A definable failure of the singular cardinal hypothesis

We show first that it is consistent that κ is a measurable cardinal where the GCH fails, while there is a lightface definable wellorder of H(κ ⁺). Then with further forcing we show that it is consistent that GCH fails at ? _ω , ? _ω strong limit, while there is a lightface definable wellorder of H(? _ω+1) (“definable failure” of the singular cardinal hypothesis at ? _ω ). The large cardinal hypothesis used is the existence of a κ ⁺⁺-strong cardinal, where κ is κ ⁺⁺-strong if there is an embedding j: V → M with critical point κ such that H(κ ⁺⁺) ? M. By work of M. Gitik and W. J. Mitchell [12], [20], our large cardinal assumption is almost optimal. The techniques of proof include the “tuning-fork” method of [10] and [3], a generalisation to large cardinals of the stationary-coding of [4] and a new “definable-collapse” coding based on mutual stationarity. The fine structure of the canonical inner model L[E] for a κ ⁺⁺-strong cardinal is used throughout.     

Separation and identification of highly fluorescent compounds derived from trans-resveratrol in the leaves of Vitis vinifera infected by Plasmopara viticola

A method for identification of highly fluorescent compounds in vine leaves infected by Plasmopara viticola was developed using reversed phase liquid chromatography with simultaneous diode array and fluorometric detection. Fluorescent compounds were extracted from leaves with a methanol-water mixture (70:30). Separation by HPLC was performed using a C(18) column and gradient elution with water-acetonitrile mixtures (20-80% of acetonitrile). The main unknown fluorescent compound was identified by line spectral comparison with a standard obtained by UV photoisomerization of trans-resveratrol glucoside, and its structure was confirmed by liquid chromatography-mass spectrometry. Identification and structural elucidation of the fluorescent compound in the leaves of Vitis vinifera allows early detection of Plasmopara viticola invasion.     

Platinum-modified adenines: unprecedented protonation behavior revealed by NMR spectroscopy and relativistic density-functional theory calculations

Two novel Pt(IV) complexes of aromatic cytokinins with possible antitumor properties were prepared by reaction of selected aminopurines with K(2)PtCl(6). The structures of both complexes, 9-[6-(benzylamino)purine] pentachloroplatinate (IV) and 9-[6-(furfurylamino)purine] pentachloroplatinate (IV), were characterized in detail by using two-dimensional NMR spectroscopy ((1)H, (13)C, (15)N, and (195)Pt) in solution and CP/MAS NMR techniques in the solid state. We report for the first time the X-ray structure of a nucleobase adenine derivative coordinated to Pt(IV) via the N9 atom. The protonation equilibria for the complexes in solution were characterized by using NMR spectroscopy (isotropic chemical shifts and indirect nuclear spin-spin coupling constants) and the structural conclusions drawn from the NMR analysis are supported by relativistic density-functional theory (DFT) calculations. Because of the presence of the Pt atom, hybrid GGA functionals and scalar-relativistic and spin-orbit corrections were employed for both the DFT calculations of the molecular structure and particularly for the NMR chemical shifts. In particular, the populations of the N7-protonated and neutral forms of the complexes in solution were characterized by correlating the experimental and the DFT-calculated NMR chemical shifts. In contrast to the chemical exchange process involving the N7-H group, the hydrogen atom at N3 was determined to be unexpectedly rigid, probably because of the presence of the stabilizing intramolecular interaction N3-H···Cl. The described methodology combining the NMR spectroscopy and relativistic DFT calculations can be employed for characterizing the tautomeric and protonation equilibria in a large family of transition-metal-modified purine bases.     

Band gaps and structural properties of graphene halides and their derivates: a hybrid functional study with localized orbital basis sets

Density functional theory calculations of the electronic structure of graphane and stoichiometrically halogenated graphene derivatives (fluorographene and other analogous graphene halides) show: (i) localized orbital basis sets can be successfully and effectively used for such two-dimensional materials; (ii) several functionals predict that the band gap of graphane is greater than that of fluorographene, whereas HSE06 gives the opposite trend; (iii) HSE06 functional predicts quite good values of band gaps with respect to benchmark theoretical and experimental data; (iv) the zero band gap of graphene is opened by hydrogenation and halogenation and strongly depends on the chemical composition of mixed graphene halides; (v) the stability of graphene halides decreases sharply with increasing size of the halogen atom--fluorographene is stable, whereas graphene iodide spontaneously decomposes. In terms of band gap and stability, the C(2)FBr and C(2)HBr derivatives seem to be promising materials, e.g., for (opto)electronics applications, because their band gaps are similar to those of conventional semiconductors, and they are expected to be stable under ambient conditions. The results indicate that other fluorinated compounds (C(a)H(b)F(c) and C(a)F(b)Y(c), Y = Cl, Br, I) are stable insulators.     

On the convergence of a dual-primal substructuring method

Summary.   In the Dual-Primal FETI method, introduced by Farhat et al. [5], the domain is decomposed into non-overlapping subdomains, but the degrees of freedom on crosspoints remain common to all subdomains adjacent to the crosspoint. The continuity of the remaining degrees of freedom on subdomain interfaces is enforced by Lagrange multipliers and all degrees of freedom are eliminated. The resulting dual problem is solved by preconditioned conjugate gradients. We give an algebraic bound on the condition number, assuming only a single inequality in discrete norms, and use the algebraic bound to show that the condition number is bounded by for both second and fourth order elliptic selfadjoint problems discretized by conforming finite elements, as well as for a wide class of finite elements for the Reissner-Mindlin plate model. Received January 20, 2000 / Revised version received April 25, 2000 / Published online December 19, 2000     

OXYGEN REQUIREMENT FOR NEAR-UV MEDIATED CYTOTOXICITY OF PHENYLHEPTATRIYNE TO Escherichia coli

Abstract— Phenylheptatriyne (PHT) is a good singlet oxygen sensitizer in vitro. In vivo , its phototoxicity toward E. coli B has been proved unequivocally to depend on the presence of oxygen. The literature reports indicating that phenylheptatriyne was representative of a new class of sensitizers were probably based on experiments conducted under conditions which were not strictly anaerobic.