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

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

Generation of an ultrastable 578 nm laser for Yb lattice clock

In this paper we described the development and the characterization of a 578 nm laser source to be the clock laser for an Ytterbium Lattice Optical clock. Two independent laser sources have been realized and the characterization of the stability with a beat note technique is presente

investigation of bearings overloads due to misaligned splined shafts

Abstract Bearings may be subjected to overloads due to shaft unwanted loads, caused, as an example, by tiling moments related to spline coupling misalignment. Misalignment is mainly generated by manufacturing of mounting errors (due to machining tolerances) or by the transmission working conditions. These kind of overload is critical because may reduce both bearing life and system efficiency, moreover it is quite complicated to be evaluated. In this work, the overload generated on bearings supporting a misaligned splined shafts have been investigated by means of a commercial simulation software (Romax Designer). The simulations have been performed considering a standard transmission scheme composed of two shafts connected by a spline coupling and supported by four roller bearings (two for each shaft), mounted in isostatic configuration. The effect of spline coupling teeth microgeometry has been taken into account along with the misalignment angle magnitude and the torque level. In particular, the influence of these parameters on teeth contact pressure has been evaluated, as tilting moment is mainly driven by the contact pressure distribution among engaging teeth and by the position of maximum pressure distribution along teeth in axial direction. Results obtained in this work may be useful to designers, suggesting some basic criteria to reduce the bearings overload, allowing designing more reliable and efficient machines

Editors' Introduction

Emilio Betti was not only one of the greatest Romanists and jurists of the contemporary era, but he was also a historian and philosopher. As a legal scholar, his writings on the great themes of legal his-tory and on the philosophers who have dealt with them certainly de-serve reconsideration and critical evaluation. In addition, Betti’s anal-ysis of the role of jurists and their prudential deserves attention. These include analyses and reflections on the different eras of Ro-man history, both during the Republic and in subsequent eras, which are still of absolute relevance today. In particular, it is the debate on pandectics and the importance of the critique of European pandectics that marks an epochal shift in the study of law. Betti was an eminent scholar of law, who studied it in all its forms, always studying law from a historical and dynamic perspective, and had been a teacher not only of Roman law, but of various legal disciplines, and above all of subjects that had the current law as its object, in particular con-temporary law

Novel Findings about Double-Loaded Curcumin-in-HPβcyclodextrin-in Liposomes: Effects on the Lipid Bilayer and Drug Release

In this study, the encapsulation of curcumin (Cur) in “drug-in-cyclodextrin-in-liposomes (DCL)” by following the double-loading technique (DL) was proposed, giving rise to DCL–DL. The aim was to analyze the effect of cyclodextrin (CD) on the physicochemical, stability, and drug-release properties of liposomes. After selecting didodecyldimethylammonium bromide (DDAB) as the cationic lipid, DCL–DL was formulated by adding 2-hydroxypropyl-α/β/γ-CD (HPβCD)–Cur complexes into the aqueous phase. A competitive effect of cholesterol (Cho) for the CD cavity was found, so cholesteryl hemisuccinate (Chems) was used. The optimal composition of the DCL–DL bilayer was obtained by applying Taguchi methodology and regression analysis. Vesicles showed a lower drug encapsulation efficiency compared to conventional liposomes (CL) and CL containing HPβCD in the aqueous phase. However, the presence of HPβCD significantly increased vesicle deformability and Cur antioxidant activity over time. In addition, drug release profiles showed a sustained release after an initial burst effect, fitting to the Korsmeyer-Peppas kinetic model. Moreover, a direct correlation between the area under the curve (AUC) of dissolution profiles and flexibility of liposomes was obtained. It can be concluded that these “drug-in-cyclodextrin-in-deformable” liposomes in the presence of HPβCD may be a promising carrier for increasing the entrapment efficiency and stability of Cur without compromising the integrity of the liposome bilayer

Non-Markovian stochastic processes and their applications: from anomalous diffusion to time series analysis

This work provides a forward step in the study and comprehension of the relationships between stochastic processes and a certain class of integral-partial differential equation, which can be used in order to model anomalous diffusion and transport in statistical physics. In the first part, we brought the reader through the fundamental notions of probability and stochastic processes, stochastic integration and stochastic differential equations as well. In particular, within the study of H-sssi processes, we focused on fractional Brownian motion (fBm) and its discrete-time increment process, the fractional Gaussian noise (fGn), which provide examples of non-Markovian Gaussian processes. The fGn, together with stationary FARIMA processes, is widely used in the modeling and estimation of long-memory, or long-range dependence (LRD). Time series manifesting long-range dependence, are often observed in nature especially in physics, meteorology, climatology, but also in hydrology, geophysics, economy and many others. We deepely studied LRD, giving many real data examples, providing statistical analysis and introducing parametric methods of estimation. Then, we introduced the theory of fractional integrals and derivatives, which indeed turns out to be very appropriate for studying and modeling systems with long-memory properties. After having introduced the basics concepts, we provided many examples and applications. For instance, we investigated the relaxation equation with distributed order time-fractional derivatives, which describes models characterized by a strong memory component and can be used to model relaxation in complex systems, which deviates from the classical exponential Debye pattern. Then, we focused in the study of generalizations of the standard diffusion equation, by passing through the preliminary study of the fractional forward drift equation. Such generalizations have been obtained by using fractional integrals and derivatives of distributed orders. In order to find a connection between the anomalous diffusion described by these equations and the long-range dependence, we introduced and studied the generalized grey Brownian motion (ggBm), which is actually a parametric class of H-sssi processes, which have indeed marginal probability density function evolving in time according to a partial integro-differential equation of fractional type. The ggBm is of course Non-Markovian. All around the work, we have remarked many times that, starting from a master equation of a probability density function f(x,t), it is always possible to define an equivalence class of stochastic processes with the same marginal density function f(x,t). All these processes provide suitable stochastic models for the starting equation. Studying the ggBm, we just focused on a subclass made up of processes with stationary increments. The ggBm has been defined canonically in the so called grey noise space. However, we have been able to provide a characterization notwithstanding the underline probability space. We also pointed out that that the generalized grey Brownian motion is a direct generalization of a Gaussian process and in particular it generalizes Brownain motion and fractional Brownain motion as well. Finally, we introduced and analyzed a more general class of diffusion type equations related to certain non-Markovian stochastic processes. We started from the forward drift equation, which have been made non-local in time by the introduction of a suitable chosen memory kernel K(t). The resulting non-Markovian equation has been interpreted in a natural way as the evolution equation of the marginal density function of a random time process l(t). We then consider the subordinated process Y(t)=X(l(t)) where X(t) is a Markovian diffusion. The corresponding time-evolution of the marginal density function of Y(t) is governed by a non-Markovian Fokker-Planck equation which involves the same memory kernel K(t). We developed several applications and derived the exact solutions. Moreover, we considered different stochastic models for the given equations, providing path simulations

Prove di tossicità da S C P nell'ovino: nota 7.: rilievi sul comportamento della microflora ruminale

During chronic and acute toxicity trials on ovines, fed with an alkanegrown SCP, observations were also made on the behaviour of the ruminaI microflora. The different diet supplied to both experimental and control groups of animals, did not seem to have affected the total count and the total numbers of Starch digesters, Cellulose digesters and Proteolytic bacteria. During the chronic toxicity test, 194 strains of yeast were identified belonging to the following species: Candida boidinii, Candida slooffii, Candida tropicalis, Cryptococcus albidus var. albidus, Cryptococcus albidus var. diffluens, Cryptococcus dimennae, Cryptococcus kuetzingii, Rhodotorula glutinis var. dairenensis, Rhodotorula glutinis var. glutinis, Rhodotorula graminis, Rhodotorula pallida, Rhodotorula rubra, Torulopsis versatilis, Trichosporon cutaneum, Debaryomyces hansenii, Debaryomyces phaffi, Debaryomyces tamarii, Saccharomyces vafer . The yeast species that were isolated were not so different from those discovered by other authors in similar researches, carried cut, however, in animals fed differently. A marked diffusion of the genus Debaryomyces was to be observed, together with a notable lipolytic and caseinolytic activity in most of the strains isolated. At first the introduction of SCP in the diet at concentrations of 15% and 40% seemed to favour the multiplication of the yeasts in the rumen fluid, but their numbers diminished towards the end of both test in all groups under observation. The type of protein given, does not seem to have affected even the species of yeasts that are usually lodged in the animals rumen. Screening of the isolated strains is now in course for the SCP production on glucose, lactose, xylose, starch, fruit and citrus pulps, and other conventional substrata

Remote Sensing Image Classification Using Attribute Filters Defined over the Tree of Shapes

International audience—Remotely sensed images with very high spatial resolution provide a detailed representation of the surveyed scene with a geometrical resolution that at the present can be up to 30 cm (WorldView-3). A set of powerful image processing operators have been defined in the mathematical morphology framework. Among those, connected operators (e.g., attribute filters) have proven their effectiveness in processing very high resolution images. Attribute filters are based on attributes which can be efficiently implemented on tree-based image representations. In this work, we considered the definition of min, max, direct and subtractive filter rules for the computation of attribute filters over the tree of shapes representation. We study their performance on the classification of remotely sensed images. We compare the classification results over the tree of shapes with the results obtained when the same rules are applied on the component trees. The random forest is used as a baseline classifier and the experiments are conducted using multispectral data sets acquired by QuickBird and IKONOS sensors over urban areas