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     

Convergence in [2+2+2] synthesis of β-phenylnaphthalene motif in polyaromatic natural products

Two optional routes to β-phenylnaphthalene structure are developed by introducing α- and β-styryl groups onto different positions in the benzocyclobutene ring followed by ring enlargement.     

Status of heavy element research using a gas-filled recoil separator at RIKEN

A gas-filled type of recoil separator for heavy element research was installed at an experimental hall of RIKEN Linear Accelerator facility to realize getting higher intensity of primary beam and long beam time. Performance of the separator was studied using target recoils and various nuclear reactions. The results show the high performance of the separator for heave element research. As an application of the GARIS, production and identification of an isotope of the 110th element ²⁷¹[110] have been performed using the ²⁰⁸Pb(⁶⁴Ni,1n)²⁷¹[110] reaction. Three decay chains coincide well both in decay times and energies with the ones reported by the group of SHIP experiment at GSI, Germany. Our results provide a confirmation of the synthesis of an isotope ²⁷¹[110] of element 110.     

Trinucleon cluster structure at high-excitation energies in A=6 nuclei

Trinucleon molecular structures in ⁶He and ⁶Be were investigated by using the ⁶Li(⁷Li, ⁷Be)⁶He reaction at 455 MeV and ⁶Li(³He, t)⁶Be reaction at 450 MeV, respectively. Binary decays into t + t from a broad state at E _x =18.0±1.0 MeV in ⁶He and into ³He + ³He from one at E _x =18.0±1.2 MeV in ⁶Be, respectively, were observed by measuring trinucleon cluster decays in coincidence with reaction particles. The branching ratios for binary decay were estimated to be about 0.7 for ⁶He and ⁶Be. These large branching ratios show that a trinucleon cluster state exists as an isobaric partner around E _x =18 MeV in ⁶He and ⁶Be.     

Structural characterization of polypyrrole in the solid state by high resolution 15N NMR spectroscopy [II]

The solid-state ¹⁵N CP/MAS NMR spectra and ¹⁵N spin-lattice relaxation times (T₁) of doped and dedoped ¹⁵N-labeled polypyrroles prepared by electrochemical polymerization, have been measured by means of high-resolution solid-state ¹⁵N NMR. The ¹⁵N signal of polypyrrole consists of four peaks decomposed by line shape analysis. The four peaks obtained have been assigned to the various structures of polypyrrole. Further, the half-width of the ¹⁵N NMR spectra of polypyrroles is discussed as related to the electrical conductivity. © 1995 John Wiley & Sons, Inc.     

Development and features of hydro-membrane gas chromatography.

Hydro-membrane gas chromatography (HMGC) is achieved by the annular condensation of water in a capillary column at less than 70 degrees C. The annular membrane of water is formed as a result of the wettability of the stationary phase, which is induced at a water contact angle ranging from 75 degrees to 79 degrees, as derived from a solubility parameter (delta) range of 15.7 +/- 0.3 MPa(1/2) of the coated resin. The range of the liquid to gas volume ratio (beta) required to support the annular membrane should be kept between 0.00005 and 0.0003. In the case of a 0.25-mm i.d. column, the ratio can be set by the combination of a 0.1 to 0.2 microl min(-1) water supply rate and helium gas flow rate. Separation by HMGC develops not only a gas-solid partition but also a focusing effect on the water membrane. One feature of HMGC is that it gives a non-adsorption chromatogram based on the blocking effect of pre-adsorbed water; furthermore, despite the presence of a relatively large quantity of water, the electron impact ionization efficiency is kept the same as in the usual GC/MS condition. The detection limit with the injection of 1 microl of aquatic solution was estimated to be less than 0.1 ppb of low-molecular-weight fatty acids with s/n = 5 on a mass chromatogram at m/z 45. The HMGC/EI-MS system can be applied to the trace analysis of C1 to C3 volatile acids, volatile inorganic acids, and halogenated organic acids in water.     

A convergent approach to the formal total synthesis of hemibrevetoxin B

A convergent synthesis of the key synthetic intermediate of hemibrevetoxin B was achieved via the intramolecular allylation of an α-chloroacetoxy ether and subsequent ring-closing metathesis.     

Application of total reflection X-ray fluorescence spectrometry to small glass fragments.

Total reflection X-ray fluorescence spectrometry (TXRF) has been applied for trace elemental analysis of small glass fragments. A small glass sample (a fragment with weight less than 0.5 mg) was decomposed by 100 microg of HF/HNO3 acid; the material was condensed to 10 microl and was dried on a Si wafer. Since the size of the dried residue on the Si wafer was less than 1 cm in diameter, an incident X-ray beam with about 1 cm in width could effectively excite elemental components in such a small glass fragment. The precision of the present technique was checked by analyzing the glass fragments (<0.5 mg) from NIST SRM612; the relative standard deviations (RSD) of less than 8.1% were achieved for elemental ratios that were normalized by Sr. Fragments (<0.5 mg) obtained from 23 figured sheet glasses were used as samples for estimating the utility of this technique to forensic discrimination. Comparison of five elemental ratios of Ti/Sr, Mn/Sr, Zn/Sr, Rb/Sr, and Pb/Sr calculated from X-ray fluorescence spectra was effective in distinguishing glass fragments that could not be differentiated by their refractive indexes (RI).     

The Canonical Solutions of the Q-Systems¶ and the Kirillov–Reshetikhin Conjecture

We study a class of systems of functional equations closely related to various kinds of integrable statistical and quantum mechanical models. We call them the finite and infinite $Q$-systems according to the number of functions and equations. The finite Q-systems appear as the thermal equilibrium conditions (the Sutherland–Wu equation) for certain statistical mechanical systems. Some infinite Q-systems appear as the relations of the normalized characters of the KR modules of the Yangians and the quantum affine algebras. We give two types of power series formulae for the unique solution (resp. the unique canonical solution) for a finite (resp. infinite) Q-system. As an application, we reformulate the Kirillov–Reshetikhin conjecture on the multiplicities formula of the KR modules in terms of the canonical solutions of Q-systems. Received: 2 August 2001 / Accepted: 27 December 2001     

On a certain move generating link-homology

Dedicated to Professor Kunio Murasugi on his sixtieth birthday