On the extendedness of eigenstates in a hierarchical lattice: A critical view

We take a critical view at the basic definition of extended single particle states in a non-translationally invariant system. For this, we present the case of a hierarchical lattice and incorporate long range interactions that are also distributed in a hierarchical fashion. We show that it is possible to explicitly construct eigenstates with constant amplitudes (normalized to unity) at every lattice point for special values of the electron-energy. However, the end-to-end transmission, corresponding to the above energy of the electron in such a hierarchical system depends strongly on a special correlation between the numerical values of the parameters of the Hamiltonian. Keeping the energy and the distribution of the amplitudes invariant, one can transform the lattice from conducting to insulating simply by tuning the numerical values of the long range interaction. The values of these interactions themselves display a fractal character.     

ON NECESSARY AND SUFFICIENT CONDITIONS FOR DUALS OF WAVELET FRAMES

（张泽银）（王建忠）ＯＮＮＥＣＥＳＳＡＲＹＡＮＤＳＵＦＦＩＣＩＥＮＴＣＯＮＤＩＴＩＯＮＳＦＯＲＤＵＡＬＳＯＦＷＡＶＥＬＥＴＦＲＡＭＥＳ￥ＺｈａｎｇＺｅｙｉｎ（Ｄｅｐｔ．ｏｆＭａｔｈ．，ＨｕｂａｉＵｎｉｖｅｒｓｉｔｙ，Ｗｕｈａｎ４３００６２，Ｃｈｉｎａ...     

Structure dependent sampling in compressed sensing: Theoretical guarantees for tight frames

Many of the applications of compressed sensing have been based on variable density sampling, where certain sections of the sampling coefficients are sampled more densely. Furthermore, it has been observed that these sampling schemes are dependent not only on sparsity but also on the sparsity structure of the underlying signal. This paper extends the result of Adcock, Hansen, Poon and Roman (arXiv:1302.0561, 2013) [2] to the case where the sparsifying system forms a tight frame. By dividing the sampling coefficients into levels, our main result will describe how the amount of subsampling in each level is determined by the local coherences between the sampling and sparsifying operators and the localized level sparsities – the sparsity in each level under the sparsifying operator.     

Quading triangular meshes with certain topological constraints

In computer graphics and geometric modeling, shapes are often represented by triangular meshes (also called 3D meshes or manifold triangulations). The quadrangulation of a triangular mesh has wide applications. In this paper, we present a novel method of quading a closed orientable triangular mesh into a quasi-regular quadrangulation, i.e., a quadrangulation that only contains vertices of degree four or five. The quasi-regular quadrangulation produced by our method also has the property that the number of quads of the quadrangulation is the smallest among all the quasi-regular quadrangulations. In addition, by constructing the so-called orthogonal system of cycles our method is more effective to control the quality of the quadrangulation.     

钠原子团簇的相变

采用紧密结合的分子动力学模型，对Ｎａ４、Ｎａ８、Ｎａ２０的结构特性进行了分析。通过对这些钠原子团簇的键长涨落和径向密度分布的分析，发现在２００Ｋ到２５０Ｋ的温度范围内有从类固相到类液相的改变     

金属Zn液态结构变化的研究

利用ＴＢ模型给出的原子间相互作用势详细计算了不同温度下Ｚｎ的双体分布函数ｇ（ｒ），结果发现随着温度的不断降低，液态金属Ｚｎ的ｇ（ｒ）第一峰变得高而尖，第二峰由弱变强，说明了液态金属Ｚｎ的有序度随温度降低而不断增强；利用键对分析技术统计了液态金属Ｚｎ在不同温度下的键取向序参数、键对数。键取向序参数及键对数随温度的变化，进一步证明了低温液态的有序度高于高温液态，从而充分说明液态金属在不同温度下有不同的结构形式，而不像人们想象得那样杂乱无章。     

Some LC experiments with capillary columns

Some experimental results of LC in capillary columns are presented. The possible effect of turbulence which has been much emphasised lately is overrated. The future of LC in capillary columns lies in extreme miniaturization.     

A Characteristic p Analog of Multiplier Ideals and Applications #

We present two applications of a characteristic p analog of multiplier ideals, which is a generalization of the test ideal in the theory of tight closure. Namely, we give alternative proofs to Smith's result on base-point-freeness of adjoint bundles in characteristic p > 0 and results on uniform behavior of symbolic powers in a regular local ring due to Ein, Lazarsfeld and Smith, and Hochster and Huneke.