The main result of this paper is that an elliptic curve having good reduction everywhere over a real quadratic field has a 2-rational point under certain hypotheses (primarily on class numbers of related fields). It extends the earlier case in which no ramification at 2 is allowed. Small fields satisfying the hypotheses are then found, and in four cases the non-existence of such elliptic curves...

The peak-to-average power (PAPR) is one of the main challenges in multicarrier transmissions. Aiming at reducing the PAPR, we propose a residue number system (RNS)-based OFDM parallel transmission scheme. The key idea of the proposed scheme is to utilize the parallel property of RNS to convert the input signals into the parallel smaller residue signals while utilizing the characteristic of RNS ...

Let A be a commutative ring and I an ideal of A with a reduction Q. In this paper we give an upper bound on the reduction number of I with respect to Q, when a suitable family of ideals in A is given. As a corollary it follows that if some ideal J containing I satisfies J = QJ , then I = QI, where v denotes the number of generators of J/I as an A-module.