A class of piecewise interpolating functions based on barycentric coordinates

Piecewise interpolation methods, as spline or Hermite cubic interpolation methods, define the interpolant function by means of polynomial pieces and ensure that some regularity conditions are guaranteed at the break-points. In this work, we propose a novel class of piecewise interpolating functions whose expression depends on the barycentric coordinates and a suitable weight function. The underlying idea is to specialize to the 1D settings some aspects of techniques widely used in multi-dimensional interpolation, namely Shepard’s, barycentric and triangle-based blending methods. We show the properties of convergence for the interpolating functions and discuss how, in some cases, the properties of regularity that characterize the weight function are reflected on the interpolant function. Numerical experiments, applied to some case studies and real scenarios, show the benefit of our method compared to other interpolant models.     

Special issue on “Advances on model-based clustering and classification”

Advances in Data Analysis and Classification -     

Enveloping algebras that are principal ideal rings

Let L be a restricted Lie algebra over a field of positive characteristic. We prove that the restricted enveloping algebra of L is a principal ideal ring if and only if L is an extension of a finite-dimensional torus by a cyclic restricted Lie algebra.     

On the Bullwhip Avoidance Phase: The Synchronised Supply Chain

The aim of this paper is to analyse the operational response of a Synchronised Supply Chain (SSC). To do so, first a new mathematical model of a SSC is presented. An exhaustive Latin Square design of experiments is adopted in order to perform a boundary variation analysis of the main three parameters of the periodic review smoothing (S, R) order-up-to policy: i.e., lead time, demand smoothing forecasting factor, and proportional controller of the replenishment rule. The model is then evaluated under a variety of performance measures based on internal process benefits and customer benefits. The main results of the analysis are: (I) SSC responds to violent changes in demand by resolving bullwhip effect and by creating stability in inventories under different parameter settings and (II) in a SSC, long production–distribution lead times could significantly affect customer service level. Both results have important consequences for the design and operation of supply chains.     

DBS-Based Eutectogels: Organized Vessels to Perform the Michael Addition Reaction**

Supramolecular eutectogels were obtained from the gelation of 1,3 : 2,4-dibenzylidene-D-sorbitol (DBS) in cholinium chloride-based deep eutectic solvents (DES), differing for the nature of the hydrogen bond donor. Ethylene glycol, diethylene glycol, triethylene glycol, glycerol and urea were tested. Soft materials were fully characterized, determining critical gelation concentration, gel-sol transition temperatures and mechanical properties. Furthermore, to have information about the organization of the gelator in the tridimensional network, resonance light scattering, circular dichroism and microscopy investigations were performed. Eutectogels were used as organized “vessels” to perform the L-proline catalyzed Michael addition reaction. The probe reaction was carried out in gel phase and in DES solution. Data collected shed light on the effect that gel microenvironment exerts on the outcome of the reaction. In general, gel phases allowed having comparable or even better results than the ones collected in DES solution, with better results obtained in soft materials with the highest organization, as accounted for by the presence of larger aggregates and the occurrence of stronger intermolecular interactions. In turn, this accounts also for the effect of substrates structure that indicates that better yields could be obtained in the presence of more flexible nucleophile and dienones, having more extended π-surface.     

Orange Peel Biomass-derived Carbon Supported Cu Electrocatalysts Active in the CO2-Reduction to Formic Acid

We report a green, wet chemistry approach towards the production of C-supported Cu electrocatalysts active in the CO₂ reduction to formic acid. We use citrus peels as a C support precursor and as a source of reducing agents for the Cu cations. We show that orange peel is a suitable starting material compared to lemon peel for the one-pot hydrothermal synthesis of Cu nanostructures affording better Cu dispersion as well as productivity and selectivity towards formic acid. We rationalize this finding in terms of the beneficial chemical composition of the orange peel, which favors both the reduction of the Cu precursor as well as the carbon matrix. This work demonstrates new viable opportunities for the reuse of citrus waste on a rational basis.