NAD(P)+-NAD(P)H model. 38. Reduction of aldehyde by 1,4-dihydroquinolin derivative

Benzaldehyde are reduced to benzyl alcohol by a model compound of NAD(P)H almost quantitatively. Reductions of some other aldehydes are also mentioned.     

X-ray structural study of a zinc(II) inclusion complex of a phenolate-pendant cyclam

The molecular structure of phenol-pendant cyclam-zinc(II) complex,4a, has been determined by X-ray structure analysis. Crystals of4a · ClO₄ · CH₃OH (C₁₆H₂₇N₄OZn · ClO₄ · CH₃OH) are monoclinic, space groupP2₁/nn, with four molecules in the unit cell of dimensionsa=31.198(2) Å,b=8.426(1) Å,c=8.214(1) Å, and=93.96(1)°. The structure was solved by the heavy atom method and refined anisotropically toR=0.044,R _w=0.062 for 1551 independent reflections. The complex assumes a five-coordinate, square pyramidal geometry, where zinc(II) is surrounded by the cyclam moiety in a planar fashion with the pendant phenolate anion occupying an axial position. An extremely short Zn-O(phenolate) bond distance of 1.983(5) Å, in conjunction with the 0.288 Å displacement of Zn(II) above the cyclam N₄ plane toward the phenolate, accounts for the extremely low pK _a value of 5.8 for the pendant phenol. These facts about4a, in comparison with the previous findings for the Ni(II) (4b) and Cu(II) complexes (4c) with the same ligand, illustrate well the characteristics of zinc(II) ion coordination properties.This paper is dedicated to the memory of the late Dr C. J. Pedersen.     

Finite Time Extinction for Nonlinear Schrödinger Equation in 1D and 2D

We consider a nonlinear Schrödinger equation with power nonlinearity, either on a compact manifold without boundary, or on the whole space in the presence of harmonic confinement, in space dimension one and two. Up to introducing an extra superlinear damping to prevent finite time blow up, we show that the presence of a sublinear damping always leads to finite time extinction of the solution in 1D, and that the same phenomenon is present in the case of small mass initial data in 2D.     

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     

Space-time analytic smoothing effect for the pseudo-conformally invariant Schrödinger equations

We study the global Cauchy problem for the mass critical nonlinear Schrödinger equations. We prove the global existence of analytic solutions in both space and time variables for sufficiently small and exponentially decaying Cauchy data. The method of proof depends on the Leibniz rule for the generator of pseudo-conformal transforms at the L ² critical level.     

Invariant elliptic estimates

In this paper, we revisit elliptic estimates invariant under domain expansion. We improve the invariant elliptic estimates in the previous paper [Y. Cho, T. Ozawa, Y. Shim, Calc. Var. PDE 34 (2009) 321-339] via gradient estimate and discuss an application to the Lamé system.     

Energy method in the partial Fourier space and application to stability problems in the half space

The energy method in the Fourier space is useful in deriving the decay estimates for problems in the whole space Rn. In this paper, we study half space problems in and develop the energy method in the partial Fourier space obtained by taking the Fourier transform with respect to the tangential variable x^′∈Rn−1. For the variable x₁∈R₊ in the normal direction, we use L² space or weighted L² space. We apply this energy method to the half space problem for damped wave equations with a nonlinear convection term and prove the asymptotic stability of planar stationary waves by showing a sharp convergence rate for t→∞. The result obtained in this paper is a refinement of the previous one in Ueda et al. (2008) [13].     

Exponential decay of solutions to nonlinear elliptic equations with potentials

Exponential decay estimates are obtained for complex-valued solutions to nonlinear elliptic equations in \mathbbRⁿ ,\mathbb{R}^{n} , where the linear term is given by Schr?dinger operators H =  − Δ  +  V with nonnegative potentials V and the nonlinear term is given by a single power with subcritical Sobolev exponent in the attractive case. We describe specific rates of decay in terms of V, some of which are shown to be optimal. Moreover, our estimates provide a unified understanding of two distinct cases in the available literature, namely, the vanishing potential case V = 0 and the harmonic potential case V(x) = |x|².     

Global existence of strong solutions to a time‐dependent 3D Ginzburg‐Landau model for superconductivity with partial viscous terms

We study an initial boundary value problem for a time‐dependent 3D Ginzburg‐Landau model of superconductivity with partial viscous terms. We prove the global existence of strong solutions.     

Rank 2 Ample Vector Bundles on Some Smooth Rational Surfaces

Several classification results for ample vector bundles of rank 2 on Hirzebruch surfaces, and on Del Pezzo surfaces, are obtained. In particular, we classify rank 2 ample vector bundles with _c2 less than seven on Hirzebruch surfaces, and with _c2 less than four on Del Pezzo surfaces.