Spinor Green’s functions via spherical means on products of space forms

We explicitly compute the Green’s function of the spinor Klein–Gordon equation on the Riemannian and Lorentzian manifolds of the form _M0×?×_MN$M_0\times ?\times M_N$, with each factor being a space of constant sectional curvature. Our approach is based on an extension of the method of spherical means to the case of spinor fields and on the use of Riesz distributions.     

Sparse representation-based classification algorithm for optical Tibetan character recognition

A sparse representation-based two-phase classification algorithm is proposed for off-line handwritten Tibetan character recognition. The first phase realizes coarse classification with the K-NN classifier by finding the K nearest neighbours of a test sample in the dictionary constructed by K-SVD with samples of all classes, and the classes of these neighbours are regarded as the candidate classes of the test sample. The second phase performs fine classification with the sparse representation classifier by sparsely representing the test sample with all elements of the dictionary constructed by K-SVD with samples of all candidate classes, and the test sample is finally classified into the candidate class with the maximal contribution in sparse representation. Experiments on the Tibetan off-line handwritten character database show that an optimal recognition rate of 97.17% has been reached and it is 2.12% higher than that of K-NN.     

Lattice and continuum wavelets and the block renormalization group

We obtain a resolution of the identity operator, for functions on a latticeZ ^d, which is derived from the block renormalization group. We use eigenfunctions of the terms of the decomposition to form a basis forl ₂(Z^d) and show how the basis is generated from lattice wavelets. The lattice spacing is taken to zero and continuum wavelets are obtained.     

Accurate, high-order representation of complex three-dimensional surfaces via Fourier continuation analysis

We present a new method for construction of high-order parametrizations of surfaces: starting from point clouds, the method we propose can be used to produce full surface parametrizations (by sets of local charts, each one representing a large surface patch – which, typically, contains thousands of the points in the original point-cloud) for complex surfaces of scientific and engineering relevance. The proposed approach accurately renders both smooth and non-smooth portions of a surface: it yields super-algebraically convergent Fourier series approximations to a given surface up to and including all points of geometric singularity, such as corners, edges, conical points, etc. In view of their C^∞ smoothness (except at true geometric singularities) and their properties of high-order approximation, the surfaces produced by this method are suitable for use in conjunction with high-order numerical methods for boundary value problems in domains with complex boundaries, including PDE solvers, integral equation solvers, etc. Our approach is based on a very simple concept: use of Fourier analysis to continue smooth portions of a piecewise smooth function into new functions which, defined on larger domains, are both smooth and periodic. The “continuation functions” arising from a function f converge super-algebraically to f in its domain of definition as discretizations are refined. We demonstrate the capabilities of the proposed approach for a number of surfaces of engineering relevance.     

An occlusion-adaptive tracker based on sparse representation using alternating direction method of multipliers

Recently, sparse representation has been applied to visual tracking with satisfactory performance. However, partial occlusion and computational complexity are two main obstructions in developing sparse-based tracking. In this paper, a simple yet robust tracker based on patch-based sparse representation is proposed. An adaptive motion model, including adaptive sampling regions and adaptive particle numbers, is proposed to improve the sampling efficiency. A self-adjustable segmentation approach is proposed to segment the target into local patches. A patch-based observation model, which is occlusion-adaptive, is constructed by solving a set of L1-regularized least squares problems. The L1-regularized least squares problem is solved using the alternating direction method of multipliers (ADMM). Both quantitative and qualitative experiments are conducted on several challenging image sequences and the comparisons with several state-of-the-art trackers demonstrate the effectiveness and efficiency of our tracker.     

基于可见-近红外光谱与稀疏表示的注水肉识别

为了能快速准确的识别原料肉与注水肉, 提出了一种基于可见-近红外光谱和稀疏表示的无损的识别方法。通过向猪肉样本(包括猪皮、脂肪层和肌肉层)注水的方法建立注水肉模型, 采集未注水的原料肉和6类不同注水量的注水肉的可见和近红外漫反射光谱数据。为了消除光谱数据中的冗余信息并提高分类效果, 对光谱数据进行光调制和归一化等预处理并截取有效波段, 根据是否注水以及注水量的多少对样本进行分类。用所有训练样本构成原子库(字典), 通过ｌ1最小化将测试样本表示为这些原子的最稀疏的线性组合。计算测试样本与各类的投影误差, 将最小投影误差对应的类作为测试样本的所属类别, 并应用留一法进行交叉检验, 比较了稀疏表示法与支持向量机的识别结果。实验结果表明, 利用稀疏表示法对于原料肉与注水肉的识别准确率可达到90%以上, 获得了较好的分类效果, 优于支持向量机的识别结果。而对于不同注水量的注水肉识别准确率与注水量之差正相关。稀疏方法不需要进行传统模式识别模型的前期学习与特征提取, 适用于高维、小样本量数据的处理, 计算成本低, 将其用于注水肉的光谱数据识别具有一定的创新性, 并取得了较满意的结果, 为原料肉和注水肉的无损识别提供了一种有效方法。     

Application of Bipartite and Tripartite Entangled State Representations in Quantum Teleportation of Continuous Variables

We mostly investigate two schemes. One is to teleport a multi-mode W-type entangled coherent state using a peculiar bipartite entangled state as the quantum channel different from other proposals. Based on our formalism,teleporting multi-mode coherent state or squeezed state is also possible. Another is that the tripartite entangled state is used as the quantum channel of controlled teleportation of an arbitrary and unknown continuous variable in the case of three participators.     

正三角形上本征函数的对称性

由D3群一维表示,得到了正三角形上满足Dirichlet边界条件拉普拉斯算子的本征值和本征函数,并讨论了本征函数的对称性.     

Theoretical study of the electronic structure of LiNa and LiNa<Superscript>+</Superscript> molecules

Adiabatic potential energy, spectroscopic constants, dipole moments, and vibrational levels of the lowest electronic states of the alkali dimer LiNa molecule dissociating into Na (3s, 3p, 4s, 3d, and 4p) + Li (2s, 2p, 3s, and 3p) in ^1,3Σ, ^1,3Π, and ^1,3Δ symmetries are presented. Adiabatic results are also reported for ²Σ, ²Π, and ²Δ electronic states of the molecular ion LiNa⁺ dissociating into Li (2s, 2p, 3s, and 3p) + Na⁺ and Li⁺  + Na(3s, 3p, 4s, 3d, and 4p). We use an ab initio approach involving a non-empirical pseudopotential for the Li (1s²) and Na (1s²2s²2p⁶) cores and core valence correlation correction. A very good agreement is obtained for some lowest states of the LiNa and LiNa⁺ molecules for spectroscopic constants with the available theoretical works. The existence of numerous avoided crossings between electronic states of ²Σ and ²Π symmetries is related to the charge transfer process between the two ionic systems Li⁺Na and LiNa⁺.     

Integrable Noncommutative Equations on Quad-graphs. The Consistency Approach

We extend integrable systems on quad-graphs, such as the Hirota equation and the cross-ratio equation, to the noncommutative context, when the fields take values in an arbitrary associative algebra. We demonstrate that the three-dimensional consistency property remains valid in this case. We derive the noncommutative zero curvature representations for these systems, based on the latter property. Quantum systems with their quantum zero curvature representations are particular cases of the general noncommutative ones.