Results 11 to 20 of about 50 (43)
Lagrangian structures and multidimensional consistency [PDF]
, 2010 The conventional point of view is that the Lagrangian is a scalar object (or equivalently a volume form), which through the Euler-Lagrange equations provides us with one single equation (i.e., one per component of the dependent variable ...
Lobb, Sarah Beverley
core +6 more sources
Finiteness theorems on elliptical billiards and a variant of the dynamical Mordell–Lang conjecture
Proceedings of the London Mathematical Society, Volume 127, Issue 5, Page 1268-1337, November 2023., 2023 Abstract We offer some theorems, mainly finiteness results, for certain patterns in elliptical billiards, related to periodic trajectories; these seem to be the first finiteness results in this context. For instance, if two players hit a ball at a given position and with directions forming a fixed angle in (0,π)$(0,\pi )$, there are only finitely many ...
Pietro Corvaja, Umberto Zannier
wiley +1 more source
A sharp upper bound for the 2‐torsion of class groups of multiquadratic fields
Mathematika, Volume 68, Issue 1, Page 237-258, January 2022., 2022 Abstract Let K be a multiquadratic extension of Q$\mathbb {Q}$ and let Cl+(K)$\text{Cl}^{+}(K)$ be its narrow class group. Recently, the authors (Koymans and Pagano, Int. Math. Res. Not. 2022 (2022), no. 4, 2772–2823) gave a bound for |Cl+(K)[2]|$|\text{Cl}^{+}(K)[2]|$ only in terms of the degree of K and the number of ramifying primes.
Peter Koymans, Carlo Pagano
wiley +1 more source
Continued Fractions and Hankel Determinants from Hyperelliptic Curves
Communications on Pure and Applied Mathematics, Volume 74, Issue 11, Page 2310-2347, November 2021., 2021 Abstract Following van der Poorten, we consider a family of nonlinear maps that are generated from the continued fraction expansion of a function on a hyperelliptic curve of genus g. Using the connection with the classical theory of J‐fractions and orthogonal polynomials, we show that in the simplest case g = 1 this provides a straightforward ...
Andrew N. W. Hone
wiley +1 more source
IET Electric Power Applications, Volume 15, Issue 1, Page 63-78, January 2021., 2021 Abstract Generalized predictive control (GPC) is promising for permanent magnet synchronous machine drive systems, due to its outstanding dynamic performance and disturbance rejection capability. However, the speed measurement noise introduced by the encoder and the unmodelled disturbances introduced by the non‐ideal machine characteristics deteriorate
Tao Wang +5 more
wiley +1 more source
Integrality and the Laurent phenomenon for Somos 4 and Somos 5 sequences [PDF]
, 2008 Somos 4 sequences are a family of sequences defined by a fourth-order quadratic recurrence relation with constant coefficients. For particular choices of the coefficients and the four initial data, such recurrences can yield sequences of integers.
Swart, Christine, Hone, Andrew N.W.
core +1 more source
Central L‐values of elliptic curves and local polynomials
Proceedings of the London Mathematical Society, Volume 120, Issue 5, Page 742-769, May 2020., 2020 Abstract Here we study the recently introduced notion of a locally harmonic Maass form and its applications to the theory of L‐functions. In particular, we find a criterion for vanishing of certain twisted central L‐values of a family of elliptic curves, whereby vanishing occurs precisely when the values of two finite sums over canonical binary ...
Stephan Ehlen +3 more
wiley +1 more source
A finiteness theorem for universal m$m$‐gonal forms
Bulletin of the London Mathematical Society, Volume 57, Issue 2, Page 625-637, February 2025.Abstract In this paper, we study the universal m$m$‐gonal forms. More precisely, we study the growth of the size of the finite set {1,2,…,γm}$\lbrace 1,2,\ldots, \gamma _m\rbrace$ (γm$\gamma _m$ asymptotically increases as m$m$ increases) which characterize the universality of m$m$‐gonal forms.
Byeong Moon Kim, Dayoon Park
wiley +1 more source
Laurent Polynomials and Superintegrable Maps [PDF]
, 2007 This article is dedicated to the memory of Vadim Kuznetsov, and begins with some of the author's recollections of him. Thereafter, a brief review of Somos sequences is provided, with particular focus being made on the integrable structure of Somos-4 ...
Andrew N.W. Hone, Hone, Andrew N.W.
core
Journal of the London Mathematical Society, Volume 110, Issue 4, October 2024.Abstract Using a two‐dimensional version of the delta method, we establish an asymptotic formula for the number of rational points of bounded height on non‐singular complete intersections of cubic and quadric hypersurfaces of dimension at least 23 over Fq(t)$\mathbb {F}_q(t)$, provided char(Fq)>3$\operatorname{char}(\mathbb {F}_q)>3$.
Jakob Glas
wiley +1 more source