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⁺.     

Semi-supervised Discriminant Analysis and Sparse Representation-based self-training for Face Recognition

In this paper, we consider the problem of automatic face recognition with limited manually labeled training data. We propose a new semi-supervised self-training approach which is used to automatically augment the manually labeled training set with new unlabeled data. Semi-supervised Discriminant Analysis is used in each iteration of self-training for discriminative dimensionality reduction by making use of both labeled and unlabeled training data. Sparse representation is applied for classification. Experimental results on four independent databases show that our algorithm outperforms other face recognition methods under 3 different configurations, namely transductive, semi-supervised and single training image.     

Hermitian Operators Conjugate to Two-Mode Number-Difference Operator Studied in Entangled State Representation

In similar to the derivation of phase angle operator conjugate to the number operator by Arroyo Carrasco- Moya Cessay we deduce the Hermitian phase operators that are conjugate to the two-mode number-difference operator and the three-mode number combination operator. It is shown that these operators are on the same footing in the entangled state representation as the one of Turski in the coherent state representation.     

Differential Representations of SO（4） Dynamical Group

In this paper we present systematic differential representations for the dynamical group SO（4）. These representations include the left and the right differential representations and the left and the right adjoint differential representations in both the group parameter space and its coset spaces. They are the generalization of the differential representations of the SO（3） rotation group in the Euler angles. These representations may find their applications in the study of the physical systems with SO（4） dynamical symmetry.     

基于广义逆矩阵的Bézier曲线近似合并

Bézier曲线近似合并算法在几何数据压缩方面有着重要的应用.研究了两条相邻Bézier曲线近似合并的问题,用矩阵的形式给出了相邻Bézier曲线可精确合并的条件,并在此基础上通过广义逆矩阵的方法求解合并逼近后的Bézier曲线.同时,对保端点插值条件的近似合并也给出了结果.最后用实例说明了算法的有效性,得到了很好的逼近效果.     

Uniqueness of the standard model neutral current predictions

In view of an excellent agreement between the recently determinedv _μ-hadron couplings and predictions of the standard model, the basic question discussed is how far its neutral current predictions can be mimiced in going either from the isodoublet to an isotriplet (or an even higher isospin) left-handed representation or from SU _L (2) × U(1) toG × U(1), whereG is a simple group of rank two. This question is addressed with reference to a sufficiently broad class of schemes. Their most distinctive properties are: in the higher isospin scheme, neutrino couplings are precisely in the form obtainable with standard l.h. representation; the higher g.g. scheme isL+R type in which, to each light fermion of evenRU parity, a superheavy fermion of the same charge and oddRU parity is associated, parity conservation forbidding their mixing. Reasons for excluding theL-type andG ₂ higher g.g. schemes are given. Their neutral current predictions are compared with those of the standard model. A higher isospin representation can mimic the predictions of the standard model in inclusive and semi-inclusivev _μ-hadron reactions but is conclusively discriminated from the isodoublet representation by elasticv _μ ⁽⁻ p scattering. TheG × U(1) scheme can mimic standard model neutrino sector but is conclusively discriminated from minimal scheme by parity violating effects.