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     

Isolation of mitogenic substance from sclerotia of Sclerotinia sclerotiorum IFO 9395 extracted with phosphate buffer.

The buffer extracts (3S) of sclerotia of Sclerotinia sclerotiorum IFO 9395 contained mitogenic substance(s) to murine splenocytes (Shinohara et al. Chem. Pharm. Bull., 38, 2219 (1990)). Although the native 3S was slightly mitogenic, heating of 3S induced significant mitogenic activity. To isolate the mitogen, we separated 3S by ion-exchange and gel filtration chromatographies. The isolated mitogen, named sclerogen, has a molecular mass of 32 kilodaltons (kDa) on sodium dodecyl sulfate-polyacrylamide gel electrophoresis (SDS-PAGE) and the isoelectric point (pI) of 5.9 by chromatofocusing. Sclerogen was significantly mitogenic in vitro against murine splenocytes after heat denaturation, and also showed the augmentation of the primary mixed lymphocyte reaction (MLR) in vitro. However, sclerogen did not show the activation of an alternative pathway of complement and hemagglutination activity. These results suggest that sclerogen is a unique mitogen which differs from lectins and shows mitogenicity after heat denaturation.     

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.     

Determination of midodrine in human plasma by high-performance liquid chromatography with fluorescence detection.

A simple and sensitive fluorometric high-performance liquid chromatographic method was developed for the determination of midodrine in human plasma. After liquid-liquid extraction from plasma, the drug and 2-phenylglycinol (internal standard) were convened into the corresponding fluorescent derivatives by reaction with 3,4-dihydro-6,7-dimethoxy-4-methyl-3-oxoquinoxaline-2-carbonyl chloride, a fluorescence derivatization reagent for amines. The derivatives were separated within 30 min on a reversed-phase column using isocratic elution with acetonitrile-methanol-water (10:30:60, v/v) and were detected spectrofluorometrically at 485 nm with excitation at 400 nm. The detection limit for midodrine was 0.3 pmol (76 pg) per mL plasma at a signal-to-noise ratio of 3.     

Stability analysis of abnormal multiplication of plankton using parameter identification technique

This paper presents the mathematical approach for the abnormal multiplication of plankton. An abnormal multiplication can be expressed as an unstable problem and the stability of the system is investigated by introducing eigenvalues of a mathematical equation. The stability of the system can be judged by an eigenvalue based on the Lyapunov's stability theory. In this paper, the Arnoldi‐QR method is used to obtain eigenvalues and eigenvectors of the system. The mode superposition method is employed to create spatial distribution needed to analyse the stability. To obtain the objective eigenvalue, the parameter identification technique is employed. The finite element method is used for the discretization in space. Lake Kasumigaura, which is located in Ibaraki Prefecture in Japan, is selected and actual data in 1975, 1976, 1991 and 2000 are used in order to investigate the stability of the specified lake in Japan. Copyright © 2004 John Wiley & Sons, Ltd.     

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.