Several modifications of DPR estimator of the tail index

In this paper, we continue the investigation of an estimator proposed in [Yu. Davydov, V. Paulauskas, and A. Račkauskas, More on p-stable convex sets in Banach spaces, J. Theor. Probab., 13:39–64, 2000] and [V. Paulauskas, A new estimator for tail index, Acta Appl. Math., 79:55–67, 2003] and considered in [V. Paulauskas and M. Vaičiulis, Once more on comparison of tail index estimators, preprint, 2010]. We propose a class of modifications of the so-called DPR estimator and demonstrate that these modifications can have better asymptotic properties than the original DPR estimator.     

On an improvement of Hill and some other estimators

In the paper, we propose a new idea in the tail-index estimation. This idea allows us to improve the asymptotic performance of the classical Hill estimator and other most popular estimators over the range of the parameters present in the second-order regular-variation condition. We prove the asymptotic normality of the introduced estimators and provide a comparison (using the asymptotic mean-squared error) with other estimators of the tail index.     

Effect of refractive index-mismatch on laser microfabrication in silica glass

We studied the peculiarities of femtosecond laser microfabrication in silica glass with a refractive index that did not exactly match the value for which the focusing optics is designed. Spherical aberrations resulting from a small refractive index mismatch were found to increase the size and distort the shape of photodamaged regions, thus reducing the spatial resolution of the microfabrication. However, these undesirable effects can be minimized, providing that the focusing depth inside the glass is not too large, and the laser intensity is kept close to the light-induced damage threshold. Received: 3 December 2001 / Accepted: 11 April 2002 / Published online: 10 September 2002 RID="*" ID="*"Corresponding author. Fax: +81-88/656-7598, E-mail: misawa@eco.tokushima-u.ac.jp     

A note on linear processes with tapered innovations

Lithuanian Mathematical Journal - In the paper, we consider the partial-sum process $$ {\sum}_{k=1}^{\left[ nt\right]}{X}_k^{(n)}, $$ where $$ \left\{{X}_n^{(n)},k\in \mathbb{Z}\right\},n\ge 1, $$...     

On operator-norm approximation of some semigroups by quasi-sectorial operators

We use some results and methods of the probability theory to improve bounds for the convergence rates in some approximation formulas for operators.     

Stimulated secondary emission from semiconductor microcavities.

We find strong influence of final-state stimulation on the time-resolved light emission dynamics from semiconductor microcavities after pulsed excitation allowing angle-resonant polariton-polariton scattering on the lower-polariton branch. The polariton dynamics can be controlled by injection of final-state polaritons at densities below a polariton saturation density of 5x10(8) cm(-2). A bosonic enhancement factor in the dynamics of up to 700 is evaluated.     

Estimation of the tail index in the max-aggregation scheme

In this paper, we continue the investigation of an estimator proposed in [V. Paulauskas and M. Vai?iulis, Several modifications of DPR estimator of the tail index, Lith. Math. J., 51(1):36?C50, 2011]. Specifically, we investigate the asymptotic behavior of the so-called DPR estimator under several mostly popular max-aggregation schemes.     

On unit roots for spatial autoregressive models

In this paper we consider the unit root problem for one rather simple autoregressive model Y_t,s=aY_t-1,s+bY_t,s-1+?_t,s on a two-dimensional lattice. We show that the growth of variance of Y_t,s is essentially different from corresponding growth in the unit root case for AR(1) or AR(2) time series models. We also show that the dimension of the lattice plays an important role: the growth of variance of autoregressive field on a d-dimensional lattice is different for d=2,3 and d≥4.     

Optical and ultrasonic monitoring of femtosecond laser filamentation in fused silica

Millimeter-long filaments and accompanying luminous plasma and defect channels created in fused silica (FS) by single focused femtosecond laser pulses with supercritical powers were probed in situ using optical imaging and contact ultrasonic techniques. Above the threshold pulse energy E_opt = 5 μJ corresponding to a few megawatt power levels pulses collapse due to self-focusing, producing channels filled by electron-hole plasma and luminescent defects, and exhibits predominantly compressive pressure transients. Analysis of the optical and ultrasonic response versus the laser pulse energy suggests that filamentary pulse propagation in the channels occurs with considerable dissipation of about ∼10 cm⁻¹. The predominant ionization mechanism is most likely associated with avalanche ionization, while the main mechanism of optical absorption is free-carrier absorption via inverse Bremsstrahlung interaction with the polar lattice.     

Laser induced memory bits in photorefractive LiNbO3 and LiTaO3

We study experimentally the formation of refractive index voxels (volume elements) in photorefractive LiNbO₃ and LiTaO₃ crystals illuminated with high irradiance femtosecond laser pulses. We used 150 fs pulses at 800 nm wavelength (energy 6–50 nJ) tightly focused inside the crystals in a single shot regime. This resulted in a formation of a micrometer size region of elevated refractive index, which may be used as memory bits in information storage/retrieval application. The maximum refractive index change of 5×10⁻⁴ was recorded in undoped LiNbO₃ at an average light intensity of ∼TW/cm² that is close to the breakdown threshold. A simple setup for photorefractive recording and in situ monitoring of the refractive index changes has been proposed. M. Sūdžius leaves from: the Institute of Materials Science and Applied Research of Vilnius University, Lithuania.