Mathematica软件在微分流形中的应用

本文利用Mathematica软件描绘向量场和流,通过具体的例子,探讨该软件在微分流形教学科研中的应用.     

基于RTD可编程逻辑门的n变量函数实现算法

共振隧穿二极管（RTD）可编程逻辑门是一种由单双稳态转换逻辑单元（MOBILE）及正、负输入分支组成的阈值逻辑电路。基于二进制神经元模型中的三层网络结构,提出了基于RTD可编程逻辑门的n变量函数实现算法。按照汉明距离由大到小的顺序,搜索最优输入向量,用定理1或定理2方法产生隐层函数,通过变换次数,确定输入向量的真假及隐层函数的权重。由于定义了最优输入向量及变换次数,提高了算法的准确性;又由于采用了定理2方法,令设计的电路更简单。     

红外光谱结合最小二乘支持向量机掺杂牛奶判别方法研究

基于红外光谱和最小二乘支持向量机建立掺杂牛奶与纯牛奶的判别模型。分别配置含有葡萄糖牛奶(0.01~0.3gL-1)和三聚氰胺牛奶(0.01~0.3gL-1)样品各36个,采集纯牛奶及掺杂牛奶样品的红外光谱。采用最小二乘支持向量机分别建立掺杂葡萄糖、掺杂三聚氰胺、两种掺杂牛奶与纯牛奶的判别模型,并利用这些模型对未知样品进行判别,其判别正确率都为95.8%。研究结果表明:与线性的偏最小二乘判别建模方法相比,最小二乘支持向量机方法具有更强的预测能力。     

Metastable and spin-polarized states in electron systems with localized electron–electron interaction

We study the formation of spontaneous spin polarization in inhomogeneous electron systems with pair interaction localized in a small region that is not separated by a barrier from surrounding gas of non-interacting electrons. Such a system is interesting as a minimal model of a quantum point contact in which the electron–electron interaction is strong in a small constriction coupled to electron reservoirs without barriers. Based on the analysis of the grand potential within the self-consistent field approximation, we find that the formation of the polarized state strongly differs from the Bloch or Stoner transition in homogeneous interacting systems. The main difference is that a metastable state appears in the critical point in addition to the globally stable state, so that when the interaction parameter exceeds a critical value, two states coexist. One state has spin polarization and the other is unpolarized. Another feature is that the spin polarization increases continuously with the interaction parameter and has a square-root singularity in the critical point. We study the critical conditions and the grand potentials of the polarized and unpolarized states for one-dimensional and two-dimensional models in the case of extremely small size of the interaction region.     

Role of electron correlation effects in δ-Pu and “115”-Pu-based unconventional superconductors

Electronic structure calculations combining the local density approximation with an exact diagonalization of the Anderson impurity model show intermediate 5f⁵–5f⁶-valence ground state and delocalization of the 5f⁵ multiplet of the Pu atom 5f-shell in PuCoGa₅, and δ-Pu. The 5f-local magnetic moment is compensated by a moment formed in the surrounding cloud of conduction electrons. For PuCoGa₅ and δ-Pu the compensation is complete and the Anderson impurity ground state is a singlet. This can be important for analyses of the superconducting pairing mechanism in PuCoGa₅. It is likely that in PuCoGa₅ unconventional d-wave superconductivity is mediated by the 5f-states valence fluctuations, rather than antiferromagnetic fluctuations.     

基于HOG纹理的全天时十字路口车尾检测算法

HOG纹理因其良好的鲁棒性,在纹理描述中被广泛使用。提出了一种将HOG纹理应用于十字路口全天候车尾检测的算法。即分别采集了白天和夜间该场景下的车尾作为正样本、非车辆和车辆的一部分作为负样本,经预处理后,提取较低维数的HOG纹理送入支持向量机进行训练,得到白天和夜间的识别模型,在检测中根据一定的条件进行切换。对多段视频进行测试证明,该种算法对不同时段的交通场景都具有较高的稳定的车尾识别率,且优于单模型的识别效果。     

A high order energy preserving scheme for the strongly coupled nonlinear Schrōdinger system

A high order energy preserving scheme for a strongly coupled nonlinear Schrōdinger system is roposed by using the average vector field method. The high order energy preserving scheme is applied to simulate the soliton evolution of the strongly coupled Schrōdinger system. Numerical results show that the high order energy preserving scheme can well simulate the soliton evolution, moreover, it preserves the discrete energy of the strongly coupled nonlinear Schrōdinger system exactly.     

Sum rates for multi-user MIMO vector perturbation precoding with regularization

In this paper, we analyze the sum rate performance of multiuser multi-antenna downlink channel. We consider Rayleigh fading environment when regularized vector perturbation precoding (R-VPP) method is used at the transmitter. We derive expressions for the sum rate in terms of the variance of the received signal. We also provide a closed form approximation for the mean squared error (MSE) which is shown to work well for the whole range of SNR. Further, we also propose a simpler expression for R-VPP sum rate based on MSE. The simulation results show that the proposed expressions for R-VPP sum rate closely match the sum rate found by the entropy estimation. Our results show that when compared with other linear and non-linear precoding methods (like zero-forcing precoder, linear minimum mean square error (MMSE) precoder and VPP), R-VPP sum rate performance is very close to DPC for all SNR values. It is also noted that the sum rate performance of the linear MMSE precoder is very close to the R-VPP at low to medium SNR range. Finally we also compared the merits of performing regularization for VPP as compared to the greedy rate maximizing user scheduling. It turns out that the R-VPP with or without user selection performs better than the VPP systems with user selection.     

Monotonically increasing functions of any quantum correlation can make all multiparty states monogamous

Monogamy of quantum correlation measures puts restrictions on the sharability of quantum correlations in multiparty quantum states. Multiparty quantum states can satisfy or violate monogamy relations with respect to given quantum correlations. We show that all multiparty quantum states can be made monogamous with respect to all measures. More precisely, given any quantum correlation measure that is non-monogamic for a multiparty quantum state, it is always possible to find a monotonically increasing function of the measure that is monogamous for the same state. The statement holds for all quantum states, whether pure or mixed, in all finite dimensions and for an arbitrary number of parties. The monotonically increasing function of the quantum correlation measure satisfies all the properties that are expected for quantum correlations to follow. We illustrate the concepts by considering a thermodynamic measure of quantum correlation, called the quantum work deficit.