society
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Let be the moduli space of -pointed Riemann surfaces of genus . Denote by the Deligne-Mumford compactification of . In the present paper, we calculate the orbifold and the ordinary Euler characteristic of for any and such that .
Yuri Bilu, Pierre Parent, Marusia Rebolledo (2013)
Annales de l’institut Fourier
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Using the recent isogeny bounds due to Gaudron and Rémond we obtain the triviality of , for and a prime number exceeding . This includes the case of the curves . We then prove, with the help of computer calculations, that the same holds true for in the range , . The combination of those results completes the qualitative study of rational points on undertook in our previous work, with the only exception of .