We prove that if the exponent function p((.)) satisfies log-Holder continuity conditions locally and at infinity, then the fractional maximal operator M(alpha), 0 < alpha < n, maps L(p(.)) to L(q(.)), where 1/p(x) - 1/q(x) = alpha/n. We also prove a weak-type inequality corresponding to the weak (1, n/(n - a)) inequality for M(alpha). We build upon earlier work on the Hardy-Littlewood maximal operator by Cruz-Uribe, Fiorenza and Neugebauer [3]. As a consequence of these results for M(alpha), we show that the fractional integral operator I(alpha) satisfies the same norm inequalities. These in turn yield a generalization of the Sobolev embedding theorem to variable L(p) spaces.

The objective of the present paper is to develop a truly functional Bayesian method specifically designed for time series microarray data. The method allows one to identify differentially expressed genes in a time-course microarray experiment, to rank them and to estimate their expression profiles. Each gene expression profile is modeled as an expansion over some orthonormal basis, where the coefficients and the number of basis functions are estimated from the data. The proposed procedure deals successfully with various technical difficulties that arise in typical microarray experiments such as a small number of observations, non-uniform sampling intervals and missing or replicated data. The procedure allows one to account for various types of errors and offers a good compromise between nonparametric techniques and techniques based on normality assumptions. In addition, all evaluations are performed using analytic expressions, so the entire procedure requires very small computational effort. The procedure is studied using both simulated and real data, and is compared with competitive recent approaches. Finally, the procedure is applied to a case study of a human breast cancer cell line stimulated with estrogen. We succeeded in finding new significant genes that were not marked in an earlier work on the same dataset.

Precise knowledge of X-ray diffraction profile shape is crucial in the investigation of the properties of matter in crystals powder. Line-broadening analysis is the fourth pre-processing step in most of the full powder pattern fitting softwares. The final result of line-broadening analysis strongly depends on three further steps: noise filtering, removal of background signal, and peak fitting. In this work a new model independent procedure for two of the aforementioned steps (background suppression and peak fitting) is presented. The former is dealt with by using morphological mathematics, while the latter relies on the Hankel–Lanczos singular value decomposition technique. Real X-ray powder diffraction (XRPD) intensity profiles of Ceria samples are used to test the performance of the proposed procedure. Results show the robustness of this approach and its capability of efficiently improving the disentangling of instrumental broadening. These features make the proposed approach an interesting and user-friendly tool for the pre-processing of XRPD data.

Spatial distributions of heavy particles suspended in an incompressible isotropic and homogeneous turbulent flow are investigated by means of high resolution direct numerical simulations. In the dissipative range, it is shown that particles form fractal clusters with properties independent of the Reynolds number. Clustering is there optimal when the particle response time is of the order of the Kolmogorov time scale tau(eta). In the inertial range, the particle distribution is no longer scale invariant. It is, however, shown that deviations from uniformity depend on a rescaled contraction rate, which is different from the local Stokes number given by dimensional analysis. Particle distribution is characterized by voids spanning all scales of the turbulent flow; their signature in the coarse-grained mass probability distribution is an algebraic behavior at small densities.

Uno degli interventi proposti dal protocollo di Kyoto per la stabilizzazione delle concentrazionidi gas serra si riferisce alla necessità di determinare la localizzazione delle sorgenti e delle fonti ditali gas. Il metodo del bilancio di massa, implementato a partire da misure rilevate da piattaforma aerea,presenta la potenzialità di poter quantificare gli scambi gassosi superficiali su aree di diversi chilometriquadrati, permettendo una stima anche in condizioni di eterogeneità superficiale, contrariamente ai metoditradizionali. In questo studio il metodo è stato applicato ad un sito nei pressi di Forlì utilizzando dati telerilevatiad alta frequenza nello strato limite planetario. La scarsa risoluzione verticale ottenuta in fase dirilevamento dati è stata risolta attraverso un metodo di regressione non parametrico. I campi di concentrazionedel gas e del vento in corrispondenza dell'altezza dello strato limite planetario sono determinaticon un modello additivo non parametrico. Risulta che la superficie del territorio esaminato emette un flussodi anidride carbonica di 13±0.3 ?moli/m2/s, a causa della presenza di un centro industriale all'internodell'area esaminata.

We present a set of difference equations which represents the discrete counterpart of a large class of continuous model concerning the dynamics of an infection in an organism or in a host population. The limiting behavior of the discrete model is studied and a threshold parameter playing the role of the basic reproduction number is derived.

We apply the techniques of monotone and relative rearrangements to the non rearrangement invariant spaces Lp(·) (? ) with variable exponent. In particular, we show that the maps u ? L p( ·) (? ) -> k(t )u* ? L p * (·)(0, meas? ) and u ? L p( ·) (? ) -> u* ? Lp* (·) (0, meas? ) are locally ?-Ho?lderian (u * (resp. p* ) is the decreasing (resp. increasing) rearrangement of u (resp. p)). The pointwise relations for the relative rearrangement are applied to derive the Sobolev embedding with eventually discontinuous exponents.

Stationary thermography can be used for investigating the functional form of a nonlinear cooling lawthat describes heat exchanges through an inaccessible part of the boundary of a conductor. In this paper, we obtain a logarithmic stability estimate for the associated nonlinear inverse problem. This stability estimate is obtained from the convergence and sensitivity analysis of a finite difference method for the numerical solution of the Cauchy problem for Laplace's equation, based on the Störmer-Verlet scheme.

We present a numerical investigation of a degenerate nonlinear parabolic-elliptic system, which describes the chemical aggression of limestones under the attack of SO_2, in high permeability regime. This system has been introduced in the first part of this paper. We present a finite element scheme for our model and its numerical stability is given under suitable CFL conditions. Numerical tests are discussed as well as some examples of the numerical behavior of the solutions.

The interaction of a Reissner-Nordstro ̈m black hole and a charged massive particle is studied in the framework of perturbation theory. The particle backreaction is taken into account, studying the effect of general static perturbations of the hole following the approach of Zerilli. The solutions of the combined Einstein-Maxwell equations for both perturbed gravitational and electromagnetic fields to first order of the perturbation are exactly reconstructed by summing all multipoles, and are given explicit closed form expressions. The existence of a singularity-free solution of the Einstein-Maxwell system requires that the charge-to-mass ratios of the black hole and of the particle satisfy an equilibrium condition which is in general dependent on the separation between the two bodies. If the black hole is undercritically charged (i.e. its charge-to-mass ratio is less than one), the particle must be overcritically charged, in the sense that the particle must have a charge-to-mass ratio greater than one. If the charge-to-mass ratios of the black hole and of the particle are both equal to one (so that they are both critically charged, or ‘‘extreme’’), the equilibrium can exist for any separation distance, and the solution we find coincides with the linearization in the present context of the well-known Majumdar-Papapetrou solution for two extreme Reissner- Nordstro ̈m black holes. In addition to these singularity-free solutions, we also analyze the corresponding solution for the problem of a massive particle at rest near a Schwarzschild black hole, exhibiting a strut singularity on the axis between the two bodies. The relations between our perturbative solutions and the corresponding exact two-body solutions belonging to the Weyl class are also discussed.

The dependence on applied shear of the morphological and rheological properties of diffusive binary systems after a quench from the disordered state into the coexistence region is investigated. In particular the behavior of the late-time transversal size of domains L-y and of the maximum of excess viscosity (Delta eta)(M) is considered. Numerical results show the existence of two regimes corresponding to weak and strong shear separated by a shear rate of the order of gamma(c)similar to 1/t(D) where t(D) is the diffusive time. L-y and (Delta eta)(M) behave as L-y similar to gamma(-alpha) and (Delta eta)(M)similar to gamma(nu) with alpha=alpha(s)=0.18 +/- 0.02, nu=nu(s)=-2.00 +/- 0.01 and alpha=alpha(w)=0.25 +/- 0.01, nu=nu(w)=-0.68 +/- 0.04 in the strong- and weak-shear regimes, respectively. Differently from what was found in systems with fluctuating velocity field, it is confirmed that domains continue to grow at all times.

Vehicle routing and scheduling are two main issues in the hazardous material (hazmat) transportation problem. In this paper, we study the problem of managing a set of hazmat transportation requests in terms of hazmat shipment route selection and actual departure time definition. For each hazmat shipment, a set of minimum and equitable risk alternative routes from origin to destination points and a preferred departure time are given. The aim is to assign a route to each hazmat shipment and schedule these shipments on the assigned routes in order to minimize the total shipment delay, while equitably spreading the risk spatially and preventing the risk induced by vehicles traveling too close to each other. We model this hazmat shipment scheduling problem as a job-shop scheduling problem with alternative routes. No-wait constraints arise in the scheduling model as well, since, supposing that no safe area is available, when a hazmat vehicle starts traveling from the given origin it cannot stop until it arrives at the given destination. A tabu search algorithm is proposed for the problem, which is experimentally evaluated on a set of realistic test problems over a regional area, evaluating the provided solutions also with respect to the total route risk and length.

This paper deals with the generation of minimal risk paths for the road transportation of hazardous materials between an origin–destination pair of a given regional area. The main considered issue is the selection of paths that minimize the total risk of hazmat shipments while spreading the risk induced on the population in an equitable way. The problem is mathematically formulated, and two heuristic algorithms are proposed for its solution. Substantially, these procedures are modified versions of Yen's algorithm for the k-shortest path problem, which take into due consideration the risk propagation resulting from close paths and spread the risk equitably among zones of the geographical region in which the transportation network is embedded. Furthermore, a lower bound based on a Lagrangean relaxation of the given mathematical formulation is also provided. Finally, a series of computational tests, referring to a regional area is reported.

A filter based on the Hankel-Lanczos singular value decomposition (HLSVD) technique is presented and applied for the first time to X-ray diffraction (XRD) data. Synthetic and real powder XRD intensity profiles of nanocrystals are used to study the filter performances with different noise levels. Results show the robustness of the HLSVD filter and its capability to extract easily and effciently the useful crystallographic information. These characteristics make the filter an interesting and user-friendly tool for processing of XRD data.

A reliable and automatic method is applied to crystallographic data for tissue typing. The technique is based on canonical correlation analysis, a statistical method which makes use of the spectral-spatial information characterizing X-ray diffraction data measured from bone samples with implanted tissues. The performance has been compared with a standard crystallographic technique in terms of accuracy and automation. The proposed approach is able to provide reliable tissue classification with a direct tissue visualization without requiring any user interaction.