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 role of Mittag-Leffler functions in anomalous relaxation

The inertia-corrected Debye model of rotational Brownian motion of polar molecules was generalized by Coffey et al. [Phys. Rev. E, 65, 32 102 (2002)] to describe fractional dynamics and anomalous rotational diffusion. The linear- response theory of the normalized complex susceptibility was given in terms of a Laplace transform and as a function of frequency. The angular-velocity correlation function was parametrized via fractal Mittag-Leffler functions. Here we apply the latter method and complex-contour integral- representation methods to determine the original time-dependent amplitude as an inverse Laplace transform using both analytical and numerical approaches, as appropriate. (C) 2004 Elsevier B.V. All rights reserved.

Welfare Effort and Poverty from the Monetary and Capabilities Approach: A Cross-Country Analysis in Latin American and the Caribbean (1990-2010)

There is abundant empirical evidence on the negative relationship between welfare effort and poverty. However, poverty indicators traditionally used have been representative of the monetary approach, excluding its multidimensional reality from the analysis. Using three regression techniques for the period 1990-2010 and controlling for demographic and cyclical factors, this paper examines the relationship between social spending per capita —as the indicator of welfare effort— and poverty in up to 21 countries of the region. The proportion of the population with an income below its national basic basket of goods and services (PM1) and the proportion of population with an income below 50% of the median income per capita (PM2) were the two poverty indicators considered from the monetarist approach to measure poverty. From the capability approach the proportion of the population with food inadequacy (PC1) and the proportion of the population without access to improved water sources or sanitation facilities (PC2) were used. The fi ndings confi rm that social spending is actually useful to explain changes in poverty (PM1, PC1 and PC2), as there is a high negative and signifi cant correlation between the variables before and after controlling for demographic and cyclical factors. In two regression techniques, social spending per capita did not show a negative relationship with the PM2. Countries with greater welfare effort for the period 1990-2010 were not necessarily those with the lowest level of poverty. Ultimately social spending per capita was more useful to explain changes in poverty from the capability approach.

Polarisation analysis of VUV synchrotron radiation emitted from a bending magnet source in the energy range 20-50 eV: A comparison between measurements and theoretical predictions

The results of a study to characterise the polarisation properties of the photon beam emerging from beamline 5D, mounted on a bending magnet source at the Synchrotron Radiation Source, Daresbury Laboratory, are presented. The expectation values for the Stokes parameters corresponding to the light transmitted by the beamline have been calculated by combining ray-tracing and optical methods. The polarisation of the light at the source is modified both by the beamline geometry and by the reflections at the optical components. Although it is often assumed that the polarising properties of grazing incidence optics are negligible, this assumption leads to rather inaccurate results in the VUV region. A study of the reflectivity shows that even at incidence angles (theta(i) = 80-85degrees) which are far from the Brewster angle (theta(B) similar to 45degrees for VUV and soft X-ray radiation) the residual changes in the amplitudes of the reflected light can result in non-negligible polarisation effects. Furthermore, reflection at grazing incidence gives rise to a substantial change in the phase, and this has the effect of rotating the elliptically polarised state. Theoretical Stokes parameters have been compared with full polarisation measurements obtained using a reflection polarimeter in the energy range 20-40 eV. (C) 2003 Elsevier B.V. All rights reserved.

Factores determinantes del uso de Internet en la comercialización del aceite de oliva. Análisis del sector en Cataluña

Las cooperativas son entidades con una gran presencia económica y social en España, y tienen una gran influencia en la economía rural de las zonas donde están ubicadas. El principal objetivo del presente trabajo es el análisis del uso de las nuevas tecnologías por parte de las cooperativas agroalimentarias, centrándose en las productoras de aceite de oliva para determinar los principales factores que condicionan su comportamiento en la Red. En el presente estudio se analizan sus sitios web y se determina qué tipo de información aporta, tanto datos generales como datos de comercialización. A partir de los resultados obtenidos, se busca la relación que pueda existir entre el tamaño de la cooperativa, su actividad exportadora o la actividad de comercio electrónico con la presencia online, mediante una regresión logística. De esta manera podremos conocer si realmente la implantación de nuevas tecnologías en las cooperativas permite desarrollar una óptima actividad económica.

Clinical Features of Dominant and Recessive Interferon γ Receptor 1 Deficiencies

Background Interferon ? receptor 1 (IFN? R1) deficiency is a primary immunodeficiency with allelic dominant and recessive mutations characterised clinically by severe infections with mycobacteria. We aimed to compare the clinical features of recessive and dominant IFN?R1 deficiencies. Methods We obtained data from a large cohort of patients worldwide. We assessed these people by medical histories, records, and genetic and immunological studies. Data were abstracted onto a standard form. Findings We identified 22 patients with recessive complete IFN?R1 deficiency and 38 with dominant partial deficiency. BCG and environmental mycobacteria were the most frequent pathogens. In recessive patients, 17 (77%) had environmental mycobacterial disease and all nine BCG-vaccinated patients had BCG disease. In dominant patients, 30 (79%) had environmental mycobacterial disease and 11 (73%) of 15 BCG-vaccinated patients had BCG disease. Compared with dominant patients, those with recessive deficiency were younger at onset of first environmental mycobacterial disease (mean 3·1 years [SD 2·5] vs 13·4 years [14·3], p=0·001), had more mycobacterial disease episodes (19 vs 8 per 100 person-years of observation, p=0·0001), had more severe mycobacterial disease (mean number of organs infected by Mycobacterium avium complex 4·1 [SD 0·8] vs 2·0 [1·1], p=0·004), had shorter mean disease-free intervals (1·6 years [SD 1·4] vs 7·2 years [7·6], p