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...

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...

Absrtact: In this study, a numerical algorithm for solving a generalization of a functional differential equation known as the pantograph equation is presented. Firstly, the proposed algorithm produces an approximate polynomial solution as a power series for the problem. Then, we transform the obtained power series into Padé series form to obtain an approximate polynomial of an arbitrary order ...

Wind power point forecasting is the primary method to deal with its uncertainty. However, in many applications, the probabilistic interval of wind power is more useful than traditional point forecasting. Methods to determine the probabilistic interval of wind power point forecasting value is very essential to power system operations. Based on the bootstrap method, this paper proposed a wavelet ...

In this paper, a new identification of the Lagrange multipliers by means of the Sumudu transform, is employed to  btain a quick and accurate solution to the fractional Black-Scholes equation with the initial condition for a European option pricing problem. Undoubtedly this model is the most well known model for pricing financial derivatives. The fractional derivatives is described in Caputo sen...

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.