An extended body orbiting a compact object undergoes tidal deformations by the background gravitational field. Tidal invariants built up with the Riemann tensor and their derivatives evaluated along the worldline of the body are essential tools to investigate both geometrical and physical properties of the tidal interaction. For example, one can determine the tidal potential in the neighborhood of the body by constructing a body-fixed frame, which requires Fermi-type coordinates attached to the body itself, the latter being in turn related to the spacetime metric and curvature along the considered worldline. Similarly, in an effective field theory description of extended bodies, finite size effects are taken into account by adding to the point mass action certain nonminimal couplings which involve integrals of tidal invariants along the orbit of the body. In both cases such a computation of tidal tensors is required. Here we consider the case of a spinning body also endowed with a nonvanishing quadrupole moment in a Kerr spacetime. The structure of the body is modeled by a multipolar expansion around the "center-of-mass line" according to the Mathisson-Papapetrou-Dixon model truncated at the quadrupolar order. The quadrupole tensor is assumed to be quadratic in spin, accounting for rotational deformations. The behavior of tidal invariants of both electric and magnetic type is discussed in terms of gauge-invariant quantities when the body is moving along a circular orbit as well as in the case of an arbitrary (equatorial) motion. The analysis is completed by examining the associated eigenvalues and eigenvectors of the tidal tensors. The limiting situation of the Schwarzschild solution is also explored both in the strong field regime and in the weak field limit.

Continuing our analytic computation of the first-order self-force contribution to the "geodetic" spin precession frequency of a small spinning body orbiting a large (nonspinning) body, we provide the exact expressions of the 10 and 10.5 post-Newtonian terms. We also introduce a new approach to the analytic computation of self-force regularization parameters based on a WKB analysis of the radial and angular equations satisfied by the metric perturbations.

We study Weitzenböck's torsion and discuss its properties. Specifically, we calculate the measured components of Weitzenböck's torsion tensor for a frame field adapted to static observers in a Fermi normal coordinate system that we establish along the world line of an arbitrary accelerated observer in general relativity. A similar calculation is carried out in the standard Schwarzschild-like coordinates for static observers in the exterior Kerr spacetime; we then compare our results with the corresponding curvature components. Our work supports the contention that in the extended general relativistic framework involving both the Levi-Civita and Weitzenböck connections, curvature and torsion provide complementary representations of the gravitational field.

Continuing our analytic computation of the first-order self-force contribution to Detweiler's redshift variable we provide the exact expressions of the ninth and ninth-and-a-half post-Newtonian terms.

The influence of an arbitrary spin orientation on the quadrupolar structure of an extended body moving in a Schwarzschild spacetime is investigated. The body dynamics is described by the Mathisson-Papapetrou-Dixon model, without any restriction on the motion or simplifying assumption on the associated spin vector and quadrupole tensor, generalizing previous works. The equations of motion are solved analytically in the limit of small values of the characteristic length scales associated with the spin and quadrupole variables with respect to the characteristic length of the background curvature. The solution provides all corrections to the circular geodesic on the equatorial plane taken as the reference trajectory due to both the dipolar and quadrupolar structures of the body as well as the conditions which the nonvanishing components of the quadrupole tensor must fulfill in order for the problem to be self-consistent.

Modulated enhanced diffraction (MED) is a technique allowing the dynamic structural characterization of crystalline materials subjected to an external stimulus, which is particularly suited for in situ and operando structural investigations at synchrotron sources. Contributions from the (active) part of the crystal system that varies synchronously with the stimulus can be extracted by an offline analysis, which can only be applied in the case of periodic stimuli and linear system responses. In this paper a new decomposition approach based on multivariate analysis is proposed. The standard principal component analysis (PCA) is adapted to treat MED data: specific figures of merit based on their scores and loadings are found, and the directions of the principal components obtained by PCA are modified to maximize such figures of merit. As a result, a general method to decompose MED data, called optimum constrained components rotation (OCCR), is developed, which produces very precise results on simulated data, even in the case of nonperiodic stimuli and/or nonlinear responses. The multivariate analysis approach is able to supply in one shot both the diffraction pattern related to the active atoms (through the OCCR loadings) and the time dependence of the system response (through the OCCR scores). When applied to real data, OCCR was able to supply only the latter information, as the former was hindered by changes in abundances of different crystal phases, which occurred besides structural variations in the specific case considered. To develop a decomposition procedure able to cope with this combined effect represents the next challenge in MED analysis.

We establish a comparison result for solutions to nonlinear fully anisotropic elliptic problems by means of anisotropic symmetrization. As consequence we deduce a priori estimates for norms of the relevant solutions.

We obtain a comparison result for solutions to nonlinear fully anisotropic elliptic problems by means of anisotropic symmetrization. As consequence we deduce a priori estimates for norms of the relevant solutions.

A sharp integrability condition on the right-hand side of the p-Laplace system for all its solutions to be continuous is exhibited. Their uniform continuity is also analyzed and estimates for their modulus of continuity are provided. The relevant estimates are shown to be optimal as the right-hand side ranges in classes of rearrangement-invariant spaces, such as Lebesgue, Lorentz, Lorentz-Zygmund, and Marcinkiewicz spaces, as well as some customary Orlicz spaces.

Lo studio dell'idrologia polare e' legato alla glaciologia ma anche alla paleobio- logia e alla bioastronomia, alla planetologia. Per quest'ultima vale la similitudine fra la crosta ghiacciata dei satelliti del pianeta Giove - Europa ed Encelado - e la calotta ghiacciata Antartica, sotto cui scorre, nell'ordine, un oceano d'acqua (da accertare) e una complessa rete idrografica di 379 laghi subglaciali con torrenti col- legati al mare. Lo studio dell'idrologia polare ha un riscontro diretto e propone estrapolazioni sui pianeti. La paleobiologia e' invece interessata ai laghi subglaciali isolati, custodi di segreti della vita primordiale: microrganismi antichi, nell'oscurita', con bassissimi scambi energetici, senza contatti con altre forme di vita. Siamo al confine con la bioastronomia che ricerca sui pianeti tracce di acqua e di vita. La modellistica matematica e la simulazione numerica giungono a supporto di opera- zioni di carotaggio o, al contrario, per evitarle al fine di non contaminare queste banchedati naturali, oppure per proiezioni diagnostiche o prognostiche. Discutero' il problema dell'accertamento del primo lago subglaciale alle isole Svalbard, di cui e' traccia (da interpretare) nei rilevamenti Ground Penetrating Radar. Il modello matematico adottato contiene la descrizione della dinamica e termodinamica del si- stema ghiacciaio/lago corredato di dati da spedizione polare. Il sistema differenziale viene risolto con il metodo ai volumi finiti e uno schema implicito di secondo ordine; la tecnica di front-tracking viene adottata per la frontiera di fase evolutiva (dettagli in [1]). La procedura di validazione della congettura da noi proposta, totalmente nuova ai glaciologi, ha portato a risultati numerici con ottimo riscontro con i dati di misura e conferma la possibilita' di esistenza del lago subglaciale (conclusioni in [2]). Bibliografia [1] Mansutti, D., E. Bucchignani, J. Otero and P. Glowacki, 'Modelling and numerical sensitivity study on the conjecture of a subglacial la- ke at Amundsenisen, Svalbard', (in stampa) Appl. Math. Modelling, http://dx.doi.org/10.1016/j.apm.2014.12.043, 2015. [2] Mansutti, D., E. Bucchignani, J. Otero and P. Glowacki, 'Numerical validation of the conjecture of a subglacial lake at Amundsenisen, Svalbard', (sottomesso) Appl. Math. Modelling, 2015.

First asymptotic relations of Voronovskaya-type for rational operators of Shepard-type are shown. A positive answer in some senses to a problem on the pointwise approximation power of linear operators on equidistant nodes posed by Gavrea, Gonska and Kacs is given. Direct and converse results, computational aspects and Gruss-type inequalities are also proved. Finally an application to images compression is discussed, showing the outperformance of such operators in some senses.

The accurate segmentation of the optic disc (OD) offers an important cue to extract other retinal features in an automated diagnostic system, which in turn will assist ophthalmologists to track many retinopathy conditions such as glaucoma. Research contributions regarding the OD segmentation is on the rise, since the design of a robust automated system would help prevent blindness, for instance, by diagnosing glaucoma at an early stage and a condition known as ocular hypertension. Among the evaluated OD segmentation schemes, the active contour models (ACMs) have often been preferred by researchers, because ACMs are endowed with several attractive properties. To this end, we designed an OD segmentation scheme to infer how the performance of the well-known gradient vector flow (GVF) model compares with nine popular/recent ACM algorithms by supplying them with the initial OD contour derived from the circular Hough transform. The findings would hopefully equip a diagnostic system designer with an empirical support to ratify the choice of a specific model as we are bereft of such a comparative study. A dataset comprising 169 diverse retinal images was tested, and the segmentation results were assessed by a gold standard derived from the annotations of five domain experts. The segmented ODs from the GVF-based ACM coincide to a greater degree with those of the experts in 94% of the cases as predicted by the least overall Hausdorff distance value (33.49 +/- 18.21). Additionally, the decrease in the segmentation error due to the suggested ACM has been confirmed to be statistically significant in view of the p values (<= 1.49e-09) from the Wilcoxon signed-rank test. The mean computational time taken by the investigated approaches has also been reported. (C) 2014 Elsevier Ltd. All rights reserved.

We evaluate a mathematical model of the predator-prey population dynamics in a fragmented habitat where both migration processes between habitat patches and prey control policies are taken into account. The considered system is examined by applying the aggregation method and different dynamical scenarios are generated. The resulting implications are then discussed, their primary aim being the conservation of the wolf population in the Alta Murgia National Park, a protected area situated in the Apulian Foreland and also part of the Natura 2000 network. The Italian wolf is an endangered species and the challenge for the regional authorities is how to formulate conservation policies which enable the maintenance of the said wolf population while at the same time curbing that of the local wild boars and its negative impact on agriculture. We show that our model provides constructive suggestions in how to combine wild boar abatement programs awhile maintaining suitable ecological corridors which ensure wolf migration, thus preserving wolves from extinction.

We examine spatially explicit models described by reaction-diffusion partial differential equations for the study of predator-prey population dynamics. The numerical methods we propose are based on the coupling of a finite difference/element spatial discretization and a suitable partitioned Runge-Kutta scheme for the approximation in time. The RK scheme here implemented uses an implicit scheme for the stiff diffusive term and a partitioned RK symplectic scheme for the reaction term (IMSP schemes). We revisit some results provided in the literature for the classical Lotka-Volterra system and the Rosenzweig-MacArthur model. We then extend the approach to metapopulation dynamics in order to numerically investigate the effect of migration through a corridor connecting two habitat patches. Moreover, we analyze the synchronization properties of subpopulation dynamics, when the migration occurs through corridors of variable sizes.

In this paper we consider the final distribution of fuel oil from a storage depot to a set of petrol stations faced by an oil company, which has to decide the weekly replenishment plan for each station, and determine petrol station visiting sequences (vehicle routes) for each day of the week, assuming a fleet of homogeneous vehicles (tankers). The aim is to minimize the total distance travelled by tankers during the week, while loading tankers possibly near to their capacity in order to maximize the resource utilization. The problem is modelled as a generalization of the Periodic Vehicle Routing Problem (PVRP). Due to the large size of the real instances which the company has to deal with, we solve the problem heuristically. We propose a hybrid genetic algorithm that successfully address the problem inspired to a known hybrid genetic algorithm from the literature for the PVRP. However, the proposed algorithm adopts some techniques and features tailored for the particular fuel oil distribution problem, and it is specifically designed to deal with real instances derived from the fuel oil distribution in the European context that are profoundly different from the PVRP instances available from literature. The proposed algorithm is evaluated on a set of real case studies and on a set of randomly generated instances that hold the same characteristics of the former.

The aim of this paper is to study a Bike Sharing Touring (BST) applying a mathematical model known in operation research as Orienteering Problem (OP). Several European Cities are developing BST in order to reduce the exhaust emissions and to improve the sustainability in urban areas. The authors offer a Decision Support Tool useful for the tourist and the service's manager to organize the tourists' paths on the basis of tourists' desires, subject to usable time, place of interest position and docking station location. The model analyzed presents two innovative aspects compared to a classic OP. The first one is that the start and the arrival point of routes aren't necessary coinciding and pre-conditioned. The last one is that the knowledge of tourist tours allows to book the visit to a point of interest and doing so to optimize efficiency of the whole system and not only of the single tourist tour.

In this work we proposed an integrated support system combining a meta-heuristic algorithm and a multicriteria decision analysis method to solve an orienteering problem applied to car-pooling system. For this purpose a Genetic Algorithm (GA), an Analytical Hierarchy Process (AHP) are implemented. The research is based on the awareness that decision makers (DMs) often face situations in which different conflicting viewpoints (goals or criteria) are to be considered. Current car-pooling web platforms are focused on the exchange of information among potential users and drivers. The aim of this work is to include in web platform a decision procedure to support driver to organize the tour considering more criteria. The driver has to decide which tour does and which users to take into the trip Preliminary test are given to validate the functionality and usefulness of created integrated decision support system.

This work describes two applications of the vehicle routing problem (VRP) to the design of fixed and periodic routes. The first application is an industrial case in the field of touristic cruise planning where point of interests should be visited within exactly one of multiple time windows on a weekly time basis. The second application is in retail distribution of fuel oils where petrol stations must be refueled with given fuel oil amounts periodically within a given time horizon. The work studies the VRP models for the two described applications evaluating intersections between them and studying possible unified modeling formulation.

Bruno de Finetti è senza dubbio una delle figure più importanti per la storia della Statistica e del Calcolo delle Probabilità in Italia. Però i suoi interessi furono molto più ampi e compresero molti settori della cosiddetta matematica applicata. In particolare giocò un ruolo importante nella nascita del calcolo numerico e dell'informatica in Italia, settori che peraltro costituiscono importanti strumenti per l'applicazione dei suoi studi principali. Come è naturale questa sua attività venne svolta nell'ambito di un'intensa collaborazione con Mauro Picone e con l'Istituto Nazionale per le Applicazioni del Calcolo. Essa nasce dal comune interesse per le applicazioni della matematica in ambito economico e finanziario e raggiunge forse il suo apice nell'immediato dopoguerra, periodo in cui de Finetti ha un incarico presso l'INAC. Oltre a sviluppare ricerche comuni, si reca con Picone e Fichera negli Stati Uniti per esaminare i nuovi calcolatori elettronici, cura l'installazione all'INAC di un sistema IBM a schede perforate e conduce, di concerto con Picone, un'intensa campagna per promuovere l'arrivo in Italia di un primo calcolatore elettronico.

Eugenio Elia Levi (1883-1917) fu uno dei più grandi matematici italiani del 900, come del resto il fratello Beppo. La sua produzione scientifica fu tanto profonda quanto differenziata, venne immediatamente apprezzata negli ambienti matematici internazionali e, a distanza di un secolo, conserva grande attualità in diversi campi della matematica. Momento importantissimo per la sua formazione fu la permanenza nella Scuola Normale Superiore di Pisa. Qui, dal punto di vista scientifico, venne formato da grandi maestri come Luigi Bianchi e Ulisse Dini e, nonostante la minima differenza di età, influenzò moltissimo la formazione di Mauro Picone che lo considerò sempre un proprio maestro. Dal punto di vista politico-culturale, sempre in Normale, il Levi venne in contatto e condivise le idee di diversi giovani esponenti del socialismo riformista, con i quali condividerà gli ideali irredentisti. Tra queste amicizie ha particolare importanza quella con Giuseppe Lombardo Radice per la fitta corrispondenza che intratterranno negli anni successivi e che si estenderà anche ai fratelli di Levi, continuando anche dopo la morte di quest'ultimo. Allo scoppio del conflitto, le forti convinzioni interventiste porteranno Levi ad arruolarsi ed a rifiutare qualsiasi richiamo in università o in seconda linea finché, nelle giornate convulse che seguirono Caporetto, venne ucciso da un cecchino mentre, al comando di una compagnia di genieri, tentava di allestire una linea di difesa sopra Cormons.