Hybrid Polyoxotungstates as Functional Comonomers in New Cross‐Linked Catalytic Polymers for Sustainable Oxidation with Hydrogen Peroxide

Anchoring terminal octenyl tails on molecular polyoxotungstates yield polymerizable organic–inorganic monomers with formula [{CH₂?CH(CH₂)₆Si}_xO_ySiW_wO_z]^4? [x=2, w=11, y=1, z=39 ( 1 ); x=2, w=10, y=1, z=36 ( 2 ); and x=4, w=9, y=3, z=34 ( 3 )]. These molecular hybrids can use aqueous hydrogen peroxide to catalyze the selective oxidation of organic sulfides in CH₃CN. Copolymerization of 1 – 3 with methyl methacrylate and ethylene glycol dimethacrylate leads to porous materials with a homogeneous distribution of the functional monomers, as indicated by converging evidence from FTIR spectroscopy and electronic microscopy. The catalytic polymers activate hydrogen peroxide for oxygen transfer, as demonstrated by the quantitative and selective oxidation of methyl p‐tolyl sulfide, which was screened as model substrate. The hybrid material containing monomer 2 was also tested in n‐octane to evaluate its potential for the oxidation and removal of dibenzothiophene, a well‐known gasoline contaminant.     

Allometry and growth: A unified view

Allometry is crucial in biology; scaling relations are implied in laws of growth of living systems. The self similarity of Gompertzian growths of biological organisms plays a key role, in this regard, in biological similitude. The origin of allometric relationships and values of the scaling exponents is a source of debate, as well as the origin of the range of biological scales. But, besides biology, scaling and growth characterize many different complex systems. Encompassing these aspects in a unified view is an interesting target. In this paper we propose a coarse but significant model that is applied to astrophysical structures and biological organisms. The inclusion of such different systems suggests applications to fields where allometry is emerging, such as economics, urban planning and the social sciences.     

Existence and concentration of positive solutions for a super-critical fourth order equation

In this paper we investigate the problem of existence of solutions for a super-critical fourth order Yamabe type equation and we exhibit a family of solutions concentrating at two points, provided the domain contains one hole and we give a multiplicity result if we are given multiple holes.     

Influence of solvent and crystallization method on the crystal habit of metronidazole

In the present study, metronidazole was crystallized in several solvents, according to both the “cooling crystallization” and the “crystallization by non‐solvent addition”. Particle properties, such as crystal habit, elongation ratio, and mean particle size, were determined by SEM analysis. Structural changes and development of polymorphic forms were excluded by both Differential Scanning Calorimetry (DSC) and X‐Ray Powder Diffractometry (XRPD). Crystal habit (and thus elongation ratio) was typically influenced by both the solvent polarity index and the crystallization method: solvents with higher polarity index tended to promote acicular or stick‐shaped crystals with a high elongation ratio, while isodimensional crystals were promoted by decreasing the polarity index, as was particle aggregation. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Trap levels in Y-aluminum garnet scintillating crystals

Point defects acting as trap levels were investigated on undoped, Ce- and (Ce, Si)-doped Y₃Al₅O₁₂ (YAG) crystals by TSL measurements performed over a wide temperature range (10–800 K). Below room temperature, a composite glow curve was observed, whose intensity strongly increased after Ce doping. Moreover, Ce doping introduced new trap levels giving rise to glow peaks in the 100–200 K range. On the other hand, Si co-doping did not influence the low T glow curve in a significant way. The spectral emission of the TSL was found to be governed by the Ce³⁺ 5d–4f radiative transition, while defect related higher energy emission bands were detected only in the undoped crystal. Above RT, the glow curve was found to be much more influenced by Si co-doping since a strong increase of a glow peak at about 250°C was noticed. Scintillation time decays of Ce- and Ce,Si-doped samples are also reported and compared with TSL data. The significance of the results and the potential impact of defect states on the scintillation properties are discussed.     

Time-resolved EPR study of 3C60 in solid matrices

Using time-resolved cw EPR and pulsed EPR techniques, a study was made of the characteristics of the photoexcited triplet state of C₆₀ adsorbed in silica gel pores and embedded in a polymethylmethacrylate matrix. It was found that the time-resolved spectra from ³C₆₀ in these matrices at room temperature retain the absorption/emission features of spectra from ³C₆₀ in frozen solution (≤120 K). Apparently, the combination of molecular rotation and pseudo rotation (resulting from interconversion between Jahn-Teller states) is not fast enough, to lead to complete averaging of the dipole-dipole interaction between the unpaired electrons. The study explored the effect of introduction of solvent molecules in the silica gel pores on the ³C₆₀ spectrum and quenching of the triplet by electron donors.     

Approximation and regular perturbation of optimal control problems via Hamilton-Jacobi theory

We present two convergence theorems for Hamilton-Jacobi equations and we apply them to the convergence of approximations and perturbations of optimal control problems and of two-players zero-sum differential games. One of our results is, for instance, the following. LetT andT _h be the minimal time functions to reach the origin of two control systemsy = f(y, a) andy = f _h (y, a), both locally controllable in the origin, and letK be any compact set of points controllable to the origin. If f _h –f Ch, then |T(x) – T _h (x)| C _K h , for all x K, where is the exponent of Hölder continuity ofT(x).     

Some remarks on the degrees of faithful irreducible representations

We study a class of finite p-groups admitting faithful irreducible complex representations of distinct degrees. In particular, for every prime p, we produce an example of such a p-group having minimal order p ⁸.Dedicated to A. Wagner on the occasion of his 60th birthdayLavoro eseguito nell'ambito dei finanziamenti M.U.R.S.T.