Convexity and marginal vectors

In this paper we construct sets of marginal vectors of a TU game with the property that if the marginal vectors from these sets are core elements, then the game is convex. This approach leads to new upperbounds on the number of marginal vectors needed to characterize convexity. Another result is that the relative number of marginals needed to characterize convexity converges to zero. Received: May 2002     

Continuous dependence of solutions on a parameter in a scalarization method

This paper studies a certain behavior of maximal values, solutions, and local solutions in a scalarization method under variation of parameters. It is shown that, for a large class of vector optimization problems, this dependence is continuous.The author would like to thank the referees for their comments, which improved the presentation of the paper.     

A phase analysis of vorticity vectors associated with tropical convection

Three new vorticity vectors have been proposed by Gao et al to study the two-dimensional tropical convection. In the present paper, phase relations between surface rain rate and the vorticity vectors are analysed with the calculations of lag correlation coefficients based on hourly zonally-averaged mass-integrated cloud-resolving simulation data. The cloud-resolving model is integrated with the vertical velocity, zonal wind, horizontal thermal and moisture advections, and sea surface temperature observed and derived from tropical ocean global atmosphere - coupled ocean atmosphere response experiment （TOGA-COARE） for 10 days. Maximum local increase of the vertical component of the convective vorticity vector leads maximum surface rain rate by 2 hours mainly due to the interaction between vorticity and zonal gradient of ice heating. While maximum local increase of the vertical component of the moist vorticity vector leads maxfinum surface rain rate by 2 hours mainly because of the interaction between zonal specific humidity gradient and zonal buoyancy gradient. And the maximum local decrease of the zonal component of the dynamic vorticity vector leads maximum surface rain rate by 2 hours mainly due to the interactions between vorticity and vertical pressure gradient as well as vorticity and buoyancy.     

On conformally related pp-waves

Brinkmann [1] has shown that conformally related distinct Ricci flat solutions are pp-waves. Brinkmann’s result has been generalized to include the conformally invariant source terms. It has been shown that [4] if g _ik and _ik (=w ⁻² g _ik ; w: a scalar function), are distinct metrics having the same Einstein tensor, G _ik = _ik , then both represent (generalized) pp-waves and w _i is a null covariantly constant vector of g _ik . Thus pp-waves are the only candidates which yield conformally related nontrivial solutions of G _ik =T _ik = _ik , with T _ik being conformally invariant source. In this paper the functional form of the conformal factor for the conformally related pp-waves/generalized pp-waves has been obtained. It has been shown that the most general pp-wave, conformally related to ds ²=−2du[dv−mdy=Hdu]+P ⁻²[dy ²+dz ²], turns out to be (au+b)⁻² ds ², where a,b are constants. Only in the special case when m=0, H=1, and P=P(y, z), the conformal factor is (au+b)⁻² or (a(u+v)+b)⁻².     

Remarks about global analytic hypoellipticity

We present a characterization of the operators

which are globally analytic hypoelliptic on the torus. We give information about the global analytic hypoellipticity of certain overdetermined systems and of sums of squares.

     

半径位置微扰对于不同光子晶体波导结构的影响

本文理论上分析了不同程度的位置半径微扰分别对于二维三角晶格不同空气孔形状的光子晶体波导结构透射率性能的影响。主要关注三个区域,低频带隙边缘,高频带隙边缘以及导模交叉点;三种空气孔形状,圆形,方形,椭圆形。仿真结果显示微扰对于交叉点影响最为严重。随着微扰程度变大,高低频边缘平坦的透射率区域逐渐变窄。相同形状相同微扰程度下,透射率对位置微扰更加敏感。不同形状比较发现,慢光区域正方空气孔对于位置微扰更稳健,圆形空气孔对于半径微扰更稳健。这对于光子晶体制作和实验过程中不可避免的位置和半径的随机微扰具有理论指导意义。     

Exact evaluation of limits and tangents for interpolatory subdivision surfaces at rational points

This paper presents a new method for exact evaluation of a limit surface generated by stationary interpolatory subdivision schemes and its associated tangent vectors at arbitrary rational points. The algorithm is designed on the basis of the parametric m-ary expansion and construction of the associated matrix sequence. The evaluation stencil of the control points on the initial mesh is obtained, through computation, by multiplying the finite matrices in a sequence corresponding to the expansion sequence and eigendecomposition of the contractive matrix related to the period of rational numbers. The method proposed in this paper works for other non-polynomial subdivision schemes as well.     

Regularity of eigenstates in regular Mourre theory

The present paper gives an abstract method to prove that possibly embedded eigenstates of a self-adjoint operator H lie in the domain of the kth power of a conjugate operator A. Conjugate means here that H and A have a positive commutator locally near the relevant eigenvalue in the sense of Mourre. The only requirement is Ck+1(A) regularity of H. Regarding integer k, our result is optimal. Under a natural boundedness assumption of the multiple commutators we prove that the eigenstate ‘dilated’ by exp(iθA) is analytic in a strip around the real axis. In particular, the eigenstate is an analytic vector with respect to A. Natural applications are ‘dilation analytic’ systems satisfying a Mourre estimate, where our result can be viewed as an abstract version of a theorem due to Balslev and Combes (1971) [3]. As a new application we consider the massive Spin-Boson Model.     

Li-Yorke and distributionally chaotic operators

We study Li-Yorke chaos and distributional chaos for operators on Banach spaces. More precisely, we characterize Li-Yorke chaos in terms of the existence of irregular vectors. Sufficient “computable” criteria for distributional and Li-Yorke chaos are given, together with the existence of dense scrambled sets under some additional conditions. We also obtain certain spectral properties. Finally, we show that every infinite dimensional separable Banach space admits a distributionally chaotic operator which is also hypercyclic.     

低分子量聚乙烯亚胺/金纳米棒纳米载体的制备及毒性研究

以表面修饰巯基十一烷酸的金纳米棒 (GNRs/MUA)为骨架, 将低分子量的聚乙烯亚胺(PEI)连接到GNRs/MUA表面, 构建GNRs/MUA/PEI纳米载体.首先采用MUA对GNRs进行表面修饰, 减少由于GNRs表面的十六烷基三甲基溴化铵(CTAB)所造成的生物毒性.然后采用低分子量 PEI 进一步修饰, 同时利用GNRs巨大的比表面积进一步放大 PEI 的携带基因能力, 这样既能够降低阳离子聚合物的毒性, 又能够提高整个体系的转染效率.利用透射电子显微镜(TEM)、紫外可见吸收光谱(UV-Vis)、Zeta电位等对纳米载体进行了表征.结果显示, MUA与PEI已成功修饰到GNRs表面, 并很好地保留了GNRs的光学性质, 其表面电位发生正负交替变化.采用噻唑蓝(MTT)比色法对纳米载体进行细胞毒性研究, 结果显示GNRs/MUA/PEI(1.8 kDa)非病毒纳米载体, 细胞存活率在控制聚合物浓度为300 μg/mL时仍然稳定在75%以上, 明显高于商品化的PEI(25 kDa).