SEFE without Mapping via Large Induced Outerplane Graphs in Plane Graphs

We show that every n‐vertex planar graph admits a simultaneous embedding without mapping and with fixed edges with any ‐vertex planar graph. In order to achieve this result, we prove that every n‐vertex plane graph has an induced outerplane subgraph containing at least vertices. Also, we show that every n‐vertex planar graph and every n‐vertex planar partial 3‐tree admit a simultaneous embedding without mapping and with fixed edges.     

Investigation into the reactivity of the coordinatively unsaturated phosphonodithioato [Ni(MeOpdt)2] towards 2,4,6-tris(2-pyridyl)-1,3,5-triazine: goals and achievements

The reaction between the coordinatively unsaturated phosphonodithioato complex [Ni(MeOpdt)2] (1) [MeOpdt = (MeO)(4-MeOC(6)H(4))PS2-] and tptz [2,4,6-tris(2-pyridyl)-1,3,5-triazine] has been investigated. Spectrophotometric and conductometric titrations showed the formation of a neutral and an ionic species, i.e. [Ni(MeOdtp)2(tptz)] (2) and [Ni(tptz)2](MeOdtp)2 (3), in correspondence to 1 : 1 and 2 : 1 tptz : ratios, respectively. XRD studies confirmed the formation of both complexes isolated in the compounds 2.MeOH and 3.4H(2)O. In the neutral complex 2 the central Ni(II) ion features a distorted octahedral coordination, achieved through three N-atoms of tptz and three S-atoms belonging to two MeOpdt anions, one of which unexpectedly acts as a monodentate S-donor. In 3.4H(2)O, the two phosphonodithioato anions are non-coordinating and counterbalance the charge of the [Ni(tptz)2](2+) distorted octahedral complex. From the reaction 2 of with I2 and Br2, crystals of [Ni(tptz)2](I3)2 (5) and [Ni(tptz)Br(micro-Br)]2 (6) have been obtained. The dinuclear complex 6 features a structure showing tubular canals with openings of about 6 x 6 A.     

Stereoselective synthesis of 2,3-unsaturated-aza-O-glycosides via new diastereoisomeric N-Cbz-imino glycal-derived allyl epoxides

Diastereoisomeric D,L-N-Cbz-imino glycal-derived allyl epoxides 5 and 6 have been synthesized, and their addition reactions with alcohols examined. The reactions lead to the corresponding 2,3-unsaturated-aza-O-glycosides through a new, completely regioselective 1,4-addition process which proceeds with complete substrate-dependent stereoselectivity.     

A sharp uniqueness result for a class of variational problems solved by a distance function

We consider the minimization problem for an integral functional J, possibly nonconvex and noncoercive in , where is a bounded smooth set. We prove sufficient conditions in order to guarantee that a suitable Minkowski distance is a minimizer of J. The main result is a necessary and sufficient condition in order to have the uniqueness of the minimizer. We show some application to the uniqueness of the solution of a system of PDEs of Monge–Kantorovich type arising in problems of mass transfer theory.     

Ionization and tautomerization of 2-nitrocyclohexanone in aqueous solution

The keto-enol tautomerism of 2-nitrocyclohexanone (2-NCH) was studied in aqueous solution under different experimental conditions. Ketonization rate constants were measured spectrophotometrically at 25 degrees C at an ionic strength of 0.4 mol dm-3 (NaCl) in diluted hydrochloric acid, in diluted sodium hydroxide, and in several buffers by using NaHSO3 as the scavenger of the keto form. A value of pK(a)(EH) = 4.78 for the enol form was obtained from the rate-pH profile of the reaction. A value of pK(a)(KH) = 5.97 for the keto form was directly obtained from the UV-vis spectra of 2-NCH recorded at different pHs. The equilibrium constant for the keto-enol tautomerism, pK(T) = -log([enol]/[ketone]) = 1.19, was obtained by combining the two pKa values (pK(T) = pK(a)(KH) - pK(a)(EH)). A comparison of these results with the corresponding values (Keefe, J. R.; Kresge, A. J. In The Chemistry of Enols; Rappoport, Z., Ed.; Wiley & Sons: New York, 1990; pp 399-480) for cyclohexanone shows the dramatic effects of an alpha-nitro substituent on the keto-enol acidities and the tautomerization constant of alicyclic ketones. Rates and equilibria were discussed in the light of the Br?nsted equation, the principle of nonperfect synchronization, and the Marcus theory. It turns out that, on passing from nitroalkanes to nitroketones, the resonance contribution to pKa and deprotonation rate decreases, being overwhelmed by steric and inductive effects.     

New insight into the reaction of singlet oxygen with sulfur-containing cyclic alkenes: dye-sensitized photooxygenation of 5,6-dihydro-1,4-dithiins

The reaction of 3-methyl-5,6-dihydro-1,4-dithiins with singlet oxygen affords dicarbonyl compounds and/or ring-contracted ketosulfoxides, the latter regio- and stereoselectively, depending on the nature of the substituent at C-2 and on the reaction conditions. In competition with normal fragmentation, the intermediate dioxetanes, derived from [2 + 2] cycloaddition of singlet oxygen to the double bond, undergo an intramolecular oxygen transfer to the sulfur-1 atom, leading to labile epoxide intermediates. The latter convert to cis- and trans-ketosulfoxides through a non-concerted S-4 migration. This pathway is promoted by the electron-withdrawing group at C-2 and, for monosubstituted amide, by the solvent basicity. S-Oxidation of dithiins is insignificant, except for the monosubstituted amide derivative or in the presence of protic species, and occurs selectively at the S-1 atom.     

The distance function from the boundary in a Minkowski space

Let the space be endowed with a Minkowski structure (that is, is the gauge function of a compact convex set having the origin as an interior point, and with boundary of class ), and let be the (asymmetric) distance associated to . Given an open domain of class , let be the Minkowski distance of a point from the boundary of . We prove that a suitable extension of to (which plays the rôle of a signed Minkowski distance to ) is of class in a tubular neighborhood of , and that is of class outside the cut locus of (that is, the closure of the set of points of nondifferentiability of in ). In addition, we prove that the cut locus of has Lebesgue measure zero, and that can be decomposed, up to this set of vanishing measure, into geodesics starting from and going into along the normal direction (with respect to the Minkowski distance). We compute explicitly the Jacobian determinant of the change of variables that associates to every point outside the cut locus the pair , where denotes the (unique) projection of on , and we apply these techniques to the analysis of PDEs of Monge-Kantorovich type arising from problems in optimal transportation theory and shape optimization.

     

Fruit Wastes as a Valuable Source of Value-Added Compounds: A Collaborative Perspective

The by-products/wastes from agro-food and in particular the fruit industry represents from one side an issue since they cannot be disposed as such for their impact on the environment but they need to be treated as a waste. However, on the other side, they are a source of bioactive healthy useful compounds which can be recovered and be the starting material for other products in the view of sustainability and a circular economy addressing the global goal of “zero waste” in the environment. An updated view of the state of art of the research on fruit wastes is here given under this perspective. The topic is defined as follows: (i) literature quantitative analysis of fruit waste/by-products, with particular regards to linkage with health; (ii) an updated view of conventional and innovative extraction procedures; (iii) high-value added compounds obtained from fruit waste and associated biological properties; (iv) fruit wastes presence and relevance in updated databases. Nowadays, the investigation of the main components and related bioactivities of fruit wastes is being continuously explored throughout integrated and multidisciplinary approaches towards the exploitation of emerging fields of application which may allow to create economic, environmental, and social value in the design of an eco-friendly approach of the fruit wastes.     

Enzyme-Mediated Preparation of (+)- and (–)-cis-α-Irone and (+)- and (–)-trans-α-Irone

The preparation of (−)- and (+)-trans-α-irone ( 1a and 1b , resp.) and of (+)- and (−)-cis-α-irone ( 1c and 1d , resp.) from commercially available Irone alpha ^® is reported. The relevant step in the synthetic sequence is the initial chromatographic separation of crystalline (±)-4,5-epoxy-4,5-dihydro-cis-α-irone ((±)- 5 ) from oily (±)-4,5-epoxy-4,5-dihydro-trans-α-irone ((±)- 4 ). The latter was subsequently converted, after NaBH₄ reduction, into the crystalline 3,5-dinitrobenzoate ester (±)- 8 , thus allowing a complete separation of the two corresponding diastereoisomeric alcohol derivatives. Suitable enantiomerically pure precursors of the desired products 1a – d were obtained by kinetic resolution of the racemic allylic alcohols derived from (±)- 5 and (±)- 8 , mediated by lipase PS (Amano). The last steps consisted of MnO₂ oxidation and removal of the epoxy moiety with Me₃SiCl/NaI in MeCN. External panel olfactory evaluation showed that (−)-cis-α-irone ( 1d ) has the finest and most distinct `orris butter' character.