1,721,076 research outputs found
Construction of multifractal measures in dynamical systems from their invariance properties
No full textOrthogonal polynomials associated to almost periodic Schrödinger operators. A trend towards random orthogonal polynomials
No full textAbstractWe introduce a special class of Schrödinger type H-operators in l2 as (φ,Hψ) = ∑∞n=0 φ∗Rn+1ψn+1 +Rnψn−1,Rn being a nonnegative real number. H satisfies the renormalization equation HD = D(H2 - λ), with λ real, λ ⩾ 2. D is the decimation operator defined by (φ,Dψ) = ∑∞n=0φ∗nψ2n. A consequence of the renormalization equation is that the Rn fulfil the recursion relation R0 = 0, R2nR2n−1 = Rn, R2n + R2n+1 = λ. From the above relations, it can be shown that the Rn are quasi-periodic functions of their index n.The components of the eigenfunctions of H corresponding to the eigenvalue x are the orthonormalized polynomials Pn (x) satisfying Rn+1Pn+1(x) + RnPn−1(x) = (x)Pn(x). The spectrum of H is the support of the measure associated to the polynomials. In the present case it is a compact perfect set of Lebesque measure zero (Cantor set). It is therefore purely singular continuous.We are led to study classes of orthogonal polynomials whose three-terms recursive relations are quasi periodic functions of their index. We will present several results, conjectures and open questions which may have relevant physical applications. We study the randomness of the eigenfunctions, and we discuss their algorithmic complexity
Universal statistical behavior of the complex zeros of Wiener transfer functions
No full textTo N real random variables the sample autocorrelation coefficients, which are also the N Fourier coefficients of a measure on the unit circle are associated. The polynomials orthogonal with respect to this measure define the transfer functions of the Wiener-Levinson predictors. We show that the statistics of the zeros of those random polynomials exhibits a universal law of crystallization on a circle of radius [1 - (lnN)/2n], n being the order of the predictor. These results are supported by extensive computer experiments and backed by a theoretical scaling argument in the asymptotic domain In N << n << N. These results are independent of the nature of the noise and robust for signals of finite length N
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
- …
