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     

Visible-light-sensitive photocatalytic reaction on chromium-containing mesoporous silica: selective partial oxidation of propane with molecular oxygen

The photocatalytic reactivities of chromium-containing mesoporous silica molecular sieves (Cr-HMS) under visible light irradiation have been investigated. Cr-HMS involves tetrahedral chromium oxide (Cr-oxide) moieties which are highly dispersed and incorporated in the framework of molecular sieve with two terminal Cr=O groups. In the presence of propane with molecular oxygen, a partial oxidation proceeded under visible light irradiation to produce acetone and acrolein, with high selectivity, while a complete oxidation proceeded under UV light irradiation mainly to produce CO₂. The charge-transfer excited state of the tetrahedral Cr-oxide moieties plays a significant role in the photocatalytic reactions.     

Fabrication and transport properties of multiwall carbon nanotube crossroads

A multiwall carbon nanotube crossroads has been fabricated by a manipulation technique using a glass microcapillary, and the low temperature transport properties investigated. The two-terminal conductance of an individual tube shows Tomonaga–Luttinger liquid behavior G∝T^α at high temperature and dI/dV ∝V ^α at low temperature. However, no evidence of such a power-law behavior is obtained in the four-terminal conductance at the junction, where the conductance shows an almost metallic behavior ‘corrected’ by weak localization. Weak localization would essentially appear in electron states at the junctions of MWNTs.     

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.     

Fluorometric sensing of alkaline Earth metal cations by new lariat ethers having plural pyrenylmethyl groups on the electron-donating sidearms

[structure: see text] New fluorescent compounds (1), lariat ethers having plural pyrenylmethyl groups on the sidearms, were prepared, and their complexation behavior with alkaline earth metal cations was examined by fluorescence spectrometry. The pyrene excimer emission decreased accompanied with an increase in the monomer emission upon complexation with the metal ion. This finding is ascribed to the cooperative participation of one of the two sidearms in the complexation of the crown ring with the metal ion.     

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.     

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.