A rational elliptic balance method is introduced to obtain exact and approximate solutions of nonlinear oscillators by using Jacobi elliptic functions. To illustrate the applicability of the proposed rational elliptic forms in the solution of nonlinear oscillators, we first investigate the exact solution of the non-homogenous, undamped Duffing equation. Then, we introduce first and second order...

In this paper, we give an explicit description of the complex and p-adic polylogarithms for elliptic curves using the Kronecker theta function. We prove in particular that when the elliptic curve has complex multiplication and good reduction at p, then the specializations to torsion points of the p-adic elliptic polylogarithm are related to p-adic Eisenstein-Kronecker numbers, proving a p-adic ...

Signcryption is a new cryptographic approach which provides authentication and encryption simultaneously in a single logical step. The aim is to reduce the cost of signature-then-encryption approach. This cost includes computational cost and communication cost. Furthermore some signcryption schemes are based on RSA while some are based on elliptic curve. This paper provides a critical review of...

that is both analytic (as a mapping of complex manifolds) and algebraic: addition of points in E(C) corresponds to addition in C modulo the lattice L. This correspondence between lattices and elliptic curves over C is known as the Uniformization Theorem; we will spend this lecture and part of the next proving it. To make the correspondence explicit, we need to specify the map Φ from C/L and an ...

This paper describes synthesizable VDHL implementation of elliptic curve Point Multiplication. Elliptic curves used for ECC are defined over mathematical structures called Galois fields. Based on the theory of ECC, this paper has carried out Modular addition/subtraction, EC Point doubling/addition, Modular multiplicative inversion, EC point multiplier, projective to affine coordinates conversio...

This paper is concerned with the construction of extremal elliptic K3 surfaces. It gives a complete treatment of those fibrations which can be derived from rational elliptic surfaces by easy manipulations of their Weierstrass equations. In particular, this approach enables us to find explicit equations for 38 semi-stable extremal elliptic K3 fibrations, 32 of which are indeed defined over Q. Th...

brain-computer interfaces (bci) record brain signals, analyze and translate them into control commands which are relayed to output devices that carry out desired actions. these systems do not use normal neuromuscular output pathways. actually, the principal goal of bci systems is to provide better life style for physically-challenged people which are suffered from cerebral palsy, amyotrophic la...

We start from an interpretation of the BC2-symmetric “Type I” (elliptic Dixon) elliptic hypergeometric integral evaluation as a formula for a Casoratian of the elliptic hypergeometric equation, and give an extension to higher-dimensional integrals and higher-order hypergeometric functions. This allows us to prove the corresponding elliptic beta integral and transformation formula in a new way, ...

Differential elliptic flow out to p⊥ ∼ 5 GeV/c is calculated using the MPC elastic parton cascade model for Au+Au at Ecm ∼ 130 A GeV. The results are compared to recent STAR/RHIC elliptic flow data. An elliptic flow pattern comparable to the data seems to require initial parton densities at least twice higher than the predicted by the HIJING model. Elliptic flow is also shown to be sensitive to...

The rank conjecture says that rank of an elliptic curve is one less the arithmetic complexity of the corresponding non-commutative torus. We prove the conjecture for elliptic curves E(K) over a number field K. As a corollary, one gets a simple estimate for the rank in terms of the length of period of a continued fraction attached to the E(K). As an illustration, we consider a family of elliptic...