Search results for "Length"

Highly angular resolving beam separator based on total internal reflection

2019

We present an optical element for the separation of superimposed beams that only differ in angle. The beams are angularly resolved and separated by total internal reflection at an air gap between two prisms. As a showcase application, we demonstrate the separation of superimposed beams of different diffraction orders directly behind acousto-optic modulators for an operating wavelength of 800 nm. The wavelength as well as the component size can easily be adapted to meet the requirements of a wide variety of applications. The presented optical element allows one to reduce the lengths of beam paths and thus to decrease laser system size and complexity.

Diffraction-free beams in thin films

2009

The propagation and transmission of Bessel beams through nano-layered structures has been discussed recently. Within this framework we recognize the formation of unguided diffraction-free waves with the spot size approaching and occasionally surpassing the limit of a wavelength when a Bessel beam of any order n is launched onto a thin material slab with grazing incidence. On the basis of the plane-wave representation of cylindrical waves, a simple model is introduced providing an exact description of the transverse pattern of this type of diffraction-suppressed localized wave. Potential applications in surface science are put forward for consideration. Ministerio de Ciencia e Innovación (MI…

Lipschitz conditions,b-arcwise connectedness and conformal mappings

1982

Fine and Wilf's Theorem for Three periods and a Generalization of Sturmian Words

1999

AbstractWe extend the theorem of Fine and Wilf to words having three periods. We then define the set 3-PER of words of maximal length for which such result does not apply. We prove that the set 3-PER and the sequences of complexity 2n + 1, introduced by Arnoux and Rauzy to generalize Sturmian words, have the same set of factors.

On the size of transducers for bidirectional decoding of prefix codes

2012

In a previous paper [L. Giambruno and S. Mantaci, Theoret. Comput. Sci. 411 (2010) 1785–1792] a bideterministic transducer is defined for the bidirectional deciphering of words by the method introduced by Girod [ IEEE Commun. Lett. 3 (1999) 245–247]. Such a method is defined using prefix codes. Moreover a coding method, inspired by the Girod’s one, is introduced, and a transducer that allows both right-to-left and left-to-right decoding by this method is defined. It is proved also that this transducer is minimal. Here we consider the number of states of such a transducer, related to some features of the considered prefix code X . We find some bounds of such a number of states in relation wi…

Context Trees, Variable Length Markov Chains and Dynamical Sources

2012

Infinite random sequences of letters can be viewed as stochastic chains or as strings produced by a source, in the sense of information theory. The relationship between Variable Length Markov Chains (VLMC) and probabilistic dynamical sources is studied. We establish a probabilistic frame for context trees and VLMC and we prove that any VLMC is a dynamical source for which we explicitly build the mapping. On two examples, the "comb" and the "bamboo blossom", we find a necessary and sufficient condition for the existence and the uniqueness of a stationary probability measure for the VLMC. These two examples are detailed in order to provide the associated Dirichlet series as well as the genera…

On a fundamental variational lemma for extremal quasiconformal mappings

1986

Burrows-Wheeler transform and Run-Length Enconding

2017

In this paper we study the clustering effect of the Burrows-Wheeler Transform (BWT) from a combinatorial viewpoint. In particular, given a word w we define the BWT-clustering ratio of w as the ratio between the number of clusters produced by BWT and the number of the clusters of w. The number of clusters of a word is measured by its Run-Length Encoding. We show that the BWT-clustering ratio ranges in ]0, 2]. Moreover, given a rational number \(r\,\in \,]0,2]\), it is possible to find infinitely many words having BWT-clustering ratio equal to r. Finally, we show how the words can be classified according to their BWT-clustering ratio. The behavior of such a parameter is studied for very well-…

Characterizing varieties of colength ≤4

2009

Let A be an associative algebra over a field F of characteristic zero, and let χ n (A), n = 1,2,…, be the sequence of cocharacters of A. For every n ≥ 1, let l n (A) denote the nth colength of A, counting the number of S n -irreducibles appearing in χ n (A). In this article, we classify the algebras A such that the sequence of colengths l n (A), n = 1,2,…, is bounded by four. Moreover we construct a finite number of algebras A 1,…, A d , such that l n (A) ≤ 4 if and only if A 1,…, A d  ∉ var(A).

Fractal Dimension Logarithmic Differences Method for Low Voltage Series Arc Fault Detection

2021

Series arc faults introduce singularities in the current signal and changes over time. Fractal dimension can be used to characterize the dynamic behaviour of the current signal by providing a degree of signal chaos. This measure of irregularity exhibits changes in signal behaviour that can suitably be used as a basis for series arc fault detection. In this paper, an efficient low voltage series arc fault detection method based on the logarithmic differences of the estimate of the fractal dimension of the current signal using the multiresolution length-based method is presented. The discrete wavelet transform and the hard thresholding denoising with the universal threshold are also used. Exp…