In this paper we make use of the power series facility of Scratchpad2 , a symbolic computer language under development at the IBM Research Mathematics Department , to construct algebraic ECC on the elliptic Riemann surface of genus one. The construction method described uses products of elliptic theta series with rational characteristics and finite field coefficients to define the projective co...

This paper proposes a unified frame work for identification and control using time moments(TM) in which delta operator is used. Dynamic systems modelling with delta operator provides a unified framework in rapprochement between discrete-time systems and its continuous-time counterpart at fast sampling The theory of delta time moments(DTM) is utilized to develop algorithms for load frequency con...

A novel non-paraxial Time-Domain technique based on Pade approximant for modeling ultra short optical pulses has been formulated and tested. The new method is an extension to the parabolic Time-Domain Beam Propagation Method (TDBPM) that solves the time domain wave equation along one direction that allows the time window to follow the evolution of the pulse. In this work the technique was appli...

We propose a modification of the famous step-by-step process of solving the Nevanlinna-Pick problems for Nevanlinna functions. The process in question gives rise to three-term recurrence relations with coefficients depending on the spectral parameter. These relations can be rewritten in the matrix form by means of two Jacobi matrices. As a result of the considered approach, we prove a convergen...

This work is aimed at the development of a state observer (steady state Kalman filter) for a multivariable system with unknown time delays, which is subjected to unmeasured disturbances. To design such a filter, we explore the feasibility of capturing system dynamics using generalized orthonormal basis filters (GOBF). A two step identification procedure is proposed by exploiting the fact that t...

Let F(z) be a vector-valued function, F : e _ eN, which is analytic at z= 0 and meromorphic .. in a neighbourhood ofz = 0, and let its Maclaurin series be given. In this work we develop vector­ valued rational approximation procedures for F(z) by applying vector extrapolation methods to the sequence of partial sums of its Maclaurin series. We analyze some of the algebraic and analytic propertie...