Near-transform-limited picosecond pulses from a gain-switched InGaAs diode laser with fiber Bragg gratings

We have generated near-transform-limited picosecond pulses(ΔτΔν≈0.45) from a gain-switched diode laser using periodic and chirped fiber Bragg gratings. This configuration reduced the spectral bandwidth from 11 to 0.08 nm and the pulse duration was reduced, from 30 to<18 ps. Average and peak powers of 27 and 770 mW, respectively, were obtained.

An Algorithm for Fresnel Diffraction Computing Based on Fractional Fourier Transform

The fractional Fourier transform (FrFT) is used for the solution of the diffraction integral in optics. A scanning approach is proposed for finding the optimal FrFT order. In this way, the process of diffraction computing is speeded up. The basic algorithm and the intermediate results at each stage are demonstrated.

On some Generalizations of a Class of Discrete Functions

In this paper we examine discrete functions that depend on their variables in a particular way, namely the H-functions. The results obtained in this work make the “construction” of these functions possible. H-functions are generalized, as well as their matrix representation by Latin hypercubes.

Models of Alternating Renewal Process at Discrete Time

We study a class of models used with success in the modelling of climatological sequences. These models are based on the notion of renewal. At first, we examine the probabilistic aspects of these models to afterwards study the estimation of their parameters and their asymptotical properties, in particular the consistence and the normality. We will discuss for applications, two particular classes of alternating renewal processes at discrete time. The first class is defined by laws of sojourn time that are translated negative binomial laws and the second class, suggested by Green is deduced from alternating renewal process in continuous time with sojourn time laws which are exponential laws with parameters α^0 and α^1 respectively.

Online learning in discrete hidden Markov models

We present and analyze three different online algorithms for learning in discrete Hidden Markov Models (HMMs) and compare their performance with the Baldi-Chauvin Algorithm. Using the Kullback-Leibler divergence as a measure of the generalization error we draw learning curves in simplified situations and compare the results. The performance for learning drifting concepts of one of the presented algorithms is analyzed and compared with the Baldi-Chauvin algorithm in the same situations. A brief discussion about learning and symmetry breaking based on our results is also presented. © 2006 American Institute of Physics.

Optimization of Discrete-Time, Stochastic Systems

* This research was supported by a grant from the Greek Ministry of Industry and Technology.

Finding the Relationship between a Search Algorithm and a Class of Functions on Discrete Space by Exhaustive Search

* The work is supported by RFBR, grant 04-01-00858-a.

Multiplierless DCT Algorithm for Image Compression Applications

This paper presents a novel error-free (infinite-precision) architecture for the fast implementation of 8x8 2-D Discrete Cosine Transform. The architecture uses a new algebraic integer encoding of a 1-D radix-8 DCT that allows the separable computation of a 2-D 8x8 DCT without any intermediate number representation conversions. This is a considerable improvement on previously introduced algebraic integer encoding techniques to compute both DCT and IDCT which eliminates the requirements to approximate the transformation matrix ele- ments by obtaining their exact representations and hence mapping the transcendental functions without any errors. Apart from the multiplication-free nature, this new mapping scheme fits to this algorithm, eliminating any computational or quantization errors and resulting short-word-length and high-speed-design.

Discrete solitons in coupled active lasing cavities

We examine the existence and stability of discrete spatial solitons in coupled nonlinear lasing cavities (waveguide resonators), addressing the case of active defocusing media, where the gain exceeds damping in the low-amplitude limit. A new family of stable localized structures is found: these are bright and gray cavity solitons representing the connections between homogeneous and inhomogeneous states. Solitons of this type can be controlled by discrete diffraction and are stable when the bistability of homogenous states is absent. © 2012 Optical Society of America.

The Hough Transform and Uncertainity

The paper deals with the generalisations of the Hough Transform making it the mean for analysing uncertainty. Some results related Hough Transform for Euclidean spaces are represented. These latter use the powerful means of the Generalised Inverse for description the Transform by itself as well as its Accumulator Function.

On the Range of the Fourier Transform Associated with the Spherical Mean Operator

We characterize the range of some spaces of functions by the Fourier transform associated with the spherical mean operator R and we give a new description of the Schwartz spaces. Next, we prove a Paley-Wiener and a Paley-Wiener-Schawrtz theorems.

Discrete Models of Time-Fractional Diffusion in a Potential Well

Mathematics Subject Classification: 26A33, 45K05, 60J60, 60G50, 65N06, 80-99.

An Analogue of Beurling-Hörmander’s Theorem for the Dunkl-Bessel Transform

Mathematics Subject Classification: Primary 35R10, Secondary 44A15

Hankel Transform in Quantum Calculus and Applications

Mathematics Subject Classification: 44A15, 33D15, 81Q99

Spectrum of Functions for the Dunkl Transform on R^d

Mathematics Subject Classification: 42B10