To process the vibration signal fault diagnosis automatically and effectively, a method to calculate the generalized fractal dimension (Dq) based on the traditional G-P correlation dimension algorithm is presented. First, the vibration signal, a kind of random fractal that meets the statistical self-similarity, is reconstructed according to the phase space reconstruction theory. Second, for var...

We construct perturbation series for the qth moment of eigenfunctions of various critical random-matrix ensembles in the strong multifractality regime close to localization. Contrary to previous investigations, our results are valid in the region q<1/2. Our findings allow one to verify, at first leading orders in the strong multifractality limit, the symmetry relation for anomalous fractal dime...

is surjective. If W is a Q-vector space, Q-algebra or Q-Lie algebra then we write WC for the correspondingC-vector space (respectively, C-algebra orC-Lie algebra) W ⊗Q C. Let f(x) ∈ C[x] be a polynomial of degree n ≥ 2 without multiple roots. Suppose that p is a prime that does not divide n and a positive integer q = p is a power of p. As usual, φ(q) = (p − 1)p denotes the Euler function. Let u...

Introduction Blind source separation (BSS) refers to the problem of recovering signals from several observed linear mixtures (e.g., [1]). In this paper we deal with the convolutive mixing case as encountered, e.g., in acoustic environments, and aim at finding a corresponding demixing system, whose output signals yq(n), q = 1, . . . , P are described by yq(n) = ∑P p=1 ∑L−1 κ=0 wpq,κxp(n−κ), and ...

From scaling arguments and numerical simulations, we investigate the properties of the generalized elastic model (GEM) that is used to describe various physical systems such as polymers, membranes, single-file systems, or rough interfaces. We compare analytical and numerical results for the subdiffusion exponent β characterizing the growth of the mean squared displacement 〈(δh)(2)〉 of the field...

We present a fully automated framework to estimate derivatives nonparametrically without estimating the regression function. Derivative estimation plays an important role in the exploration of structures in curves (jump detection and discontinuities), comparison of regression curves, analysis of human growth data, etc. Hence, the study of estimating derivatives is equally important as regressio...

The demand of reliable statistics for small areas, when only reduced sizes of the samples are available, has promoted the development of small area estimation methods. In particular, an approach that is now widely used is based on linear mixed models. Chambers & Tzavidis (2006) have recently proposed an approach for small area estimation that is based on M-quantile models. However, when the fun...

Sufficient conditions for the uniform convergence of polynomials Pniz) of best qth power approximation to a given function /(z) of a complex variable on a smooth curve Y were presented in an early paper by Jackson [1]. Although his theorem has found frequent application in approximation theory (see [2]), only slight extensions of the result are to be found in the literature. The present paper g...

This paper shows a mathematical formalization, algorithms and computation software of volume optimal cycles, which are useful to understand geometric features shown in a persistence diagram. Volume optimal cycles give us concrete and optimal homologous structures, such as rings or cavities, on a given data. The key idea is the optimality on (q + 1)-chain complex for a qth homology generator. Th...

Ti, i = 1, . . . ,m the ith end-to-end task in the system Tij , j = 1, . . . , ti the jth subtask of Ti cij the estimated execution time of Tij when the processor holding Tij runs at the highest processor frequency ri the task rate of Ti and its subtasks Tij , j = 1, . . . , ti Ri = {γi1, . . . , γil} the predefined set of ri Pq , q = 1, . . . , n the qth processor in the system Sq the set of s...