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     

Anisotropic friction model of DNA electrophoresis in polymer solutions: Comparison with direct observations

The electrophoresis of DNA chains in uncrosslinked polymer solutions with a Brownian dynamics simulation with an anisotropic friction tensor was analyzed. According to the degree of anisotropy, three types of migration behavior are obtained: fluctuation without or with periodicity between U‐shaped and compact conformations, or migration with linear conformation. We found good agreement between our simulation results and the direct observations of DNA by fluorescence microscopy. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 1316–1322, 2003     

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.     

The Heat Kernel on Hyperbolic Space

The purpose of this note is to provide a new proof for the explicitformulas of the heat kernel on hyperbolic space. By definition,the hyperbolic space Hⁿ is a (unique) simply connected completen-dimensional Riemannian manifold with a constant negative sectionalcurvature –1. 1991 Mathematics Subject Classification58G32, 58G11.     

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.     

External validation of the biodegradability prediction model CATABOL using data sets of existing and new chemicals under the Japanese Chemical Substances Control Law

External validation of the biodegradability prediction model CATABOL was conducted using test data of 338 existing chemicals and 1123 new chemicals under the Japanese Chemical Substances Control Law. CATABOL predicts that 1089 chemicals will have a BOD < 60% while 925 (85%) actually have an observed BOD<60%. The percentage of chemicals with an observed BOD value <60% tends to increase as the predicted BOD values decrease. In contrast, 340 chemicals were predicted to have a BOD > or = 60% and 234 (69%) actually had an observed BOD > or = 60%. The prediction of poor biodegradability was more accurate than the predictions of high biodegradability. The features of chemical structures affecting CATABOL predictability were also investigated.     

Electrical conducting and magnetic properties of (ethylenedithiotetrathiafulvalenothioquinone-1,3-diselenolemethide)2.FeBr4 (GaBr4) crystals with two different interlayer arrangements of donor molecules

Two donor molecules newly synthesized, dimethylthio- and ethylenedithio-tetrathiafulvalenothioquinone-1,3-diselenolemethides (1 and 2), were used to prepare their charge-transfer (CT) salts with a magnetic FeBr(4)(-) counteranion. For 1, a low electrical conducting 1:1 salt (1.FeBr(4)) was obtained, in which molecules of 1 are tightly dimerized in a one-dimensional (1D) stacking column. On the other hand, 2 gave a 2:1 salt (2(2).FeBr(4)) as two different kinds of plate crystals (I and II). Both I and II possess similar stacking structures of molecules of 2 in each 1D column with a half-cut pipelike structure along the c axis. However, for I, the stacking columns are aligned in the same direction along the a and b axes, while for II they are in the same direction along the a axis, but in the reverse direction along the b axis, resulting in the difference in the relative arrangement of molecules of 2 and FeBr(4)(-) ions between the two crystals. The room-temperature electrical conductivities of the single crystals of I and II were 13.6 and 12.7 S cm(-)(1), respectively. The electrical conducting behavior in I was metallic above 170 K but changed to be semiconducting with a very small activation energy of 7.0 meV in the temperature range 4-170 K. In contrast, II showed the semiconducting behavior in the whole temperature range 77-285 K. The corresponding nonmagnetic GaBr(4)(-) salts with almost the same crystal structure as I and II showed definitively different electrical conducting properties in the metal to semiconductor transition temperature in I as well as in the magnitude of activation energy in the semiconducting region of I and II. The interaction between the d spins of FeBr(4)(-) ions was weak and antiferromagnetic in both I and II, but the magnitude of the spin interaction was unexpectedly larger compared with that in the FeBr(4)(-) salt of the corresponding sulfur derivative of 2 with closer contact between the neighboring FeBr(4)(-) ions. These electrical conducting and magnetic results suggest a significant interaction between the conducting pi electrons and the d spins of FeBr(4)(-) ions located near the columns or layers.     

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.