X-ray crystallographic analysis of N,N-diallylcoumarincarboxamides and the solid-state photochemical reaction

X-ray crystallographic analysis and the photochemical aspects of N,N-diallylcoumarincarboxamides were investigated. Irradiation of the corresponding amides promoted stereoselective intramolecular cyclobutane formation exclusively. The solid-state photoreaction of the coumarinamide without substituent on the 4-position proceeded in a crystal-to-crystal manner. On the other hand, photolysis of the amide possessing a methyl group at the 4-position also effected 2+2 cycloaddition; however, the reaction proceeded much slower. The difference in the reactivity was explainable on the basis of the molecular conformation in the crystal lattice.     

Synthesis of well‐defined aromatic polyesters by chain‐growth polycondensation under suppression of transesterification

For the synthesis of aromatic polyesters with defined molecular weights and narrow molecular weight distributions (MWDs), we investigated the chain‐growth polycondensation of active amide derivatives of 4‐hydroxybenzoic acid, 1a and 1b , having an octyl or 4,7‐dioxaoctyl side chain, respectively. To suppress the transesterification of the polymer backbone with the monomer, the polymerization of 1 was carried out in tetrahydrofuran (THF) at −30 °C in the presence of initiator 2 and Et₃SiH/CsF/18‐crown‐6, which generated a hydride ion as a base in situ. The number‐average molecular weight (M_n) of poly 1a was controlled, and narrow MWDs were maintained, until the [ 1a ]₀/[ 2 ]₀ feed ratio was 14.3 (M_n ≤ 3500), whereas that of poly 1b was controlled until the feed ratio was 30 (M_n ≤ 7250). The difference stemmed from the higher solubility of poly 1b in THF. This chain‐growth polycondensation was applied to the synthesis of a diblock copolyester of 1a and 1b of a defined architecture. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 4109–4117, 2005     

Evaluation of stoichiometric rare-earth molybdate and tungstate compounds as laser materials

Photoluminescence spectra, photoluminescence decay curves and Raman scattering spectra have been investigated for stoichiometric rare-earth molybdate and tungstate compounds. NaNd(MoO₄)₂ and NaNd(WO₄)₂ show emissions due to the transition ⁴F_3/2→⁴I_9/2 in Nd³⁺. A possibility of laser oscillation in NaNd(MoO₄)₂ is pointed from comparisons of the emission intensity and the decay time constant with NaNd(WO₄)₂ where laser oscillations have been reported. In NaLa(MoO₄)₂ and NaLa(WO₄)₂, observed emissions which are not related to La³⁺ are probably due to the transitions in MoO₄^2- and WO₄^2- molecular ions, respectively, in scheelite crystal. Raman spectra of these compounds are similar, probably related to the same crystal structure. LiEr(MoO₄)₂ shows the emissions due to transitions ²H_11/2→⁴I_15/2, ⁴S_3/2→⁴I_15/2 and ⁴F_9/2→⁴I_15/2 in Er³⁺, respectively, which are believed to be observed for the first time.     

Singularity formation in three-dimensional inviscid flow

A phenomenological model to explain finite time singularity formation in a three-dimensional inviscid vorticity field is given. The thin filament approximation for a vorticity field is used, and the model is based on the three-dimensional interaction of two approximately straight vortex filaments. It is shown that the model has a solution which exhibits finite time singularity formation in a vorticity field.     

Self-synchronization of coupled oscillators with hysteretic responses

We analyze a large system of nonlinear phase oscillators with sinusoidal nonlinearity, uniformly distributed natural frequencies and global all-to-all coupling, which is an extension of Kuramoto's model to second-order systems. For small coupling, the system evolves to an incoherent state with the phases of all the oscillators distributed uniformly. As the coupling is increased, the system exhibits a discontinuous transition to the coherently synchronized state at a pinning threshold.of the coupling strength, or to a partially synchronized oscillation coherent state at a certain threshold below the pinning threshold. If the coupling is decreased from a strong coupling with all the oscillators synchronized coherently, this coherence can persist until the depinning threshold which is less than the pinning threshold, resulting in hysteretic synchrony depending on the initial configuration of the oscillators. We obtain analytically both the pinning and depinning threshold and also expalin the discontinuous transition at the thresholds for the underdamped case in the large system size limit. Numerical exploration shows the oscillatory partially coherent state bifurcates at the depinning threshold and also suggests that this state persists independent of the system size. The system studied here provides a simple model for collective behaviour in damped driven high-dimensional Hamiltonian systems which can explain the synchronous firing of certain fireflies or neural oscillators with frequency adaptation and may also be applicable to interconnected power systems.     

Fast verification of solutions of matrix equations

Summary. In this paper, we are concerned with a matrix equation where A is an real matrix and x and b are n-vectors. Assume that an approximate solution is given together with an approximate LU decomposition. We will present fast algorithms for proving nonsingularity of A and for calculating rigorous error bounds for . The emphasis is on rigour of the bounds. The purpose of this paper is to propose different algorithms, the fastest with flops computational cost for the verification step, the same as for the LU decomposition. The presented algorithms exclusively use library routines for LU decomposition and for all other matrix and vector operations. Received June 16, 1999 / Revised version received January 25, 2001 / Published online June 20, 2001     

Ground state of a spin system with two- and four-spin exchange interactions on the triangular lattice

We study a spin system with both two- and four-spin exchange interactions on the triangular lattice as a possible model for the nuclear magnetism of solid ³He layers adsorbed on grafoil. The ground state is analyzed by the use of the mean-field approximation. It is shown that the four-sublattice state is favored by introduction of the fourspin exchange interaction. A possible phase transition at a finite temperature into a phase with the scalar chirality is predicted. Application of a magnetic field is shown to cause a variety of phase transitions.     

In situ 57Fe Mössbauer Investigation of Solid-State Redox Reactions of Lithium Insertion Electrodes for Advanced Batteries

A novel in situ electrochemical cell for ⁵⁷Fe Mössbauer measurements was developed in order to clarify the mechanisms of solid-state redox reactions in lithium insertion materials containing iron. Our in situ Mössbauer technique was successfully applied to the determination as to which transition metal ion was a redox center in the insertion electrodes, such as LiFe_0.5Mn_1.5O₄, LiFeTiO₄, or LiFe_0.25Ni_0.75O₂, for the lithium-ion batteries.