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...

We introduce elliptic analogues to the Bernoulli ( resp. Euler) numbers and functions. The first aim of this paper is to state and prove that our elliptic Bernoulli and Euler functions satisfied Raabe’s formulas (cf. Theorems 3.1.1, 3.2.1). We define two kinds of elliptic Dedekind-Rademacher sums, in terms of values of our elliptic Bernoulli (resp. Euler) functions. The second aim of this paper...

Elliptic curve cryptography (ECC) is an alternative to traditional techniques for public key cryptography. It offers smaller key size without sacrificing security level. In a typical elliptic curve cryptosystem, elliptic curve point multiplication is the most computationally expensive component. So it would be more attractive to implement this unit using hardware than using software. In this pa...

A theoretical foundation for a generalization of the elliptic difference Painlevé equation to higher dimensions is provided in the framework of birational Weyl group action on the space of point configurations in general position in a projective space. By introducing an elliptic parametrization of point configurations, a realization of the Weyl group is proposed as a group of Cremona transforma...

1 I n t r o d u c t i o n Elliptic curves can be applied to public-key cryptosystems, and as such several schemes have been proposed [3, 4, 5, 6, 9, 11]. There are two typical elliptic curve cryptosystems: E1Gamal-type scheme [4, 11] and RSA-type schemes [3, 5, 6]. The security of the EIGamal-type elliptic curve cryptosystem is based on the difficulty of solving a discrete logarithm over ellipt...