gives an equation for a curve that represents the moduli problem [Γ0(p)] for elliptic curves over a perfect field of characteristic p. This moduli problem associates to such an elliptic curve its finite flat subgroup schemes of rank p. A choice of such a subgroup scheme is equivalent to an isogeny from the elliptic curve with a prescribed kernel. The j-invariants of the source and target curves...

We use the improved general mapping deformationmethod based on the generalized Jacobi elliptic functions expansionmethod to construct some of the generalized Jacobi elliptic solutions for some nonlinear partial differential equations in mathematical physics via the generalized nonlinear Klein-Gordon equation and the classical Boussinesq equations. As a result, some new generalized Jacobi ellipt...

ABSTRACT An accurate closed-form solution for the quintic Duffing equation is obtained using a cubication method. In this method the restoring force is expanded in Chebyshev polynomials and the original nonlinear differential equation is approximated by a cubic Duffing equation in which the coefficients for the linear and cubic terms depend on the initial amplitude. The replacement of the origi...

Isogenies of elliptic curves over finite fields have been well-studied, in part because there are several cryptographic applications. Using Vélu’s formula, isogenies can be constructed explicitly given their kernel. Vélu’s formula applies to elliptic curves given by a Weierstrass equation. In this paper we show how to similarly construct isogenies on Edwards curves and Huff curves. Edwards and ...

A Hydro+Cascade model has been used to describe radial and elliptic flow at the SPS and successfully predicted the radial and elliptic flow measured by the both STAR and PHENIX collaborations. Furthermore, a combined description of the radial and elliptic flow for different particle species, restricts the Equation of State(EoS) and points towards an EoS with a phase transition to the Quark Gluo...

Using a hydrodynamical model we study how the order of phase transition in the equation of state of strongly interacting matter affects single particle spectra, elliptic flow and higher order anisotropies in Au+Au collisions at RHIC ( √ sNN = 200 GeV energy). We find that the single particle spectra are independent of the order of phase transition and that the fourth harmonic v4(pT ) shows only...

The real, nonsingular elliptic solutions of the Korteweg-deVries equation are studied through the time dynamics of their poles in the complex plane. The dynamics of these poles is governed by a dynamical system with a constraint. This constraint is shown to be solvable for any finite number of poles located in the fundamental domain of the elliptic function, often in many different ways. Specia...

is derived for surface gravity waves with nearly-elliptic front, generalising the cylindrical KP equation for nearly-concentric waves. We discuss transformations between the derived equation and two existing versions of the KP equation, for nearly-plane and nearly-concentric waves. The transformations are used to construct important classes of exact solutions of the derived equation and corresp...

Some oscillation criteria for the second order semilinear elliptic differential equation

We study Halphen’s equation and provide solutions in terms of elliptic functions of the second kind. The connection between Halphen’s equation and algebro-geometric solutions of the Boussinesq hierarchy is discussed.