A Besov class functional calculus for bounded holomorphic semigroups

It is well-known that -sectorial operators generally do not admit a bounded H^∞ calculus over the right half-plane. In contrast to this, we prove that the H^∞ calculus is bounded over any class of functions whose Fourier spectrum is contained in some interval [ε,σ] with 0<ε<σ<∞. The constant bounding this calculus grows as as and this growth is sharp over all Banach space operators of the class under consideration. It follows from these estimates that -sectorial operators admit a bounded calculus over the Besov algebra of the right half-plane. We also discuss the link between -sectorial operators and bounded Tadmor-Ritt operators.     

Functional calculus under the Tadmor-Ritt condition, and free interpolation by polynomials of a given degree

For Banach space operators T satisfying the Tadmor-Ritt condition ||(zI−T)⁻¹||?C|z−1|⁻¹, |z|>1, we prove that the best-possible constant C_T(n) bounding the polynomial calculus for T, ||p(T)||?C_T(n)||p||_∞, deg(p)?n, behaves (in the worst case) as as n→∞. This result is based on a new free (Carleson type) interpolation theorem for polynomials of a given degree.     

Integral Estimates for Transport Densities

The integration-by-parts methods introduced in this paper improveupon the L^p estimates on transport densities given in the recentpaper by L. De Pascale and A. Pratelli (Calc. Var. Partial DifferentialEquations 14 (2002) 249–274). 2000 Mathematics SubjectClassification 35Q99, 35B99.     

Polyphenol Profiling of Chestnut Pericarp,Integument and Curing Water Extracts to Qualify These Food By-Products as a Source of Antioxidants

Plant polyphenols have beneficial antioxidant effects on human health; practices aimed at preserving their content in foods and/or reusing food by-products are encouraged. The impact of the traditional practice of the water curing procedure of chestnuts, which prevents insect/mould damage during storage, was studied to assess the release of polyphenols from the fruit. Metabolites extracted from pericarp and integument tissues or released in the medium from the water curing process were analyzed by matrix-assisted laser desorption ionization-time of flight-mass spectrometry (MALDI-TOF-MS) and electrospray-quadrupole-time of flight-mass spectrometry (ESI-qTOF-MS). This identified: (i) condensed and hydrolyzable tannins made of (epi)catechin (procyanidins) and acid ellagic units in pericarp tissues; (ii) polyphenols made of gallocatechin and catechin units condensed with gallate (prodelphinidins) in integument counterparts; (iii) metabolites resembling those reported above in the wastewater from the chestnut curing process. Comparative experiments were also performed on aqueous media recovered from fruits treated with processes involving: (i) tap water; (ii) tap water containing an antifungal Lb. pentosus strain; (iii) wastewater from a previous curing treatment. These analyses indicated that the former treatment determines a 6–7-fold higher release of polyphenols in the curing water with respect to the other ones. This event has a negative impact on the luster of treated fruits but qualifies the corresponding wastes as a source of antioxidants. Such a phenomenon does not occur in wastewater from the other curing processes, where the release of polyphenols was reduced, thus preserving the chestnut’s appearance. Polyphenol profiling measurements demonstrated that bacterial presence in water hampered the release of pericarp metabolites. This study provides a rationale to traditional processing practices on fruit appearance and qualifies the corresponding wastes as a source of bioactive compounds for other nutraceutical applications.     

Free-Radical Synthesis of Block Copolymers via Dixanthogen-Linked Polymer Sequences

Abstract

Due to high chain transfer and the subsequent terminator properties of the dixanthogen moiety, (AB)_n multiblock copolymers of poly(oxyethylene-block-methyl methacrylate) and ABA triblock copolymers of poly(methyl methacrylate-block-2-ethylhexyl acrylate) could be synthesized from dixanthogen-linked poly(oxyethylene) and poly(methyl methacrylate) pre-polymer sequences, respectively, using free-radical chemistry. A simple and efficient method was developed for the synthesis of dixanthogen-linked polymers: Hydroxyl-functionalized pre-polymers were reduced using NaH to form alkoxide; CS₂ was then added to the alkoxide to form xanthate; and finally the xanthate was oxidized either in an aqueous or organic medium to form the dixanthogen. The synthesis techniques provided in this paper are general and thus, in principle, can be applied to many other block copolymer systems.     

Charge‐Assisted Halogen Bonding: Donor–Acceptor Complexes with Variable Ionicity

Charge‐assisted halogen bonding is unambiguously revealed from structural and electronic investigations of a series of isostructural charge‐transfer complexes derived from iodinated tetrathiafulvalene and tetracyanoquinodimethane derivatives, (EDT‐TTFI₂)₂(TCNQF_n), n=0–2, which exhibit variable degrees of ionicity. The iodinated tetrathiafulvalene derivative, EDT‐TTFI₂, associates with tetracyanoquinodimethane (TCNQ) and its derivatives of increasing reduction potential (TCNQF, TCNQF₂) through highly directional C? I???N≡C halogen‐bond interactions. With the less oxidizing TCNQ acceptor, a neutral and insulating charge‐transfer complex is isolated whereas with the more oxidizing TCNQF₂ acceptor, an ionic, highly conducting charge‐transfer salt is found, both of 2:1 stoichiometry and isostructural with the intermediate TCNQF complex, in which a neutral–ionic conversion takes place upon cooling. A correlation between the degree of charge transfer and the C? I???N≡C halogen‐bond strength is established from the comparison of the structures of the three isostructural complexes at temperatures from 300 to 20 K, thus demonstrating the importance of electrostatics in the halogen‐bonding interaction. The neutral–ionic conversion in (EDT‐TTFI₂)₂(TCNQF) is further investigated through the temperature dependence of its magnetic susceptibility and the stretching modes of the C≡N groups.