New reductions of integrable matrix PDEs: Sp(m)Sp(m)-invariant systems

We propose a new type of reduction for integrable systems of coupled matrix PDEs; this reduction equates one matrix variable with the transposition of another multiplied by an antisymmetric constant matrix. Via this reduction, we obtain a new integrable system of coupled derivative mKdV equations and a new integrable variant of the massive Thirring model, in addition to the already known systems. We also discuss integrable semi-discretizations of the obtained systems and present new soliton solutions to both continuous and semi-discrete systems. As a by-product, a new integrable semi-discretization of the Manakov model (self-focusing vector NLS equation) is obtained.Comment: 33 pages; (v4) to appear in JMP; This paper states clearly that the elementary function solutions of (a vector/matrix generalization of) the derivative NLS equation can be expressed as the partial $x$-derivatives of elementary functions. Explicit soliton solutions are given in the author's talks at http://poisson.ms.u-tokyo.ac.jp/~tsuchida

A Maximum Mass-to-Size Ratio in Scalar-Tensor Theories of Gravity

We derive a modified Buchdahl inequality for scalar-tensor theories of gravity. In general relativity, Buchdahl has shown that the maximum value of the mass-to-size ratio, $2M/R$, is 8/9 for static and spherically symmetric stars under some physically reasonable assumptions. We formally apply Buchdahl's method to scalar-tensor theories and obtain theory-independent inequalities. After discussing the mass definition in scalar-tensor theories, these inequalities are related to a theory-dependent maximum mass-to-size ratio. We show that its value can exceed not only Buchdahl's limit, 8/9, but also unity, which we call {\it the black hole limit}, in contrast to general relativity. Next, we numerically examine the validity of the assumptions made in deriving the inequalities and the applicability of our analytic results. We find that the assumptions are mostly satisfied and that the mass-to-size ratio exceeds both Buchdahl's limit and the black hole limit. However, we also find that this ratio never exceeds Buchdahl's limit when we impose the further condition, $\rho-3p\ge0$, on the density, $\rho$, and pressure, $p$, of the matter.Comment: 23 pages, 13 figures and 1 tabl

Exact Analysis of Soliton Dynamics in Spinor Bose-Einstein Condensates

We propose an integrable model of a multicomponent spinor Bose-Einstein condensate in one dimension, which allows an exact description of the dynamics of bright solitons with spin degrees of freedom. We consider specifically an atomic condensate in the F=1 hyperfine state confined by an optical dipole trap. When the mean-field interaction is attractive (c_0 < 0) and the spin-exchange interaction of a spinor condensate is ferromagnetic (c_2 < 0), we prove that the system possesses a completely integrable point leading to the existence of multiple bright solitons. By applying results from the inverse scattering method, we analyze a collision law for two-soliton solutions and find that the dynamics can be explained in terms of the spin precession.Comment: 4 pages, 2 figure

Complete integrability of derivative nonlinear Schr\"{o}dinger-type equations

We study matrix generalizations of derivative nonlinear Schr\"{o}dinger-type equations, which were shown by Olver and Sokolov to possess a higher symmetry. We prove that two of them are `C-integrable' and the rest of them are `S-integrable' in Calogero's terminology.Comment: 14 pages, LaTeX2e (IOP style), to appear in Inverse Problem

Microscopic Evidence for Evolution of Superconductivity by Effective Carrier Doping in Boron-doped Diamond:11B-NMR study

We have investigated the superconductivity discovered in boron (B)-doped diamonds by means of 11B-NMR on heteroepitaxially grown (111) and (100) films. 11B-NMR spectra for all of the films are identified to arise from the substitutional B(1) site as single occupation and lower symmetric B(2) site substituted as boron+hydrogen(B+H) complex, respectively. A clear evidence is presented that the effective carriers introduced by B(1) substitution are responsible for the superconductivity, whereas the charge neutral B(2) sites does not offer the carriers effectively. The result is also corroborated by the density of states deduced by 1/T1T measurement, indicating that the evolution of superconductivity is driven by the effective carrier introduced by substitution at B(1) site.Comment: 4 pages, 6 figures, to be published in Phys. Rev. B (Brief report

The direct synthesis of tertiary amines with three different substituents via the reaction of primary amines, alkyl halides, and alpha-chlorine substituted allylsilanes catalyzed by Lewis acids

ArticleTetrahedron Letters. 46(27): 4527-4530 (2005)journal articl

Nighttime temperature treatment of fruit clusters of ‘Aki Queen’ grapes during maturation and its effect on the skin color and abscisic acid content

Research Note

Erratum

Nighttime temperature treatment of fruit clusters of 'Ald Queen' grapes during maturation and its effects ofn the sldn color and abscisic acid contentVitis 46 (4), 208-209 (2007

Symmetrically coupled higher-order nonlinear Schroedinger equations: singularity analysis and integrability

The integrability of a system of two symmetrically coupled higher-order nonlinear Schr\"{o}dinger equations with parameter coefficients is tested by means of the singularity analysis. It is proven that the system passes the Painlev\'{e} test for integrability only in ten distinct cases, of which two are new. For one of the new cases, a Lax pair and a multi-field generalization are obtained; for the other one, the equations of the system are uncoupled by a nonlinear transformation.Comment: 12 pages, LaTeX2e, IOP style, final version, to appear in J.Phys.A:Math.Ge