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     

Stability of the steady state for the Falk model system of shape memory alloys

In this article a stability result for the Falk model system is proven. The Falk model system describes the martensitic phase transitions in shape memory alloys. In our setting, the steady state is a nonlocal elliptic problem. We show the dynamical stability for the linearized stable critical point of the corresponding functional. Copyright © 2007 John Wiley & Sons, Ltd.     

Hydration Structure Around the Carboxyl Group Studied by Neutron Diffraction with 12C/13C and H/D Isotopic Substitution Methods

Time-of-Flight (TOF) neutron diffraction measurements have been carried out on aqueous 8 mol% sodium acetate solutions in D₂O. Scattering cross sections that were observed for sample solutions involving ¹²C/¹³C and H/D isotopically substituted acetate ions were used to derive the first-order difference functions, Δ_H(Q) and Δ_C(Q), and corresponding distribution functions, G _H(r;r) and G _C(r;r), which describe the environmental structure around the methyl and the carboxyl groups within the acetate ion, respectively. Structural parameters concerning the first hydration shell of the carboxyl group within the acetate ion were obtained through the least squares fit to the observed intermolecular difference function, Δ_C ^inter(Q). The nearest neighbor C _O...D _W1 (C_O: carboxyl carbon atom, D_W1: water deuterium atom) distance, r(C _O...D _W1 ), and the angle, ∠ C _O ...D _W1 -O _W (O _W : water oxygen atom), were determined to be 2.63(1) Å and 120(1)°, respectively. The coordination number, n(C _O ...D _W1 ), was obtained to be 4.0(1). These results are consistent with the hydration structure in which water molecules in the first hydration shell of the carboxyl group are hydrogen-bonded with oxygen atoms of the carboxyl group.     

Direct observation of the multistep helix formation of poly-L-glutamic acids

The helix formation dynamics of poly-L-glutamic acids (PGAs) were observed by the microsecond-resolved Fourier transform infrared (FTIR) and circular dichroism (CD) spectroscopies. The helix formation of 34-residue PGA from random coil at pH (or pD for FTIR) 8.0 was initiated by a pH jump to 4.9 using the rapid solution mixer whose mixing dead time is 50 micros. The amide I' line in the time-resolved FTIR spectra exhibited the fast (<100 micros) increase of the total helical content. The time-resolved CD spectra of the same process also showed the fast (<150 micros) formation of short helical segments (5 +/- 1 residues), which was followed by the slower (<1 ms) elongation of the short helices to longer helices (>10 residues). Similar dynamics were observed for the same pH jump of approximately 190-residue PGA, although there were additional steps that made the helix formation of approximately 190-residue PGA more complex. The observed multistep helix formation is likely caused by the strong hydrogen-bonding interactions between the protonated side chains of PGAs.     

Remarkable reactivity enhancement with Sb?N inter-coordination of ethynyl-1,5-azastibocines in Pd-catalyzed cross-coupling reactions with organic halides

The reaction of 12-arylethynyl-6-methyl-5,6,7,12-tetrahydrodibenzo[c,f][1,5]-azastibocines with organic halides such as acyl halides and aryl halides in the presence of PdCl₂(PPh₃)₂ as a catalyst led to the formation of cross-coupling products, alkynyl ketones and diaryl acetylenes, in good yields. The reactivity of the ethynyl group on the 1,5-azastibocines was far superior to that on diphenyl(phenylethynyl)stibane, which brought about marked improvement in the reaction conditions (lower temperature and shorter reaction time) and in the yields of the cross-coupling products. Single-crystal X-ray analysis of the ethynyl-1,5-azastibocine showed the presence of intramolecular Sb?N interaction which should be responsible for the remarkable reactivity enhancement of the 1,5-azastibocines for this type of reaction.     

Charge-induced spin alignment in diradical donor molecules: numerical calculations of correlated many-electron-spin systems

The mechanism of charge-induced high spin is studied in pi-conjugated molecules by means of a model-Hamiltonian approach. Intersite Coulomb interactions are taken into account in a pi-conjugated moiety, which is coupled with two localized spins through exchange interactions. We clarify spin alignment in neutral and oxidized states by exact numerical calculations including all the correlation effects. In thianthrene-based molecules, one-electron oxidation induces strong ferromagnetic correlation between the localized spins irrespective of the spin alignment in the neutral state. The localized spins are coupled to the delocalized hole spin ferromagnetically, leading to a high-spin state in the oxidized molecule. Our calculations on structural dependence and effective exchange interaction are consistent with the recent experiment of thianthrene bis(nitronyl nitroxide). By comparing the thianthrene-based molecule with the anthracene-based one, we clarify the role of superexchange interactions via the sulfur atoms.     

Hydrogenation of benzaldehyde and cinnamaldehyde in compressed CO2 medium with a Pt/C catalyst: a study on molecular interactions and pressure effects

The hydrogenation of benzaldehyde and cinnamaldehyde has been studied with a 5% Pt/C catalyst in compressed CO(2). The effect of CO(2) pressure on the total conversion was found to be different between the two aldehydes. The total conversion of benzaldehyde merely decreases with increasing CO(2) pressure, while that of cinnamaldehyde shows a maximum at a certain pressure. High-pressure FTIR measurements indicate the existence of interactions of CO(2) with the aldehydes. The absorption of nu(C=O) red-shifts at increasing CO(2) pressure, and this red-shift is more significant for cinnamaldehyde than for benzaldehyde, indicating that the C=O bond of the former becomes more reactive than the latter. The difference in the mode of interactions of CO(2) with these aldehydes has also been indicated by changes of nu(C=O) of CO(2). Thus, the conversion of benzaldehyde will decrease with increasing CO(2) pressure because of a simple dilution by introducing a larger quantity of CO(2). For cinnamaldehyde, the conversion will increase at low pressures because of increasing interactions with CO(2) molecules (increasing the reactivity of the C=O bond) but decrease at high pressures because of the simple dilution effect, similar to the case of benzaldehyde. The dense CO(2) molecules are not likely to change the catalytic activity of supported Pt particles, which was previously suggested from optical absorption of supported fine metal (Au) particles in a compressed CO(2) medium.     

Enantioselectively catalyzed oxidation of 3,4-dihydroxy-l-phenylalanine by N-lauroyl L or D-histidine-Cu(II) complex in CTABr micelles.

In order to investigate the enzyme model reaction the oxidation of 3,4-dihydihydroxy-L-phenylalanine(L-DOPA) was carried out using optically active catalyst, N-lauroyl L or D-histidine-Cu(II) complex(L or D-LauHis-Cu(II)), showing appreciable enantioselectivity in the presence of the mixed micelles with CTABr.     

Precipitation of some nonionic polymers by octylammonium thiocyanate

The effects of various alkylammonium thiocyanates (ethyl, butyl, hexyl, and octyl) on aqueous solutions of polyvinylpyrrolidone (PVP) and poly(vinyl alcohol–acetate) copolymer (PVA-Ac) were studied and compared with the effects caused by the respective chlorides. Whereas the PVP solution was hardly affected by the chlorides, it was precipitated by n-octylammonium thiocyanate (OASCN) at dilute concentrations and dissolved at higher concentrations. On taking the effects of ammonium chloride and thiocyanate on the solubility of PVA-Ac as references, with increasing of alkyl chain length, alkylammonium chlorides raised the polymer solubility steadily; on the contrary, the thiocyanates at dilute concentrations, except for ethylammonium thiocyanate, lowered it, and OASCN at dilute concentrations, except for ethylammonium thiocyanate, lowered it, and OASCN at dilute concentrations was a particularly strong salting-out agent. The amount of binding of OASCN to the polymers in the precipitated systems was measured. The precipitation was attributed to ion-pair binding of OASCN to the polymers, and the mechanism was discussed in terms of the interaction between the water structure-breaking SCN^? and the water structure-making hydrophobic groups.