The M-Wright function in time-fractional diffusion processes: a tutorial survey

In the present review we survey the properties of a transcendental function of the Wright type, nowadays known as M-Wright function, entering as a probability density in a relevant class of self-similar stochastic processes that we generally refer to as time-fractional diffusion processes. Indeed, the master equations governing these processes generalize the standard diffusion equation by means of time-integral operators interpreted as derivatives of fractional order. When these generalized diffusion processes are properly characterized with stationary increments, the M-Wright function is shown to play the same key role as the Gaussian density in the standard and fractional Brownian motions. Furthermore, these processes provide stochastic models suitable for describing phenomena of anomalous diffusion of both slow and fast type.Comment: 32 pages, 3 figure

The two forms of fractional relaxation of distributed order

The first-order differential equation of exponential relaxation can be generalized by using either the fractional derivative in the Riemann-Liouville (R-L) sense and in the Caputo (C) sense, both of a single order less than 1. The two forms turn out to be equivalent. When, however we use fractional derivatives of distributed order (between zero and 1), the equivalence is lost, in particular on the asymptotic behaviour of the fundamental solution at small and large times. We give an outline of the theory providing the general form of the solution in terms of an integral of Laplace type over a positive measure depending on the order-distribution. We consider with some detail two cases of fractional relaxation of distributed order: the double-order and the uniformly distributed order discussing the differences between the R-L and C approaches. For all the cases considered we exhibit plots of the solutions for moderate and large times.Comment: 18 pages, 4 figures. International Symposium on Mathematical Methods in Engineering, (MME06), Ankara, Turkey, April 27-29, 200

Dose influence on the PMMA e-resist for the development of high-aspect ratio and reproducible sub-micrometric structures by electron beam lithography

In this work, a statistical process control method is presented showing the accuracy and the reliability obtained with of PMMA E-resist AR-P 672, using an Elphy Quantum Electron Beam Lithography module integrated on a FE-SEM Zeiss Auriga instrument. Reproducible nanostructures with an high aspect ratio between e-resist thickness and width of written geometric structure are shown. Detailed investigation of geometry features are investigated with dimension in the range of 200nm to 1-m. The adopted method will show how tuning the Area Dose factor and the PMMA thickness it was possible to determine the correct and reproducible parameters that allows to obtain well defined electron-beam features with a 4:1 aspect ratio. Such high aspect ratio opens the possibility to realize an electron-beam lithography lift-off process by using a standard e-beam resist. © 2016 Author(s)

Time-fractional diffusion of distributed order

The partial differential equation of Gaussian diffusion is generalized by using the time-fractional derivative of distributed order between 0 and 1, in both the Riemann-Liouville (R-L) and the Caputo (C) sense. For a general distribution of time orders we provide the fundamental solution, that is still a probability density, in terms of an integral of Laplace type. The kernel depends on the type of the assumed fractional derivative except for the single order case where the two approaches turn to be equivalent. We consider with some detail two cases of order distribution: the double-order and the uniformly distributed order. For these cases we exhibit plots of the corresponding fundamental solutions and their variance, pointing out the remarkable difference between the two approaches for small and large times.Comment: 30 pages, 4 figures. International Workshop on Fractional Differentiation and its Applications (FDA06), 19-21 July 2006, Porto, Portugal. Journal of Vibration and Control, in press (2007

Not invasive analyses on a tin-bronze dagger from Jericho. A case study

Tin-bronze makes its appearance in Southern Levant during the Early Bronze IV, the post-urban phase of the last centuries of the 3rdmillennium BC, when arsenical copper was still the most widespread copper alloy. Only from the following Middle Bronze Age tin-bronze will be the utmost spread alloy. The adoption of tin as alloying metal purports new technological skills, and a changed trade supply system, through new routes, thanks to itinerant coppersmiths. The examination of dagger TS.14.143 found in an EB IV (2300-2000 BC) tomb at Jericho by mean of trace elements and Energy Dispersive X-ray Diffraction analyses, provided info about its metal composition and technology. The detection of tin, testified only by a few specimens at the site so far, allows some reflections about the beginning of diffusion tin-bronze, and the presence of a small-scale melting activity in the post-urban phase in the key-site of Jericho

A panel technique for the analysis of technology convergence: The case of the Italian regions

Differences in productivity levels represent a major component of the large cross-country differences in per capita income observed in international datasets and even in some regional ones. Nowadays, few economists would dispute neither this finding, nor that differences in productivity reflects – among other things – differences in technology levels. More controversial is the question of whether such differences in technology are stationary or temporary – that is, whether technology convergence is taking place, at what speed, under what conditions. This state of affairs is the result of several different difficulties faced by the empirical analysis on cross-country differences in per capita income growth rates. Recently, things have improved on both the analytical and the empirical side. On the analytical side, simple models in which technology convergence and capital-deepening can be studied within a common framework are now available. In these models the transitional dynamics is simple enough to be useful for empirical analysis [for instance, De la Fuente (1996) and (1997)]. On the empirical side, Islam (1995) has shown that we can test for the presence of technology heterogeneity in cross-country convergence analysis by using an appropriate fixed-effect panel estimator. The contribution of the present paper is on the empirical side. We propose a method designed to test whether part of the observed economic convergence is due to technology convergence. The method is based on the contribution by Islam (1995), but it extends it as follows. Islam’s technique was originally designed – and is currently applied – to measure cross-country differences in technology levels, assuming that such (relative) differences are at their stationary values and therefore that no technology convergence is present. The extension proposed in this paper builds on the a standard implication of models of technology convergence. If such convergence is present, the cross-sectional variance of the logs of our measure of technology should decreases over time approaching its stationary value. Alternatively, if technology convergence is absent, the variance is at its stationary value and no significant time-trend should be detected in its value. We exploit this difference to test for the presence of technology convergence in the data. First, we estimate the convergence equation over several sub-periods and use the values of the individual intercepts to compute the TFP levels. Then, we obtain the cross-section variance of the logs of our measures of TFP for each sub-period, and check whether the observed pattern is consistent either with catching-up hypothesis or with the hypothesis that the current degree of technology heterogeneity is at its stationary value. In this paper we use a panel dataset of the Italian regions, 1960-95. We apply our proposed methodology to the Italian case because it is notoriously characterized by a remarkable degree of regional heterogeneity. In spite of being one of the best known cases of regional divide, no explicit analysis of technology convergence across Italian regions is available yet. We use dynamic panel techniques (LSDV and GMM) to estimates our growth regressions. We split the whole sample period in several sub-periods to check for the presence of technology convergence. Our preliminary results reveal a significant presence of technology convergence, which reached its peak between the first and the second sub-period, and stayed significant but at a slower pace in later sub-periods. The emerging picture points to the simultaneous presence of technology convergence in a context otherwise characterized by weak output per-worker convergence. This is consistent with some recent results based on international datasets (e.g. Dowrick and Rogers [OEP (2002]).

How to Measure the Unobservable: A Panel Technique for the Analysis of TFP Convergence

This paper proposes a fixed-effect panel methodology that enables us to simultaneously take into account both TFP convergence and the traditional neoclassical-type of convergence. We analyse a sample of Italian regions between 1963 and 1993 and find strong evidence that both mechanisms were at work during the process of aggregate regional convergence observed in Italy up to the mid-seventies. Finally, we find that our TFP estimates are highly positively correlated with standard human capital measures, where the latter is not statistically significant in growth regressions. This evidence confirms one of the hypotheses of the Nelson and Phelps approach, namely that human capital is the main determinant of technological catch-up. Our results are robust to the use of different estimation procedures such as simple LSDV, Kiviet-corrected LSDV, and GMM à la Arellano and Bond.TFP, Panel data, Regional convergence

Prediction of fluid responsiveness in ventilated critically ill patients

In critical care, hemodynamic monitoring has been extensively studied over the last decades as an essential tool to improve patients’ outcomes. Hemodynamic optimization is the key to provide the supply of oxygen and metabolic substrates to tissues according to their metabolic needs. Obtaining hemodynamic stabilization is particularly challenging in the context of circulatory shock. Distinguishing patients which are going to benefit from fluid resuscitation, from others for which administration of large amounts of fluids is detrimental is of paramount importance. Numerous techniques aimed at demonstrate fluid responsiveness in the critically ill patients have been developed over the years. This paper presents a comprehensive review of the various static and dynamic measurements used to study fluid responsiveness in critically ill patients with cardiocirculatory shock

Electrophoretic deposition of cobalt oxide anodes for alkaline membrane water electrolyzer

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How to measure the unobservable: a panel technique for the analysis of TFP convergence

This paper proposes a fixed-effect panel methodology that enables us to simultaneously take into account both TFP convergence and the traditional neoclassical-type of convergence. We analyse a sample of Italian regions between 1963 and 1993 and find strong evidence that both mechanisms were at work during the process of aggregate regional convergence observed in Italy up to the mid-seventies. Finally, we find that our TFP estimates are highly positively correlated with standard human capital measures, where the latter is not statistically significant in growth regressions. This evidence confirms one of the hypothesis of the Nelson and Phelps approach, namely that human capital is the main determinant of technological catch-up. Our results are robust to the use of different estimation procedures such as simple LSDV, Kiviet-corrected LSDV, and GMM à la Arellano and Bond