Non-local approximation of the Mumford-Shah functional

The Mumford-Shah functional, introduced to study image segmentation problems, is approximated in the sense of -convergence by a sequence of non-local integral functionals. Received June 6, 1996 / Accepted July 11, 1996     

New AlDy(Ni,Co) glasses - the influence of pre-aging on decomposition and modelling of the crystallisation

The decomposition of AlDy₆Ni₁₀ and AlDy₈Ni₆Co₂ glasses prepared by melt spinning after different pre-aging regimes was investigated. The modelling of the transformation at the glass transition and the crystallisation was tested by a more general Johnson-Mehl-Avrami-Kolmogorov model and by the determination of the local kinetic parameter. The relaxation was tested with an lnt kinetic model after Gibbs.     

Classification of real moduli spaces over genus 2 curves

We classify, in terms of simple algebraic equations, the fixed point sets of the moduli space of stable bundles over genus 2 curves with anti-holomorphic involutions.Research supported by SRF of University of Missouri.     

Estimation of intrinsic processes affected by additive fractal noise

Fractal Gaussian models have been widely used to represent the singular behavior of phenomena arising in different applied fields; for example, fractional Brownian motion and fractional Gaussian noise are considered as monofractal models in subsurface hydrology and geophysical studies Mandelbrot [The Fractal Geometry of Nature, Freeman Press, San Francisco, 1982 [13]]. In this paper, we address the problem of least-squares linear estimation of an intrinsic fractal input random field from the observation of an output random field affected by fractal noise (see Angulo et al. [Estimation and filtering of fractional generalised random fields, J. Austral. Math. Soc. A 69 (2000) 1-26 [2]], Ruiz-Medina et al. [Fractional generalized random fields on bounded domains, Stochastic Anal. Appl. 21 (2003a) 465-492], Ruiz-Medina et al. [Fractional-order regularization and wavelet approximation to the inverse estimation problem for random fields, J. Multivariate Anal. 85 (2003b) 192-216]. Conditions on the fractality order of the additive noise are studied to obtain a bounded inversion of the associated Wiener-Hopf equation. A stable solution is then obtained in terms of orthogonal bases of the reproducing kernel Hilbert spaces associated with the random fields involved. Such bases are constructed from orthonormal wavelet bases (see Angulo and Ruiz-Medina [Multiresolution approximation to the stochastic inverse problem, Adv. in Appl. Probab. 31 (1999) 1039-1057], Angulo et al. [Wavelet-based orthogonal expansions of fractional generalized random fields on bounded domains, Theoret. Probab. Math. Stat. (2004), in press]). A simulation study is carried out to illustrate the influence of the fractality orders of the output random field and the fractal additive noise on the stability of the solution derived.     

Regular variation of order 1 nonlinear AR-ARCH models

We prove both geometric ergodicity and regular variation of the stationary distribution for a class of nonlinear stochastic recursions that includes nonlinear AR-ARCH models of order 1. The Lyapounov exponent for the model, the index of regular variation and the spectral measure for the regular variation all are characterized by a simple two-state Markov chain.     

Stationary remaining service time conditional on queue length

In Mandelbaum and Yechiali [The conditional residual service time in the M/G/1 queue, http://www.math.tau.ac.il/∼uriy/publications (No. 30a), 1979] and in Fakinos [The expected remaining service time in a single-server queue, Oper. Res. 30 (1982) 1014-1018] a simple formula is derived for the (stationary) expected remaining service time in a M/G/1 queue, conditional on the number of customers in the system. We give a short new proof of the formula using Rate Conservation Law, and generalize to handle higher moments.     

Scientific legacy of Stanley Ruby

Stanley L. Ruby (1924–2004) made major contributions to Mössbauer spectroscopy and was the first to suggest the feasibility of observing the Mössbauer effect using synchrotron radiation. In this article we recall his scientific legacy that have inspired his scientific colleagues.     

Mössbauer studies of the re-entrant spin-glass behaviour of Fe–Al alloys

Fe–Al alloys around the concentration of 30 at. % Al present re-entrant spin-glass behaviour at low temperatures. This behaviour is not completely understood and Mössbauer spectroscopy, combined with other experimental techniques, is useful to describe and explain this behaviour. Results show that the Mössbauer spectra coincide with the magnetic behaviour showed in literature and they can be explained as a magnetic cluster system whose magnetic clusters are getting smaller when the temperature is decreasing. When the temperature is reaching to the spin-glass transition at 92 K the spins in the paramagnetic matrix are moving slower and below this transition the spins are completely frozen.     

Advances in constant-velocity Mössbauer instrumentation

A prototype of a programmable constant-velocity scaler is presented. This instrument allows the acquisition of partial Mössbauer spectra in selected energy regions using standard drivers and transducers. It can be fully operated by a remote application, thus data acquisition can be automated. The instrument consists of a programmable counter and a constant-velocity reference. The reference waveform generator is amplitude modulated with 13-bit resolution, and is programmable in a wide range of frequencies and waveforms in order to optimize the performance of the transducer. The counter is compatible with most standard SCA, and is configured as a rate-meter that provides counts per selectable time slice at the programmed velocity. As a demonstration of the instrument applications, a partial Mössbauer spectrum of a natural iron foil was taken. Only positive energies were studied in 512 channels, accumulating 20 s per channel. A line width of 0.20 mm/s was achieved, performing with an efficiency of 80%.