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...

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...

we shall extend the results of [5] and prove that if f = z o a x ? z [[x]] is algebraic over q (x), where a = 1, ƒ 1 and if ? , ? ,..., ? are p-adic integers, then 1 ? , ? ,..., ? are linkarly independent over q if and only if (1+x) ,(1+x) ,…,(1+x) are algebraically independent over q (x) if and only if f , f ,.., f are algebraically independent over q (x)

we give a proof of the generalisation of mendes-france and van der poorten's recent result over an arbitrary field of positive characteristic and then by extending a result of carlitz, we shall introduce a class of algebraically independent series.

when power systems are expanded and connected together with weak tie lines, the low-frequency oscillations are increased and the stability margin of the power system decreases. therefore, when designing the transmission system to be used, it is necessary to maintain the dynamic stability of the power system, and to make sure to have the most possible stability margin. sssc is a facts device con...