Minimal two spheres in Kähler-Einstein Fano manifolds

In this paper we show the existence of stable symplectic non-holomorphic two-spheres in Kähler manifolds of positive constant scalar curvature of real dimension four and in Kähler-Einstein Fano manifolds of real dimension six. Some of the techniques used involve deformation theory of algebraic cycles.     

New mass spectrometric approaches to structural analysis in mixtures

Structural analysis of minor components in mixtures is a vital requirement in the development of any pharmaceutical compound. Mass spectrometry is uniquely able to give this kind of information on the trace amounts of material present as minor impurities in a drug substance. In this study we show that a combination of mass spectrometric analysers with different characteristics is an even more powerful approach with a higher chance of establishing a potential structure. In particular the advent of analysers capable of accurate mass measurement on small amounts of material has enabled structures to be proposed in situations where previously no real conclusions could be made. Copyright 1999 John Wiley & Sons, Ltd.     

Rational matrix approximation with a priori error bounds for non-symmetric matrix Riccati equations with analytic coefficients

In this paper the exact solution of the non-symmetric matrixRiccati equation with analytic coefficients is approximatedby a rational matrix function with a prefixed accuracy. Thisrational matrix function is locally defined as the exact solutionof a Riccati problem with matrix polynomial coefficients obtainedby truncation of the Taylor expansions of the matrix coefficientsof the original problem.     

Combined compact difference method for solving the incompressible Navier–Stokes equations

This paper presents a numerical method for solving the two‐dimensional unsteady incompressible Navier–Stokes equations in a vorticity–velocity formulation. The method is applicable for simulating the nonlinear wave interaction in a two‐dimensional boundary layer flow. It is based on combined compact difference schemes of up to 12th order for discretization of the spatial derivatives on equidistant grids and a fourth‐order five‐ to six‐alternating‐stage Runge–Kutta method for temporal integration. The spatial and temporal schemes are optimized together for the first derivative in a downstream direction to achieve a better spectral resolution. In this method, the dispersion and dissipation errors have been minimized to simulate physical waves accurately. At the same time, the schemes can efficiently suppress numerical grid‐mesh oscillations. The results of test calculations on coarse grids are in good agreement with the linear stability theory and comparable with other works. The accuracy and the efficiency of the current code indicate its potential to be extended to three‐dimensional cases in which full boundary layer transition happens. Copyright © 2011 John Wiley & Sons, Ltd.     

Self-shrinkers for the mean curvature flow in arbitrary codimension

In this paper, we generalize Colding–Minicozzi’s recent results about codimension-1 self-shrinkers for the mean curvature flow to higher codimension. In particular, we prove that the sphere ${bf S}^{n}(\sqrt{2n})$ is the only complete embedded connected $F$ -stable self-shrinker in $\mathbf{R}^{n+k}$ with $\mathbf{H}\ne 0$ , polynomial volume growth, flat normal bundle and bounded geometry. We also discuss some properties of symplectic self-shrinkers, proving that any complete symplectic self-shrinker in $\mathbf{R}^4$ with polynomial volume growth and bounded second fundamental form is a plane. As a corollary, we show that there is no finite time Type I singularity for symplectic mean curvature flow, which has been proved by Chen–Li using different method. We also study Lagrangian self-shrinkers and prove that for Lagrangian mean curvature flow, the blow-up limit of the singularity may be not $F$ -stable.     

Szegö kernel, regular quantizations and spherical CR-structures

We compute the Szegö kernel of the unit circle bundle of a negative line bundle dual to a regular quantum line bundle over a compact Kähler manifold. As a corollary we provide an infinite family of smoothly bounded strictly pseudoconvex domains on complex manifolds (disk bundles over homogeneous Hodge manifolds) for which the log-terms in the Fefferman expansion of the Szegö kernel vanish and which are not locally CR-equivalent to the sphere. We also give a proof of the fact that, for homogeneous Hodge manifolds, the existence of a locally spherical CR-structure on the unit circle bundle alone implies that the manifold is biholomorphic to a projective space. Our results generalize those obtained by Engli? (Math Z 264(4):901–912, 2010) for Hermitian symmetric spaces of compact type.     

Investigating the role of c-Jun N-terminal kinases in the proliferation of Werner syndrome fibroblasts using diaminopyridine inhibitors

To develop more potent small molecules with enhanced free radical scavenger properties, a series of N-substituted isatin derivatives was synthesized, and the cytoprotective effect on the apoptosis of PC12 cells induced by H₂O₂ was screened. All these compounds were found to be active, and N-ethyl isatin was found with the most potent activity of 69.7% protective effect on PC12 cells. Structure-activity relationship analyses showed the bioactivity of N-alkyl isatins decline as the increasing of the chain of the alkyl group, furthermore odd-even effect was found in the activity, which is interesting for further investigation.