The concept of innovation in transport systems requires the satisfaction of two main objectives: the service flexibility and the costs minimization. The demand responsive transport systems (DRTS) seem to be the solution for the trade-off between flexibility and efficiency. They require the planning of travel paths (routing) and customers pick-up and drop-off times (scheduling) according to received requests, respecting the limited capacity of the fleet and time constraints (hard time windows) for each network's node, and the service time of the system. Even considering invariable conditions of the network a DRTS may operate according to a static or to a dynamic mode. In the static setting, all customers' requests are known beforehand and the DRTS returns routing and scheduling solutions by solving a Dial-a-Ride Problem (DaRP) instance which derives from the Pick-up and Delivery Problem with Time Windows (PDPTW). In reality, the static setting may be representative of a phase of reservation occurred the day before the execution of the service. In the dynamic mode, customers' requests arrive when the service is already running and, consequently, the solution may change whilst the vehicle is already travelling. In this mode it is necessary that the schedule is updated when each new request arrives and that this is done in a short time to ensure that the potential customer will not leave the system before a possible answer. In this work, we use an algorithm able to solve a dynamic multi-vehicle DaRP by managing incoming transport demand as fast as possible. The heuristics is a greedy method that tries to assign the requests to one of the fleet's vehicles finding each time the local optimum. The feature of this work is that, in addition to finding a plan schedule, it can be used for sizing the number of vehicles required to satisfy a percentage of demand that may be established before. Vehicles will be employed only when strictly necessary, in this way the costs will be minimized. The work is enriched by a series of tests with different values of the fleet's vehicles and their capacity, of time windows and of incoming requests' number. Finally, a set of performance indicators evaluate the solution planned by the heuristics.

We provide regularity properties for the inverse map f^-1 under suitable assumptions on q-distorsion function of f, in bounded domains of R^2.

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In this work we present a mathematical model for the description of the dynamical and thermodynamical evolution of a system consisting of an icefield locally underlaid by a subglacial lake occupying a bed depression. The representation of the phase change ice-water is the clue of the model. The numerical solution is based on a finite volume technique. The computational code is tested to describe a portion of the Amundsenisen Icefield, South-Spitsbergen, Svalbard, where the existence of subglacial lake has been hypothesized. The contribution of firn and snow upper layers to the system in terms of temperature fied, density and water content is shown to be non-negligible in the modelling, as it supports ice to overcome its metastable state and change into liquid phase thus forming the subglacial lake. Lake cavity depth (or, better, the bottom surface area) appears to be critical for the formation of the lake, being directly proportional to the amount of geothermal heat coming in. Numerical simulation results are consistent with the existence of the conjectured subglacial lake within the environmental conditions fixed to measured data. Improvements of ice water content modelling and boundary condition formulation are in progress.

In this paper, the lab-on-chip section for a protein assay is designed and optimized. To avoid severe reliability problems related to activated surface stability, a dynamic assay approach is adopted: protein-to-protein neutralization is performed while proteins diffuse freely in the reaction chamber. The related refraction index change is detected via an integrated interferometer. The structure is also design to provide a functional test of the reference protein solution, which is generally required for qualification for medical uses.

We consider a variational model for image segmentation proposed in Sandberg et al. (2010) [12]. In such a model the image domain is partitioned into a finite collection of subsets denoted as phases. The segmentation is unsupervised, i.e., the model finds automatically an optimal number of phases, which are not required to be connected subsets. Unsupervised segmentation is obtained by minimizing a functional of the Mumford-Shah type (Mumford and Shah, 1989 [1]), but modifying the geometric part of the Mumford-Shah energy with the introduction of a suitable scale term. The results of computer experiments discussed in [12] show that the resulting variational model has several properties which are relevant for applications. In this paper we investigate the theoretical properties of the model. We study the existence of minimizers of the corresponding functional, first looking for a weak solution in a class of phases constituted by sets of finite perimeter. Then we find various regularity properties of such minimizers, particularly we study the structure of triple junctions by determining their optimal angles.

We consider the regularization of linear inverse problems by means of the minimization of a functional formed by a term of discrepancy to data and a Mumford-Shah functional term. The discrepancy term penalizes the L 2 distance between a datum and a version of the unknown function which is filtered by means of a non-invertible linear operator. Depending on the type of the involved operator, the resulting variational problem has had several applications: image deblurring, or inverse source problems in the case of compact operators, and image inpainting in the case of suitable local operators, as well as the modeling of propagation of fracture. We present counterexamples showing that, despite this regularization, the problem is actually in general ill-posed. We provide, however, existence results of minimizers in a reasonable class of smooth functions out of piecewise Lipschitz discontinuity sets in two dimensions. The compactness arguments we developed to derive the existence results stem from geometrical and regularity properties of domains, interpolation inequalities, and classical compactness arguments in Sobolev spaces.

In the fracture model presented in this paper, the basic assumption is that the energy is the sum of two terms, one elastic and one cohesive, depending on the elastic and inelastic part of the deformation, respectively. Two variants are examined: a local model, and a nonlocal model obtained by adding a gradient term to the cohesive energy. While the local model only applies to materials which obey Drucker's postulate and only predicts catastrophic failure, the nonlocal model describes the softening regime and predicts two collapse mechanisms, one for brittle fracture and one for ductile fracture. In its nonlocal version, the model has two main advantages over the models existing in the literature. The first is that the basic elements of the theory (the yield function, hardening rule, and evolution laws) are not assumed, but are determined as necessary conditions for the existence of solutions in incremental energy minimization. This reduces to a minimum the number of independent assumptions required to construct the model. The second advantage is that, with appropriate choices of the analytical shape of the cohesive energy, it becomes possible to reproduce, with surprising accuracy, a large variety of observed experimental responses. In all cases, the model provides a description of the entire evolution, from the initial elastic regime to final rupture.

We extend the analysis of Chiba et al. [Phys. Rev. D 75, 124014 (2007)] of Solar System constraints on f(R) gravity to a class of nonminimally coupled (NMC) theories of gravity. These generalize f(R) theories by replacing the action functional of general relativity with a more general form involving two functions f1(R) and f2(R) of the Ricci scalar curvature R. While the function f1(R) is a nonlinear term in the action, analogous to f(R) gravity, the function f2(R) yields a NMC between the matter Lagrangian density Lm and the scalar curvature. The developed method allows for obtaining constraints on the admissible classes of functions f1(R) and f2(R), by requiring that predictions of NMC gravity are compatible with Solar System tests of gravity. Then we consider a NMC model which accounts for the observed accelerated expansion of the Universe and we show that such a model cannot be constrained by the present method.