Elliptic hypergeometric series form a natural generalization of hypergeometric and basic hypergeometric (or q-) series. It is surprising that they were introduced only very recently, by Frenkel and Turaev [FT], who expressed the 6j-symbols corresponding to certain elliptic solutions of the Yang–Baxter equation, cf. [DJ], in terms of the 10ω9-sums defined below. It is expected that elliptic hype...

Radial and elliptic flow in noncentral heavy-ion collisions can constrain the effective equation of state (EOS) of the excited nuclear matter. To this end, a model combining relativistic hydrodynamics and a hadronic transport code [Sorge, Phys. Rev. C 52, 3291 (1995)] is developed. For an EOS with a first-order phase transition, the model reproduces both the radial and elliptic flow data at the...

where z and a are some parameters. We give solutions of the equation (1-1) in terms of the elliptic and hyperelliptic ψ functions. In section 2, we give an elliptic solution of this equation. Section 3 contains our main subject, which is based upon the recent studies on ψ function [C, Ma2, MÔ, Ô1, Ô2]. The ψ function is defended over an algebraic curve itself embedded in its Jacobian rather tha...

1. Introduction. In [Z], Zagier describes several methods for explicitly computing (large) integral points on models of elliptic curves defined over Q. Here we are interested in the computation of all integral points on a given Weierstraß equation for an elliptic curve E/Q, but not merely by reducing the original diophantine equation to an equivalent finite set of Thue equations which are subse...

We prove the existence and multiplicity of solutions for a nonhomogeneous elliptic equation involving decaying cylindrical potential and critical exponent.

Let Ω ⊂ RN be the upper half strip with a hole. In this paper, we show there exists a positive higher energy solution of semilinear elliptic equations in Ω and describe the dynamic systems of solutions of equation (1) in various Ω. We also show there exist at least two positive solutions of perturbed semilinear elliptic equations in Ω.

We discuss a discretization approach for the p Laplacian equation and a variational inequality associated to fourth order elliptic operators, via a meshless approach based on duality theory. MSC: 35J20, 35J25, 65N99. keywords: nonlinear elliptic equations, Fenchel theorem, approximation, meshless method.

We construct a family of second-order linear difference equations parametrized by the hypergeometric solution of the elliptic Painlevé equation (or higher-order analogues), and admitting a large family of monodromy-preserving deformations. The solutions are certain semiclassical biorthogonal functions (and their Cauchy transforms), biorthogonal with respect to higher-order analogues of Spiridon...

We show that to solve the discrete log problem in a subgroup of order p of an elliptic curve over the finite field of characteristic p one needs O(ln p) operations in this field. Let Fq be the finite field of q = p l elements. We define an elliptic curve E over Fq to be an equation of the form

This paper is concerned with the analysis of blow-up solutions to the elliptic-elliptic Davey-Stewartson system, which appears in the description of the evolution of surface water waves. We prove a mass concentration property for H-solutions, analogous to the one known for the L-critical nonlinear Schrödinger equation. We also prove a mass concentration result for L -solutions.