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     

Potential formation and high density plasma production on the tandem mirror GAMMA 10

GAMMA 10 experiments have advanced in high density experiments after the last EPS Workshop where we reported high density plasma production by using an ion cyclotron range of frequency heating at a high harmonic frequency and neutral beam injection in the central cell. Recently a high density plasma was obtained with much improved reproducibility than before and without degradation of diamagnetic signal. The high density plasma was attained by adjusting the spacing of the conducting plates installed in the anchor transition regions. Dependencies of particle confinement time, ion energy confinement time and plasma confining potential on plasma density were obtained for the first time in the high density region. Presented at 5th Workshop “Role of Electric Fields in Plasma Confinement and Exhaust”, Montreus, Switzerland, June 23–24, 2002.     

Temperature dependence of the exafs spectrum in YBa2Cu3O7−δ compounds

The temperature dependence of the extended X-ray absorption fine structure (EXAFS) is studied in the high T_c superconductors, YBa₂Cu₃O_7−δ. The measurements were done at the Cu K-edge for samples of two orthorhombic phases (T_c≈90 K and ≈58 K, respectively) and a nonsuperconducting tetragonal phase. Interatomic distances and mean square relative displacements σ² for Cu-O bonds are determined by the least squares refinement. The results indicate that values of σ² increase near T_c for both the orthorhombic samples. It is concluded that this anomalous behavior related to T_c is caused by an anomalous vibration of oxygen atoms in the Ba-O layer. Changes in the Cu-O distances from 300 to 20 K are not found.     

In situ observations of domain wall motion in Mn–Zn and Ni–Zn ferrites by Lorentz microscopy and electron holography

Domain wall motion in Mn–Zn and Ni–Zn ferrites with applied magnetic fields is investigated by in situ observations with Lorentz microscopy and electron holography. It is found that both Mn–Zn and Ni–Zn ferrites have a mean grain size of approximately 10 μm and several pores with sizes ranging from 0.2 to 1.1 μm. In situ observations by Lorentz microscopy with an applied magnetic field reveals that in Mn–Zn ferrite, the domain walls move easily across the grain boundary, while in Ni–Zn ferrite, the domain walls move along the grain boundary but are pinned at the grain boundary and pores. From in situ observations of Ni–Zn ferrite by electron holography, it is clarified that domain wall pinning at the grain boundary retards a sensitive increase in magnetic flux parallel to the applied field direction, which is considered to result in high hysteresis loss.     

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.     

Synthesis of the LMN-ring fragment of the Caribbean ciguatoxin C-CTX-1

Ciguatoxin C-CTX-1 was isolated as a principal causative toxin of ciguatera seafood poisoning in the Caribbean Sea, and is structurally classified as a ladder-shaped polycyclic ether. In this Letter, we report the synthesis of the tricyclic LMN-ring system of C-CTX-1. SmI₂-mediated reductive cyclization efficiently constructed the seven-membered M-ring with the axially oriented 1,3-dimethyl structure.     

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。