A moment symbolic representation of Lévy processes with applications

By using a symbolic method, known in the literature as the classical umbral calculus, a symbolic representation of Lévy processes is given and a new family of time-space harmonic polynomials with respect to such processes, which includes and generalizes the exponential complete Bell polynomials, is introduced. The usefulness of time-space harmonic polynomials with respect to Lévy processes is that it is a martingale the stochastic process obtained by replacing the indeterminate x of the polynomials with a Lévy process, whereas the Lévy process does not necessarily have this property. Therefore to find such polynomials could be particularly meaningful for applications. This new family includes Hermite polynomials, time-space harmonic with respect to Brownian motion, Poisson-Charlier polynomials with respect to Poisson processes, Laguerre and actuarial polynomials with respect to Gamma processes , Meixner polynomials of the first kind with respect to Pascal processes, Euler, Bernoulli, Krawtchuk, and pseudo-Narumi polynomials with respect to suitable random walks. The role played by cumulants is stressed and brought to the light, either in the symbolic representation of Lévy processes and their infinite divisibility property, either in the generalization, via umbral Kailath-Segall formula, of the well-known formulae giving elementary symmetric polynomials in terms of power sum symmetric polynomials. The expression of the family of time-space harmonic polynomials here introduced has some connections with the so-called moment representation of various families of multivariate polynomials. Such moment representation has been studied here for the first time in connection with the time-space harmonic property with respect to suitable symbolic multivariate Lévy processes. In particular, multivariate Hermite polynomials and their properties have been studied in connection with a symbolic version of the multivariate Brownian motion, while multivariate Bernoulli and Euler polynomials are represented as powers of multivariate polynomials which are time-space harmonic with respect to suitable multivariate Lévy processes.

Optimization of purification procedures in organic semiconductor synthesis for improving the performances of organic field-effect transistors

The aim of the research activity focused on the investigation of the correlation between the degree of purity in terms of chemical dopants in organic small molecule semiconductors and their electrical and optoelectronic performances once introduced as active material in devices. The first step of the work was addressed to the study of the electrical performances variation of two commercial organic semiconductors after being processed by means of thermal sublimation process. In particular, the p-type 2,2′′′-Dihexyl-2,2′:5′,2′′:5′′,2′′′-quaterthiophene (DH4T) semiconductor and the n-type 2,2′′′- Perfluoro-Dihexyl-2,2′:5′,2′′:5′′,2′′′-quaterthiophene (DFH4T) semiconductor underwent several sublimation cycles, with consequent improvement of the electrical performances in terms of charge mobility and threshold voltage, highlighting the benefits brought by this treatment to the electric properties of the discussed semiconductors in OFET devices by the removal of residual impurities. The second step consisted in the provision of a metal-free synthesis of DH4T, which was successfully prepared without organometallic reagents or catalysts in collaboration with Dr. Manuela Melucci from ISOF-CNR Institute in Bologna. Indeed the experimental work demonstrated that those compounds are responsible for the electrical degradation by intentionally doping the semiconductor obtained by metal-free method by Tetrakis(triphenylphosphine)palladium(0) (Pd(PPh3)4) and Tributyltin chloride (Bu3SnCl), as well as with an organic impurity, like 5-hexyl-2,2':5',2''-terthiophene (HexT3) at, in different concentrations (1, 5 and 10% w/w). After completing the entire evaluation process loop, from fabricating OFET devices by vacuum sublimation with implemented intentionally-doped batches to the final electrical characterization in inherent-atmosphere conditions, commercial DH4T, metal-free DH4T and the intentionally-doped DH4T were systematically compared. Indeed, the fabrication of OFET based on doped DH4T clearly pointed out that the vacuum sublimation is still an inherent and efficient purification method for crude semiconductors, but also a reliable way to fabricate high performing devices.

Models and Algorihtm for the Optimization of Real-World Routing and Logistics Problems

Logistics involves planning, managing, and organizing the flows of goods from the point of origin to the point of destination in order to meet some requirements. Logistics and transportation aspects are very important and represent a relevant costs for producing and shipping companies, but also for public administration and private citizens. The optimization of resources and the improvement in the organization of operations is crucial for all branches of logistics, from the operation management to the transportation. As we will have the chance to see in this work, optimization techniques, models, and algorithms represent important methods to solve the always new and more complex problems arising in different segments of logistics. Many operation management and transportation problems are related to the optimization class of problems called Vehicle Routing Problems (VRPs). In this work, we consider several real-world deterministic and stochastic problems that are included in the wide class of the VRPs, and we solve them by means of exact and heuristic methods. We treat three classes of real-world routing and logistics problems. We deal with one of the most important tactical problems that arises in the managing of the bike sharing systems, that is the Bike sharing Rebalancing Problem (BRP). We propose models and algorithms for real-world earthwork optimization problems. We describe the 3DP process and we highlight several optimization issues in 3DP. Among those, we define the problem related to the tool path definition in the 3DP process, the 3D Routing Problem (3DRP), which is a generalization of the arc routing problem. We present an ILP model and several heuristic algorithms to solve the 3DRP.