Green function for the diffusion limit of one-dimensional continuous time random walks

It is shown how the fractional probability density diffusion equation for the diffusion limit of one-dimensional continuous time random walks may be derived from a generalized Markovian Chapman-Kolmogorov equation. The non-Markovian behaviour is incorporated into the Markovian Chapman-Kolmogorov equation by postulating a Levy like distribution of waiting times as a kernel. The Chapman-Kolmogorov equation so generalised then takes on the form of a convolution integral. The dependence on the initial conditions typical of a non-Markovian process is treated by adding a time dependent term involving the survival probability to the convolution integral. In the diffusion limit these two assumptions about the past history of the process are sufficient to reproduce anomalous diffusion and relaxation behaviour of the Cole-Cole type. The Green function in the diffusion limit is calculated using the fact that the characteristic function is the Mittag-Leffler function. Fourier inversion of the characteristic function yields the Green function in terms of a Wright function. The moments of the distribution function are evaluated from the Mittag-Leffler function using the properties of characteristic functions and a relation between the powers of the second moment and higher order even moments is derived. (C) 2004 Elsevier B.V. All rights reserved.

The Growth of US Credit Unions

The growth of US credit unions during the 1990s is investigated empirically, using univariate and multivariate cross sectional and panel estimation techniques. Univariate tests of the law of proportionate effect suggest that in general large credit unions grew faster than their smaller counterparts. On average credit unions with above-average growth in one period tended to experience below-average growth in the next. Smaller credit unions tended to have more variable growth than large ones. While credit unions share a common co-operative philosophy, they differ in terms of age profile, scope for membership growth, charter type and financial structure and performance. In estimations of a multivariate growth model, most of these characteristics are found to have a significant influence on the size-growth relationship. While large state chartered credit unions grew faster than their smaller counterparts, the reverse was true for federally chartered credit unions. In general, if larger credit unions grew faster than smaller ones, they tended to do so for specific reasons: because their charters were less restrictive, because they were more efficient, or because they had a financial structure that was more conducive to growth. Therefore credit union growth was not `random', but highly systematic.

Toward Self-Assembled Ferroelectric Random Access Memories: Hard-Wired Switching Capacitor Arrays with Almost Tb/in.2 Densities

We report on the successful fabrication of arrays of switchable nanocapacitors made by harnessing the self-assembly of materials. The structures are composed of arrays of 20-40 nm diameter Pt nanowires, spaced 50-100 nm apart, electrodeposited through nanoporous alumina onto a thin film lower electrode on a silicon wafer. A thin film ferroelectric (both barium titanate (BTO) and lead zirconium titanate (PZT)) has been deposited on top of the nanowire array, followed by the deposition of thin film upper electrodes. The PZT nanocapacitors exhibit hysteresis loops with substantial remnant polarizations, while although the switching performance was inferior, the low-field characteristics of the BTO nanocapacitors show dielectric behavior comparable to conventional thin film heterostructures. While registration is not sufficient for commercial RAM production, this is nevertheless an embryonic form of the highest density hard-wired FRAM capacitor array reported to date and compares favorably with atomic force microscopy read-write densities.

Analysis of the admissions tests for teacher training in Spain and Finland: knowledge or competences

One of the most decisive factors in the quality of education and academic performance of students is quality, preparation and dedication of the teachers. The exquisite system of selecting candidates for teacher training programs is one of the fundamentals of success of the Finnish Education System. The responsibility of choosing the best students to convert them into teachers is a challenge that involves a significant reform of university admission. Achieving this goal involves the choice of strategies and educational tools in accordance to the complexity of the demands presented by the teaching profession in the digital age. This study describes, analyzes and compares the admission tests in the University of Spain (PAU) and Finland (VAKAVA), for those who wish to become professional educators, in order to understand the possible influence of these tests to select the most suitable candidates to develop into future teaching professionals. The results showed that in Spain, the entrance test to universities is developed in a general way for all the students that aspire to any field of knowledge, while in Finland, the test is specific and particular for students aspiring to the field of education. The results of this study can guide and encourage the necessary changes that have to be done in the admission tests to Spanish university in general and to teacher education faculties in particular.

Willingness to Pay for Rural Landscape Improvements: Combining Mixed Logit and Random-Effects Models

This paper reports the findings from a discrete-choice experiment designed to estimate the economic benefits associated with rural landscape improvements in Ireland. Using a mixed logit model, the panel nature of the dataset is exploited to retrieve willingness-to-pay values for every individual in the sample. This departs from customary approaches in which the willingness-to-pay estimates are normally expressed as measures of central tendency of an a priori distribution. Random-effects models for panel data are subsequently used to identify the determinants of the individual-specific willingness-to-pay estimates. In comparison with the standard methods used to incorporate individual-specific variables into the analysis of discrete-choice experiments, the analytical approach outlined in this paper is shown to add considerable explanatory power to the welfare estimates.

Random walk of magnetic field lines for different values of the energy range spectral index

An analytical nonlinear description of field-line wandering in partially statistically magnetic systems was proposed recently. In this article the influence of the wave spectrum in the energy range onto field-line random walk is investigated by applying this formulation. It is demonstrated that in all considered cases we clearly obtain a superdiffusive behavior of the field-lines. If the energy range spectral index exceeds unity a free-streaming behavior of the field-lines can be found for all relevant length-scales of turbulence. Since the superdiffusive results obtained for the slab model are exact, it seems that superdiffusion is the normal behavior of field-line wandering.