Data streams are an ideal vehicle for handling power series. Stream implementations can be read off directly from simple recursive equations that define operations such as multiplication, substitution, exponentiation, and reversion of series. The bookkeeping that bedevils these algorithms when they are expressed in traditional languages is completely hidden when they are expressed in stream ter...

The division algorithm for ideals of algebraic power series satisfying Hironaka’s box condition is shown to be finite when expressed suitably in terms of the defining polynomial codes of the series. In particular, the codes of the reduced standard basis of the ideal can be constructed effectively.

We study D0L power series. We show how elementary morphisms introduced by Ehrenfeucht and Rozenberg can be used in connection with power series, characterize the sequences of rational numbers and integers which can be appear as coe cients in D0L power series and establish various decidability results. TUCS Research Group Mathematical Structures of Computer Science

Iteration semirings are Conway semirings satisfying Conway’s group identities. We show that the semirings Nrat〈〈Σ∗〉〉 of rational power series with coefficients in the semiring N of natural numbers are the free partial iteration semirings. Moreover, we characterize the semirings Nrat ∞ 〈〈Σ∗〉〉 as the free semirings in the variety of iteration semirings defined by three additional simple identitie...

The set S[[x]] of formal power series in x over a set S is the set of functions from the nonnegative integers to S. However, the way that we represent elements of S[[x]] will be as an infinite series, and operations in S[[x]] will be closely linked to the addition and multiplication of finite-degree polynomials. This paper will introduce a bit of the structure of sets of formal power series and...

with coefficients ak ∈ C (k ∈ Z ) are important in many branches of mathematics. Maple supports the computation of truncated series with its series command, and through the powerseries package [6] infinite series are available. In the latter case, the series is represented as a table of coefficients that have already been determined together with a function for computing additional coefficients...

Recently, several power estimation techniques have been proposed. Some of them can be used to accurately estimate power dissipation provided that the exact signal probability probability of a signal being logic ONE) and signal activity (probability of signal switching) of primary inputs are known. In general, very accurate specification of primary input signal probability and activity may not b...

In this paper a new method for solving fuzzy differential equation with fractional order is considered. The fuzzy solution is construct by power series in the Caputo derivatives sense. To illustrate the reliability of method some examples are provided. In this paper a new method for solving fuzzy differential equation with fractional order is considered. The fuzzy solution is construct by power...

Spectral analysis considers the problem of determining (the art of recovering) the spectral content (i.e., the distribution of power over frequency) of a stationary time series from a finite set of measurements, by means of either nonparametric or parametric techniques. This paper introduces the spectral analysis problem, motivates the definition of power spectral density functions, and reviews...