Interaction information and Markov chain

The problem of multivariate information analysis is considered. First, the interaction information in each dimension is defined analogously according to McGill [4] and then applied to Markov chains. The property of interaction information zero deeply relates to a certain class of weakly dependent random variables. For homogeneous, recurrent Markov chains with m states, m ≥ n ≥3, the zero criterion of n-dimensional interaction information is achieved only by (n ? 2)-dependent Markov chains, which are generated by some nilpotent matrices. Further for Gaussian Markov chains, it gives the decomposition rule of the variables into mutually correlated subchains.     

Low-energy charge-density excitations in MgB2: Striking interplay between single-particle and collective behavior for large momenta

A sharp feature in the charge-density excitation spectra of single-crystal MgB2, displaying a remarkable cosinelike, periodic energy dispersion with momentum transfer (q) along the c* axis, has been observed for the first time by high-resolution nonresonant inelastic x-ray scattering (NIXS). Time-dependent density-functional theory calculations show that the physics underlying the NIXS data is strong coupling between single-particle and collective degrees of freedom, mediated by large crystal local-field effects. As a result, the small-q collective mode residing in the single-particle excitation gap of the B pi bands reappears periodically in higher Brillouin zones. The NIXS data thus embody a novel signature of the layered electronic structure of MgB2.     

Dendritic effects on the ordered assembly and the interfacial one-electron oxidation of redox-active dendron-functionalized gold nanoparticles

A higher generation dendron with a long-alkyl chain thiol (DA2-SH) induced the formation of nanoparticles with a small core with quite a narrow size distribution (1.5 +/- 0.1 nm), the self-assembly of one-dimensional arrays of these gold nanoparticles (DA2-Au), and the stabilization for the formation of the radical cation of the phenothiazine of DA2-Au nanoparticles from the interfacial one-electron oxidation of the nanoparticles with NOBF4.     

Photoluminescence of SrGa2S4:Sn,Re(=Ce, Gd) phosphors

The photoluminescence (PL) spectra, PL excitation spectra, color coordinates, and X-ray diffraction spectra are reported for SrGa₂S₄:Sn,Re(=Ce and Gd, respectively) phosphors. By mixing SrGa₂S₄:Sn,Ce phosphors with different Ce³⁺ concentrations, white emissions can be obtained under the excitation of a 340-nm UV LED. Emissions in the green to yellow color range can be obtained from SrGa₂S₄:Sn,Gd phosphors. The rare earth ions enhance the green emission band, which peaks at 534 nm, instead of the yellow one. The origin of this enhancement is discussed. The resonant energy transfer rates are estimated in the cases from Ce³⁺ to the green and yellow centers of Sn²⁺ and between the yellow centers and the green centers.     

Electrical conductivity, DSC, XRD, and 7Li NMR studies of rotator crystals n-C21H43COOLi x K(1 − x) (0.33 ≤ x ≤ 0.50), n-C m H(2m + 1)COOLi, and n-C m H(2m + 1)COOK (m = 13, 15, 17, 19, and 21)

Differential scanning calorimetry (DSC) thermograms, X-ray diffraction (XRD) analysis, electrical conductivity (σ), and ⁷Li NMR spectroscopy characterization of n-C _m H_(2m?+?1)COOM solids (M = Li, Na, K; m?=?13, 15, 17, 19, 21) and mixed crystals n-C₂₁H₄₃COOLi _x K_(1???x) (0.25?≤?x?≤?0.75) was performed as a function of temperature. DSC thermograms of n-C _m H_(2m?+?1)COOM revealed several solid-solid phase transitions with large entropy changes. Electrical conductivity studies established that n-C _m H_(2m?+?1)COOLi crystals are poor electrical conductors. In contrast, n-C _m H_(2m?+?1)COOK salts were found to have σ values of 10^???7–10^???8 S·cm^???1. Since the crystal structures and phase-transition temperatures of both n-C _m H_(2m?+?1)COOLi and n-C _m H_(2m?+?1)COOK crystals were similar, they were able to form mixed crystals with the structure n-C _x H_(2m?+?1)COOLi _x K_(1???x). DSC thermograms of the mixed crystals showed a small entropy change at the melting point (ΔS _mp?<?13 J K^???1 mol^???1), in addition, large ΔS values at the solid-solid phase transition temperature. The σ values obtained for mixed crystals were roughly one order of magnitude greater than those determined for n-C₂₁H₄₃COOK crystals. ⁷Li NMR spectra of the mixed crystals recorded at various temperatures suggested that the self-diffusion of Li^?+? ions was excited in the highest-temperature solid phase. Based on these results, we have classified these mixed crystals as rotator crystals.     

Nonlinear viscoelastic properties and change in entanglement structure of linear polymer

Simultaneous measurements of stress relaxation and differential dynamic modulus were made at 268 K over a time scale of 10 to 10⁴⁵ s for nearly monodisperse polybutadiene (M _w =2.2x10⁵, 1,2-structure 70%, M _e =3600) and also one having coarse cross-linking (M _c =29000). Static shear strain ranged from 0.1 to 2.0. In a long-time region (t> _k ), the relaxation modulus G (; t) could be expressed by the product G (0; t) h (y). The observed h() agreed well with the Doi-Edwards theory without use of IA approximation. Both the cured and uncured samples showed initial drop of the differential storage modulus G (), ; t) followed by gradual recovery, but did not attain the value before shearing G (, ; t) for the uncured sample showed smaller values than that for the cured one in the whole measured time scale at the higher strain, confirming the two origins of nonlinear viscoelasticity of well entangled polymer; induced chain anisotropy and induced decrement in entanglement density. G (, ; t) curves for the cured sample agreed well with the BKZ predictions. But the curves for the uncured sample agreed well with the BKZ prediction only at the time scale of t< _k . BKZ prediction showed significant upward deviations at t> _k . Such the differences are discussed in terms of the two origins.Dedicated to Prof. John D. Ferry on the occasion of his 85th birthday.     

Synthesis of 1,8- and 2,8-dihydrocycloheptapyrazol-8-one derivatives by the reactions of 3-acetyltropolone and its methyl ethers with phenylhydrazine

3-Acetyltropolone ( 1 ) reacted with phenylhydrazine to give 3-acetyltropolone phenylhydrazone ( 3 ) and 3-methyl-1-phenyl-1,8-dihydrocycloheptapyrazol-8-one ( 4 ). The former ( 3 ) cyclized to afford the latter ( 4 ). The reaction of 3-acetyl-2-methoxytropone ( 2a ) with phenylhydrazine gave 4 , 3-methyl-2-phenyl-2,8-dihydrocyclo-heptapyrazol-8-one ( 5 ), and 3-methyl-2-phenyl-2,8-dihydrocycloheptapyrazol-8-one phenylhydrazone ( 6 ). The compound ( 5 ) reacted with phenylhydrazine to afford 6 . The reaction of 7-acetyl-2-methoxytropone ( 2b ) with phenylhydrazone gave 7-acetyl-2-methoxytropone phenylhydrazone ( 7 ), 7-acetyl-2-(N′-phenylhydrazino)-tropone phenylhydrazone ( 8 ), 3-methyl-1-phenyl-1,8-dihydrocycloheptapyrazol-8-one phenylhydrazone ( 9 ), and 6 . The compound ( 7 ) was heated to afford 4 and reacted with phenylhydrazine to afford 8 and 9 . The compound ( 8 ) was also refluxed to give 9 .     

Cross-coupling of alkenyl,aryl or allylic selenides and grignard reagents catalyzed by nickel-phosphine complexes

Alkenyl, aryl or allylic selenides smoothly couple with Grignard reagents in the presence of Ni(II)-phosphine complexes as catalysts to afford the corresponding unsaturated compounds in good yields. The reactivity order of coupling reaction with BuMgBr catalyzed by NiCl₂ [Ph₂PCH₂CH₂CH₂PPh₂] was found to be PhSeMe « PhCl > PhSMe by the competitive reactions.     

Thermal expansion of InBi

Linear thermal expansion of InBi single crystal has been measured between ?186 and 100°C. Lattice constant a shows a normal behaviour over the measured temperature range. Lattice constant c, however, contracts monotonically with increasing temperature in this range.