Search results for "Generalized Jacobian"

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The periods of the generalized Jacobian of a complex elliptic curve

2015

Abstract We show that the toroidal Lie group G = ℂ2/Λ, where Λ is the lattice generated by (1, 0), (0, 1) and (τ̂, τ͂), with τ̂ ∉ ℝ, is isomorphic to the generalized Jacobian JL of the complex elliptic curve C with modulus τ̂, defined by any divisor class L ≡ (M) + (N) of C fulfilling M − N = [℘ (τ͂) : ℘´(τ͂) : 1] ∈ C. This follows from an apparently new relation between the Weierstrass sigma and elliptic functions.

Elliptic curve point multiplicationQuarter periodGeneralized JacobianModular elliptic curveJacobian curveMathematical analysisHessian form of an elliptic curveGeometry and TopologyGeneralized Jacobians toroidal Lie groupsSettore MAT/03 - GeometriaTripling-oriented Doche–Icart–Kohel curveMathematicsJacobi elliptic functions
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The PCHIP subdivision scheme

2016

In this paper we propose and analyze a nonlinear subdivision scheme based on the monotononicity-preserving third order Hermite-type interpolatory technique implemented in the PCHIP package in Matlab. We prove the convergence and the stability of the PCHIP nonlinear subdivision process by employing a novel technique based on the study of the generalized Jacobian of the first difference scheme. MTM2011-22741

Scheme (programming language)Generalized JacobianStability (learning theory)MathematicsofComputing_NUMERICALANALYSIS010103 numerical & computational mathematics01 natural sciencesConvergence (routing)ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION0101 mathematicsMATLABMathematicscomputer.programming_languageSubdivisionNonlinear subdivision schemesbusiness.industryApplied MathematicsProcess (computing)Approximation order010101 applied mathematicsComputational MathematicsThird orderbusinessConvergencecomputerAlgorithmStability
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