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     

On K1 and K2 of Algebraic Surfaces

In this paper we study higher Chow groups of smooth, projective surfaces over a field k of characteristic zero, using some new Hodge theoretic methods which we develop for this purpose. In particular we investigate the subgroup of CH ^r+1 (X,r) with r = 1,2 consisting of cycles that are supported over a normal crossing divisor Z on X. In this case, the Hodge theory of the complement forms an interesting variation of mixed Hodge structures in any geometric deformation of the situation. Our main result is a structure theorem in the case where X is a very general hypersurface of degree d in projective 3-space for d sufficiently large and Z is a union of very general hypersurface sections of X. In this case we show that the subgroup of CH ^r+1 (X,r) we consider is generated by obvious cycles only arising from rational functions on X with poles along Z. This can be seen as a generalization of the Noether–Lefschetz theorem for r = 0. In the case r = 1 there is a similar generalization by Müller-Stach, but our result is more precise than it, since it is geometric and not only cohomological. The case r = 2 is entirely new and original in this paper. For small d, we construct some explicit examples for r = 1 and 2 where the corresponding higher Chow groups are indecomposable, i.e. not the image of certain products of lower order groups. In an appendix Alberto Collino constructs even more indecomposable examples in CH ³ (X,2) which move in a one-dimensional family on the surface X.Contribution to appendix.     

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.     

Almost automorphic solutions for abstract functional differential equations

For abstract linear functional differential equations with an almost automorphic forcing term, we establish a result on the existence of almost automorphic solutions, which extends the classical theorem due to Massera on the existence of periodic solutions for linear periodic ordinary differential equations.     

Ethylene polymerization by chromium complexes with phosphorous‐bridged bisphenoxy ligand

Chromium catalysts combined with phosphorous‐bridged bisphenoxy ligands were found to be highly active for ethylene polymerization. The most efficient catalyst precursor among them, generated by combining bis[3‐tert‐butyl‐5‐methyl‐2‐hydroxyphenyl](phenyl)phosphine hydrochloride ( 1a ) and CrCl₃(THF)₃, was characterized. X‐ray analysis of (3‐tert‐butyl‐5‐methyl‐2‐phenoxy)(3‐tert‐butyl‐5‐methyl‐ 2‐hydroxyphenyl)(phenyl)phosphine bis(tetrahydrofuran)chromium dichloride ( 6 ), obtained by the reaction of 1a and CrCl₃(THF)₃ in the presence of NaH, revealed a unique structure in which one phenol moiety of the bisphenol did not coordinate to the chromium center. Complex 6 showed higher activities than those observed in the in situ catalyst system. Polyethylene of various molecular weights was obtained with differing activators. The highest activity (113.5 kg mmol (cat)^?1 h^?1) was observed when TIBA/TB was used as a cocatalyst. A medium molecular weight polymer with narrow molecular weight distribution (M_w = 128,700, M_w/M_n = 1.8) was obtained using a 6 ‐TIBA/B(C₆F₅)₃ system. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 3668–3676, 2007     

The origin of enhanced photocatalytic decomposition of ATP on TiO2 powders as induced by surface modification with lanthanide ions: important roles of ATP adsorption to the modified surface

Surface modification of TiO₂ powders with lanthanide salts (EuCl₃ or YbCl₃) enhanced photocatalytic decomposition of ATP. In comparison with the unmodified catalyst, a 3-fold increase in the ATP decay rate was observed with TiO₂ powders as prepared in 5 mM EuCl₃ (or YbCl₃) solution. The reason was ascribed to enrichment of ATP to TiO₂ powder with the lanthanide ions. Evidence was obtained by adsorption experiments where ATP concentration was monitored after dispersing TiO₂ powders into the solution. The ATP molecules adsorbed faster to TiO₂ powder and strongly stabilized there in the presence of Yb³⁺ than otherwise.     

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.     

镍 钴 钯 铁2—（二苯基膦基）吡啶配合物的合成及其催化羰基化反应

众所周知,铑催化剂是醇类羰基化的有效催化剂,但是铑价格昂贵且对设备有腐蚀性,因此,寻找出对醇类羰基化催化活性好的非贵金属催化剂,对醇类羰化的工业化有十分重要的意义。 本文在温和条件下,合成了四种含有相同配体(Ph_2PPy)不同金属的有机配合物(金属基分别为Ni、Co、Pd、Fe),并探索了它们对乙醇羰基化反应的催化活性。     

Studies on analgesic oligopeptides. VI. Further studies of synthesis and biological properties of tripeptide alkylamides, Tyr-D-Arg-Phe-X

Nine analogs based on a structure of Tyr-D-Arg-Phe-X (X = alkylamides or alkylhydrazide containing electron-withdrawing atoms or groups) were newly synthesized and their biological properties were examined by the opioid receptor binding properties of mu-, delta- and kappa-receptors, guinea-pig ileum (GPI) assay and analgesic activity in the tail pinch test after subcutaneous administration in mice. Analogs with X = NHCF2CF3, Sar-ol, or NH(CH2)2CN showed potent activities in the GPI and analgesic assays and high affinity for mu-receptor. An analog with X = taurinamide was found to possess 4-fold higher mu-receptor selectivity than that of [D-Ala2, MePhe4, Gly-ol5]enkephalin (DAGO). The receptor binding properties of previously reported analogs [Chem. Pharm. Bull., 33, 1528 (1985); ibid., 33, 4865 (1985); ibid., 36, 4834 (1988)] were also examined for overall discussion of the structure-activity relationships of this series of tripeptide amides.     

Stereospecific polymerization of isobutyl vinyl ether catalyzed by calcined iron sulfate

The polymerization of isobutyl vinyl ether was studied in a heterogeneous system using iron (II) sulfate calcined in air at various temperatures as a catalyst. The maximum activity was shown by the catalyst calcined at 700°C, which effected the polymerization at room temperature in a few seconds, while the sulfate treated at 750°C was totally inactive. Poly(vinyl ethyl ether) was also obtained by the FeSO₄ (700°C) catalyst at room temperature. This catalyst formed the crystalline polymer (melting temperature 135–138°C) when the reaction was performed in toluene as solvent at room temperature. Poisoning experiments with Hammett indicators were carried out with the FeSO₄ (700°C) catalyst. The treatment with n-butylamine rendered it inactive in the reaction of isobutyl vinyl ether, while its catalytic activity was little affected by dicinnamalacetone. On the basis of the observed results, the nature of active sites of catalyst is discussed.