C-F?Rb interaction in a fluorinated cage compound complex

A rubidium complex of a cage compound which is composed of fluorobenzene, ethylenedioxy, and bridgehead nitrogen donor units was prepared. The C-F?Rb⁺ interaction was clarified and evaluated for the first time by crystallographic analysis. The contribution degree of the three kinds of donor atoms for the cation binding was estimated by Brown’s bond valence equation.     

On the Inozemtsev Model

The BC _N Inozemtsev model is investigated. Finite-dimensional spaces which are invariant under the action of the Hamiltonian of the BC _N Inozemtsev model are introduced and it is shown that commuting operators of conserved quantities also preserve the finite-dimensional spaces. The BC ₂ Inozemtsev model is studied in more detail.     

Hydrogen bonding in two solid phases of phenazine–chloranilic acid (1/1) determined at 170 and 93 K

The crystal structures in two solid phases, i.e. phase II stable between 146 and 253 K and phase IV below 136 K, of the title compound [phenazine–chloranilic acid (1/1), C₁₂H₈N₂·C₆H₂Cl₂O₄, in phase II, and phenazinium hydrogen chloranilate, C₁₂H₉N₂⁺·C₆HCl₂O₄⁻, in phase IV], have been determined. Both phases crystallize in P2₁, and each structure was refined as an inversion twin. In phase II, the phenazine and chloranilic acid mol­ecules are arranged alternately through two kinds of O—H⋯N hydrogen bonds. In phase IV, salt formation occurs by donation of one H atom from the chloranilic acid molecule to the phenazine mol­ecule; the resulting monocation and monoanion are linked by N—H⋯O and O—H⋯N hydrogen bonds.     

A new imaging method for gold-surface adsorbates based on anomalous reflection

A new imaging method is proposed for ultrathin films with a thickness of a few nanometers, based on the anomalous reflection (AR) of gold. In the AR effect, the reflectivity fairly decreases for blue or purple light (380 nm < λ < 480 nm) with the existence of a transparent dielectric layer at a gold surface. Thus, a thin gold film can be used as an imaging platform. Clear AR images are obtained for a microarray of protein (avidin) spots of diameter 120 μm with gaps of size 50 μm between the spots (36 spots/mm²). The resolution of the AR imaging is governed solely by the illumination spot size. AR imaging is a promising technique for high throughput analysis of biomolecular detection in a microarray format.     

Acetylation and stepwise solvent-exchange to modify hydrophilic cellulose whiskers to polychloroprene-compatible nanofiller

The acetylation of cellulose nanofiber (CNF) introduced hydrophobicity to the surface making it compatible with non-polar matrix, and also making it an effective nanofiller for polychloroprene (PCR) composite. The CNF was extracted from oil palm empty fruit bunches. Previously, CNF was dispersed in water, and this water was subsequently substituted with N,N-dimethylacetamide, in which CNF was acetylated by acetic anhydride with a pyridine catalyst. IR spectroscopy revealed that the acetylation extent was controllable by the reaction time. After the reaction, the DMAc was replaced by dichloromethane, and finally mixed with PCR. The CNF–PCR mixture was cast and composite film was formed at room temperature. Structural analysis and mechanical tests indicated that acetylation treatment made CNF compatible with PCR, and that nano-dispersed CNF raised the mechanical strength of the PCR–CNF nanocomposite.     

Nonstandard models that are definable in models of Peano Arithmetic

In this paper, we investigate definable models of Peano Arithmetic PA in a model of PA. For any definable model N without parameters in a model M, we show that N is isomorphic to M if M is elementary extension of the standard model and N is elementarily equivalent to M. On the other hand, we show that there is a model M and a definable model N with parameters in M such that N is elementarily equivalent to M but N is not isomorphic to M. We also show that there is a model M and a definable model N with parameters in M such that N is elementarily equivalent to M, and N is isomorphic to M, but N is not definably isomorphic to M. And also, we give a generalization of Tennenbaum's theorem. At the end, we give a new method to construct a definable model by a refinement of Kotlarski's method. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Integral representations of one-dimensional projections for multivariate stable densities

We consider the numerical evaluation of one-dimensional projections of general multivariate stable densities introduced by Abdul-Hamid and Nolan [H. Abdul-Hamid, J.P. Nolan, Multivariate stable densities as functions of one dimensional projections, J. Multivariate Anal. 67 (1998) 80-89]. In their approach higher order derivatives of one-dimensional densities are used, which seems to be cumbersome in practice. Furthermore there are some difficulties for even dimensions. In order to overcome these difficulties we obtain the explicit finite-interval integral representation of one-dimensional projections for all dimensions. For this purpose we utilize the imaginary part of complex integration, whose real part corresponds to the derivative of the one-dimensional inversion formula. We also give summaries on relations between various parametrizations of stable multivariate density and its one-dimensional projection.     

Hydrogen bonding in 1,2‐diazine–chloranilic acid (2/1) and 1,4‐diazine–chloranilic acid (2/1) determined at 110 K

The crystal structures of the isomeric title compounds [systematic names: pyridazine–2,5‐dichloro‐3,6‐dihydroxy‐p‐benzoquinone (2/1), (I), and pyrazine–2,5‐dichloro‐3,6‐dihydroxy‐p‐benzoquinone (2/1), (II)], 2C₄H₄N₂·C₆H₂Cl₂O₄, have been redetermined at 110 K. The H atom in the intermolecular O...H...N hydrogen bond in each compound was revealed to be disordered; the relative occupancies at the O and N sites are 0.33 (3) and 0.67 (3), respectively, for (I), and 0.56 (4) and 0.44 (4) for (II). The formal charges of the chloranilic acid in (I) and (II) estimated from the occupancy factors are ca−1.3 and −0.8, respectively. The geometries of the centrosymmetric chloranilic acid molecule in (I) and (II) are compared with the neutral, monoanionic and dianionic forms of chloranilic acid optimized by density functional theory (DFT) at the B3LYP/6–311+G(3df,2p) level. The result implies that the chloranilic acid molecule in (I) is close to the monoanionic state, while that in (II) is between neutral and monoanionic, consistent with the result derived from the H‐atom occupancies.     

On sum of 0–1 random variables II. Multivariate case

Summary Distribution of sum of vectors of 0–1 random variables is discussed generalizing the univariate results obtained in our previous article Takeuchi and Takemura (1987,Ann. Inst. Statist. Math.,39, 85–102). As in our previous article no assumption is made on the independence of the 0–1 random variables.     

Periodicity of hyperplane arrangements with integral coefficients modulo positive integers

We study central hyperplane arrangements with integral coefficients modulo positive integers q. We prove that the cardinality of the complement of the hyperplanes is a quasi-polynomial in two ways, first via the theory of elementary divisors and then via the theory of the Ehrhart quasi-polynomials. This result is useful for determining the characteristic polynomial of the corresponding real arrangement. With the former approach, we also prove that intersection lattices modulo q are periodic except for a finite number of q’s. This work was supported by the MEXT and the JSPS.