Backward stochastic differential equations with jumps and related non-linear expectations

In this paper, we are interested in real-valued backward stochastic differential equations with jumps together with their applications to non-linear expectations. The notion of non-linear expectations has been studied only when the underlying filtration is given by a Brownian motion and in this work the filtration will be generated by both a Brownian motion and a Poisson random measure. We study at first backward stochastic differential equations driven by a Brownian motion and a Poisson random measure and then introduce the notions of f$f$-expectations and of non-linear expectations in this set-up.     

β-Nitro-5,10,15-tritolylcorroles

Functionalization of the β-pyrrolic positions of the corrole macrocycle with -NO(2) groups is limited at present to metallocorrolates due to the instability exhibited by corrole free bases under oxidizing conditions. A careful choice of the oxidant can limit the transformation of corroles into decomposition products or isocorrole species, preserving the corrole aromaticity, and thus allowing the insertion of nitro groups onto the corrole framework. Here we report results obtained by reacting 5,10,15-tritolylcorrole (TTCorrH(3)) with the AgNO(2)/NaNO(2) system, to give mono- and dinitrocorrole derivatives when stoichiometry is carefully controlled. Reactions were found to be regioselective, affording the 3-NO(2)TTCorrH(3) and 3,17-(NO(2))(2)TTCorrH(3) isomers as the main products in the case of mono- and disubstitution, in 53 and 20% yields, respectively. In both cases, traces of other mono- and disubstituted isomers were detected, which were structurally characterized by X-ray crystallography. The influence of the β-nitro substituents on the corrole properties is studied in detail by UV-visible, electrochemical, and spectroelectrochemical characterization of these functionalized corroles. Density functional theory (DFT) and time-dependent DFT (TDDFT) calculations of the ground and excited state properties of these β-nitrocorrole derivatives also afforded significant information, closely matching the experimental observations. It is found that the β-NO(2) substituents conjugate with the π-aromatic system of the macrocycle, which initiates significant changes in both the spectroscopic and redox properties of the so functionalized corroles. This effect is more pronounced when the nitro group is introduced at the 2-position, because in this case the conjugation is, for steric reasons, more efficient than in the 3-nitro isomer.     

Modelling and optimization of least-cost water distribution networks with multiple supply sources and users

The proper allocation of water resources is a very important practical problem in the field of water network planning. Optimization models that are expeditious and easy to use for all stakeholders of the sector play an important role for water resource management. The present work resumes and reviews a least-cost optimization model proposed by our group (Maiolo and Pantusa in Water Sci Tech-W Sup.  https://doi.org/10.2166/ws.2015.114, 2016), able to design a water distribution network with multiple supply sources and multiple users. This approach requires of solving an optimization problem based on a nonlinear objective function which is proportional to the cost of the water distribution network. The cost of pre-existing pipelines is considered null. A more realistic scenario, able to consider the maximum flow rate allowed for existing sources-users connections, is considered here. In order to illustrate the usefulness and flexibility of the proposed approach, an application of the model to the real case of the province of Croton, Southern Italy, is presented.     

Erbium- and chlorine-doped fluorozirconate-based glasses for up-converted fluorescence

A series of glass ceramics was prepared and the structure–property relationships evaluated. The base composition of the series was comprised of fluorozirconate (FZ) and fluorochlorozirconate (FCZ) glass ceramics. Thermal processing of as-made FCZ-based glass ceramics produced sharp peaks in X-ray diffraction patterns, which was attributed to BaCl₂ nanocrystals formed in the material; this was not observed in the FZ glass. Up-conversion fluorescence experiments were carried out for both the FZ and FCZ samples doped with erbium. The fact that an increase in the up-conversion efficiency was not observed indicates that erbium ions were not embedded in the BaCl₂ nanocrystals. A comparison is made between this series and a similar series that was doped with neodymium.     

The thermal study of oxyfluoride glass with strontium fluoride

A thulium (Tm 3+) doped oxyfluoride glass ceramic containing SrF2 nanocrystals has been presented. Transparent glass ceramic was obtained by heat treating the glass from the SiO2-Al2O3-ZnO-SrF2 system at the first crystallization temperature. Cerammization of glass was studied by DTA/DSC, XRD and SEM methods. It has been found that nanocrystallization of SrF2 strongly depends on the ratio between the components and amount of SrF2. Moreover the rare earth dopant Tm3+ influenced on the thermal properties of glass. The formation of SrF2 nanocrystals in glass ceramic was confirmed by X-ray diffraction. X-ray diffraction analysis of the transparent glass ceramic revealed that the SrF2 nanocrystals are precipitated in the glass matrix. Analysis of the local atomic interactions in the structure of oxyfluoride glass has been used to explain the course of the crystallization.     

Determination of the association constant of NaS2O 3 − with the sodium-selective electrode and UV spectrophotometry

The association constant of NaS₂O ₃ ^? complex in a medium of μ=1.0M at 25.0±0.1°C was determined by two techniques: sodium-selective electrode (β₁ = 1.48 ± 0.13) and UV spectrophotometry (β₁ = 1.25 ± 0.10). There is no evidence, under our experimental conditions, of the existence of the binuclear complex Na₂S₂O₃, which might exist at the very low value of the ratio \(C_{Na_2 s_2 o_3 } /C_{Na} +\) used in our experiments.