On the evaluation of modular polynomials

We present two algorithms that, given a prime ell and an elliptic curve E/Fq, directly compute the polynomial Phi_ell(j(E),Y) in Fq[Y] whose roots are the j-invariants of the elliptic curves that are ell-isogenous to E. We do not assume that the modular polynomial Phi_ell(X,Y) is given. The algorithms may be adapted to handle other types of modular polynomials, and we consider applications to point counting and the computation of endomorphism rings. We demonstrate the practical efficiency of the algorithms by setting a new point-counting record, modulo a prime q with more than 5,000 decimal digits, and by evaluating a modular polynomial of level ell = 100,019.Comment: 19 pages, corrected a typo in equation (8) and added equation (9

Iterative Time-Varying Filter Algorithm Based on Discrete Linear Chirp Transform

Denoising of broadband non--stationary signals is a challenging problem in communication systems. In this paper, we introduce a time-varying filter algorithm based on the discrete linear chirp transform (DLCT), which provides local signal decomposition in terms of linear chirps. The method relies on the ability of the DLCT for providing a sparse representation to a wide class of broadband signals. The performance of the proposed algorithm is compared with the discrete fractional Fourier transform (DFrFT) filtering algorithm. Simulation results show that the DLCT algorithm provides better performance than the DFrFT algorithm and consequently achieves high quality filtering.Comment: 6 pages, conference pape

European Principles Governing National Administrative Proceedings

It is critical that the process of developing general principles of Community administrative law continue, notwithstanding the marked diversity of supranational administrative proceedings. Because Community law has traditionally been focused on activities relevant to the common market, an asymmetry between the regulation of market-related administrative proceedings and other types of administrative proceedings has developed

Germany and Spain lead changes towards international insolvencies in Europe

With the Council regulation (EC) No. 1346/2000 of 29 May 2000 on insolvency proceedings, that came into effect May 31, 2002 the European Union has introduced a legal framework for dealing with cross-border insolvency proceedings. In order to achieve the aim of improving the efficiency and effectiveness of insolvency proceedings having cross-border effects within the European Community, the provisions on jurisdiction, recognition and applicable law in this area are contained in a Regulation, a Community law measure which is binding and directly applicable in Member States. The goals of the Regulation, with 47 articles, are to enable cross-border insolvency proceedings to operate efficiently and effectively, to provide for co-ordination of the measures to be taken with regard to the debtor’s assets and to avoid forum shopping. The Insolvency Regulation, therefore, provides rules for the international jurisdiction of a court in a Member State for the opening of insolvency proceedings, the (automatic) recognition of these proceedings in other Member States and the powers of the ‘liquidator’ in the other Member States. The Regulation also deals with important choice of law (or: private international law) provisions. The Regulation is directly applicable in the Member States3 for all insolvency proceedings opened after 31 May 2002