Introducing elliptic, an R package for elliptic and modular functions
نویسنده
چکیده
This paper introduces the elliptic package of R routines, for numerical calculation of elliptic and related functions. Elliptic functions furnish interesting and instructive examples of many ideas of complex analysis, and package elliptic illustrates these numerically and visually. A statistical application in fluid mechanics is presented. An earlier version of this vignette was published as Hankin (2006).
منابع مشابه
Some local fixed point results under $C$-class functions with applications to coupled elliptic systems
The main objective of the paper is to state newly fixed point theorems for set-valued mappings in the framework of 0-complete partial metric spaces which speak about a location of a fixed point with respect to an initial value of the set-valued mapping by using some $C$-class functions. The results proved herein generalize, modify and unify some recent results of the existing literature. As an ...
متن کاملA two-phase free boundary problem for a semilinear elliptic equation
In this paper we study a two-phase free boundary problem for a semilinear elliptic equation on a bounded domain $Dsubset mathbb{R}^{n}$ with smooth boundary. We give some results on the growth of solutions and characterize the free boundary points in terms of homogeneous harmonic polynomials using a fundamental result of Caffarelli and Friedman regarding the representation of functions whose ...
متن کاملAn Efficient Threshold Verifiable Multi-Secret Sharing Scheme Using Generalized Jacobian of Elliptic Curves
In a (t,n)-threshold secret sharing scheme, a secret s is distributed among n participants such that any group of t or more participants can reconstruct the secret together, but no group of fewer than t participants can do. In this paper, we propose a verifiable (t,n)-threshold multi-secret sharing scheme based on Shao and Cao, and the intractability of the elliptic curve discrete logar...
متن کاملNumerical Simulation of Separation Bubble on Elliptic Cylinders Using Three-equation k-? Turbulence Model
Occurrence of laminar separation bubbles on solid walls of an elliptic cylinder has been simulated using a recently developed transitional model for boundary layer flows. Computational method is based on the solution of the Reynolds averaged Navier-Stokes (RANS) equations and the eddy-viscosity concept. Transitional model tries to simulate streamwise fluctuations, induced by freestream turbulen...
متن کاملDiffie-Hellman type key exchange protocols based on isogenies
In this paper, we propose some Diffie-Hellman type key exchange protocols using isogenies of elliptic curves. The first method which uses the endomorphism ring of an ordinary elliptic curve $ E $, is a straightforward generalization of elliptic curve Diffie-Hellman key exchange. The method uses commutativity of the endomorphism ring $ End(E) $. Then using dual isogenies, we propose...
متن کامل