Nonrelativistic limit in the energy space for nonlinear Klein-Gordon equations

We study the nonrelativistic limit of the Cauchy problem for the nonlinear Klein-Gordon equation and prove that any finite energy solution converges to the corresponding solution of the nonlinear Schr?dinger equation in the energy space, after the infinite oscillation in time is removed. We also derive the optimal rate of convergence in . Received: 13 July 2000 / Published online: 1 February 2002     

Selection principle for various modes of spatially nonuniform electrochemical oscillations

The pattern selection principle for various modes of spatially nonuniform oscillation was investigated by taking a current oscillation of negative differential resistance type, appearing in H2O2 reduction on platinum (Pt) ring electrodes, as a model system. In experiments, various modes of spatiotemporal oscillation, such as a spatially uniform oscillation, standing wave oscillation, and rotating wave oscillation, appeared depending on the applied potential and the distance between the Pt-ring electrode and the reference electrode. A simple mathematical model for the spatiotemporal patterns at the electrode surface was proposed. Numerical calculations and nonlinear bifurcation analysis based on the proposed model reproduced all the essential features of the experimental results and clarified the pattern selection principle.     

Chiral resolution of monosaccharides as 1-phenyl-3-methyl-5-pyrazolone derivatives by ligand-exchange CE using borate anion as a central ion of the chiral selector

Six reducing monosaccharides (mannose, galactose, fucose, glucose, xylose, and arabinose) were derivatized with 1-phenyl-3-methyl-5-pyrazolone (PMP) and chiral resolution of these racemic PMP-monosaccharides was studied by ligand-exchange CE using borate anion as a central ion of the chiral selector and (S)-3-amino-1,2-propanediol (SAP) as a chiral selector ligand. PMP-mannose, PMP-galactose and PMP-fucose were successfully enantioseparated. Lowering the capillary temperature increased the resolution of PMP-mannose system, but decreased that of PMP-galactose and PMP-fucose systems. Whereas the maximum resolution was obtained at pH 8.9 in the PMP-mannose system, resolution increased gradually with pH in the PMP-galactose and PMP-fucose systems. Expecting the formation of the ternary borate complexes with SAP and PMP-monosaccharide in the CE experiments, the optimized structures of the borate diastereomers were obtained by semiempirical molecular orbital calculations to discuss the structural difference of the diastereomers in connection with the enantioseparation behaviors.     

Double catalytic enantioselective Michael addition reactions of tertiary nucleophile precursors—tertiary/quaternary and quaternary/quaternary carbon–carbon bond formations

Enantioselective Michael addition reactions of tertiary nucleophile precursors, such as substituted malononitriles and cyclic 1,3-diketones, can be successfully activated by the metal complexes derived from R,R-DBFOX/Ph chiral ligand and cationic metal salts. With this method, the enantioselective tertiary/quaternary and quaternary/quaternary carbon–carbon bond formations can be achieved. Use of alcohol solvents is essential for the success, and ,β-unsaturated amides of 3,5-dimethylpyrazole are much better acceptors than those of 2-oxazolidinone.     

Preparation of monodispersed vinylpyridine–divinylbenzene porous copolymer resins and their application to high-performance liquid chromatographic separation of aromatic amines

For the separation of aromatic amines, two types of monodispersed porous polymer resins were prepared by the copolymerization of 2-vinylpyridine and 4-vinylpyridine with divinylbenzene in the presence of template silica gel particles (particle size 5 μm), followed by dissolution of the template silica gel in an alkaline solution. The transmission electron micrographs and the scanning electron micrograph revealed that these templated polymer resins have a spherical morphology with a good monodispersity and porous structure. Using these monodispersed polymer resins, the high-performance liquid chromatographic separation of aromatic amines in the mobile phases of pHs 2.0, 2.9, 4.1, 7.2 and 11.7 were carried out. The 2-vinylpyridine–divinylbenzene copolymer resins showed slightly stronger retentions for aromatic amines than the 4-vinylpyridine–divinylbenzene copolymer resins. Under acidic conditions (around pH 2.0), aniline and the toluidines showed no retention on these copolymer resins due to the repulsion between the cationic forms of these amines and pyridinium cations in the stationary phase, whereas less basic aromatic amines or non-basic acetanilide showed slight retentions. Above pH 4.1, the separation of aromatic amines with these polymer resins showed a typical reversed-phase mode separation. Therefore, the separation patterns of aromatic amines are effectively tunable by changing the pH value of the mobile phases. A good separation of eight aromatic amines was achieved at pH 2.9 using the 2-vinylpyridine–divinylbenzene copolymer resins.     

A synchrotron X‐ray study of triclinic LiCa2Nb3O10 with perovskite‐type slabs

The triclinic superstructure of a small crystal of LiCa₂Nb₃O₁₀, lithium dicalcium triniobium decaoxide, has been investigated by synchrotron X‐ray diffraction. The unit cell is an almost rectangular parallelepiped, although there is a 0.245° offset from orthogonality for β. The structure essentially belongs to a homologous series of Li[Na_n?3Ca₂Nb_nO_3n+1] with n = 3, where the moiety in square brackets has a perovskite‐type slab structure. The superstructure has a doubled unit‐cell volume with respect to the tetragonal aristotype. The NbO₆ octahedra are rotated about axes parallel to [110] by approximately 10°. Adjacent slabs are connected by Li atoms and are geo­metrically related by 4₂ pseudosymmetry lying parallel to c . There are twice as many sites as Li atoms, providing a variation of population at these Li sites.     

Physicochemical characterization of tamoxifen citrate pseudopolymorphs, methanolate and ethanolate

Two novel pseudopolymorphs, methanolate and ethanolate of tamoxifen [(Z)-2-[4-(1,2-diphenyl-1-butenyl)phenoxy]-N,N-dimethylethylamine]citrate, were prepared in addition to forms A and B reported previously. Their crystalline forms were identified and characterized by powder and single crystal X-ray diffractometry, differential scanning calorimetry, thermogravimetric analysis, hot-stage microscopy, scanning electron microscopy and diffuse reflectance infrared Fourier-transform spectroscopy, and their physicochemical stability was also evaluated. The results of single crystal X-ray analysis and thermogravimetric analysis of methanolate and ethanolate suggested that the stoichiometry of tamoxifen citrate : methanol and tamoxifen citrate : ethanol could be composed of a 1 : 1 molecular ratio for both solvates. The results of physicochemical stability evaluations at 75 and 97% RH at 40 and 60 degrees C indicated that the metastable form A was quite stable for at least 2 months even under severe storage conditions, whereas methanolate immediately transformed to a crystalline mixture of forms A and B, and subsequently changed to the stable form B.     

Enhanced skin permeation of diclofenac by ion-pair formation and further enhancement by microemulsion

Enhancement of skin permeability of anionic diclofenac from non-aqueous vehicle isopropyl myristate (IPM) by ion-pair formation with either alkylamines or benzylamine as model cationic ions was examined in guinea pig dorsal skin. Diclofenac ion flux increased in the presence of these amines due to an increase in solubility. Maximum flux was observed in the presence of n-hexylamine, which induced 7.3-fold increase accompanied by a 45-fold increase in solubility. Permeability coefficients of the ionic form of diclofenac in the presence of benzylamine, n-hexylamine and iso-octylamine as counter ions in IPM were larger than those of the non-ionic form of diclofenac. Since the solubility of diclofenac was still limited, to obtain further enhancement of skin permeation, the effects of microemulsions as a vehicle consisting of phosphate buffered saline (PBS), isopropyl myristate (IPM), polyoxyethylene sorbitan monooleate (Tween 80) and ethanol were examined for transport of diclofenac-benzylamine ion-pairs. All microemulsion formulations tested increased diclofenac flux 4.9-fold to 10.7-fold over the value without a microemulsion accompanied by a 217-fold to 302-fold improvement in the solubility of diclofenac-benzylamine ion-pairs, but permeability coefficients were decreased 28-44 fold. Maximum enhancement was observed for a microemulsion with a ratio of PBS, IPM, ethanol and Tween 80 of 25 : 8 : 47 : 20 (w/w). The present findings suggest the usefulness of combined use of ion-pairs with microemulsions for enhancement of skin permeation of ionic drugs.     

Kaempferol glycosides in the flowers of carnation and their contribution to the creamy white flower color

Three flavonol glycosides were isolated from the flowers of carnation cultivars 'White Wink' and 'Honey Moon'. They were identified from their UV, MS, 1H and 13C NMR spectra as kaempferol 3-O-neohesperidoside, kaempferol 3-O-sophoroside and kaempferol 3-O-glucosyl-(1 --> 2)-[rhamnosyl-(1 --> 6)-glucoside]. Referring to previous reports, flavonols occurring in carnation flowers are characterized as kaempferol 3-O-glucosides with additional sugars binding at the 2 and/or 6-positions of the glucose. The kaempferol glycoside contents of a nearly pure white flower and some creamy white flower lines were compared. Although the major glycoside was different in each line, the total kaempferol contents of the creamy white lines were from 5.9 to 20.9 times higher than the pure white line. Thus, in carnations, kaempferol glycosides surely contribute to the creamy tone of white flowers.