Exact Solutions for Self-Dual SU(2) and SU(3) Yang–Mills Fields

The (constrained) canonical reduction of four-dimensional self-dual SU(2) and SU(3) Yang–Mills theory to two-dimensional nonlinear Schrödinger (NS) and Korteweg–de Vries (KdV) equations are considered. The Bäcklund transformations (BTs) are implemented to obtain new classes of exact solutions for the reduced two-dimensional NS and KdV models.     

Adjoint representation admixture to weak nonleptonic decays in SU(4) and SU(8)

In order to remove some of the unsatisfactory features of the GIM model, we consider15-admixture in SU(4). ΔC=±ΔS decays remain unaffected. Lee-Sugawara sum-rule is obtained.15-admixture is extended then to63-admixture in SU(8). The most general Hamiltonian (H _w∼63⊕720⊕1232) in SU(8) is found to give Lee-Sugawara relation and Σ₊ ⁺=0 forS-wave decays of uncharmed baryons. Decay amplitude relations for ΔC=−1, ΔS=0 mode are obtained.     

基于一类SVM概率密度估计的多分类贝叶斯算法研究

为降低训练分类器的运算复杂度，并解决支持向量机（SVM）对多类分类问题没有特别有效解决方法的问 题。提出了一种基于一类支持向量机的多分类贝叶斯算法，证明了基于径向基核函数的一类SVM的分类函数归 一化为密度函数，并将所得的概率密度函数用于构造二分类及多分类贝叶斯分类器。仿真实验将提出的多分类贝 叶斯算法应用于多类通信信号调制识别，结果表明：该算法的分类准确率不低于传统SVM多分类器，而在多类属、 每类训练样本数目较大的情况下训练所需的运算量和存储量仅是传统SVM多分类算法的0.5%大大减小了核 矩阵规模和     

Universal Formulae for SU Casson Invariants of Knots

An Casson invariant of a knot is an integer which can be thought of as an algebraic-topological count of the number of characters of representations of the knot group which take a longitude into a given conjugacy class. For fibered knots, these invariants can be characterized as Lefschetz numbers which, for generic conjugacy classes, can be computed using a recursive algorithm of Atiyah and Bott, as adapted by Frohman. Using a new idea to solve the Atiyah-Bott recursion (as simplified by Zagier), we derive universal formulae which explicitly compute the invariants for all . Our technique is based on our discovery that the generating functions associated to the relevant Lefschetz numbers (and polynomials) satisfy certain integral equations.

     

SU(1,1) Lie Algebra Applied to the General Time-dependent Quadratic Hamiltonian System

Exact quantum states of the time-dependent quadratic Hamiltonian system are investigated using SU(1,1) Lie algebra. We realized SU(1,1) Lie algebra by defining appropriate SU(1,1) generators and derived exact wave functions using this algebra for the system. Raising and lowering operators of SU(1,1) Lie algebra expressed by multiplying a time-constant magnitude and a time-dependent phase factor. Two kinds of the SU(1,1) coherent states, i.e., even and odd coherent states and Perelomov coherent states are studied. We applied our result to the Caldirola–Kanai oscillator. The probability density of these coherent states for the Caldirola–Kanai oscillator converged to the center as time goes by, due to the damping constant γ. All the coherent state probability densities for the driven system are somewhat deformed. PACS Numbers: 02.20.Sv, 03.65.-w, 03.65.Fd     

The extended Bloch representation of quantum mechanics and the hidden-measurement solution to the measurement problem

A generalized Bloch sphere, in which the states of a quantum entity of arbitrary dimension are geometrically represented, is investigated and further extended, to also incorporate the measurements. This extended representation constitutes a general solution to the measurement problem, inasmuch it allows to derive the Born rule as an average over hidden-variables, describing not the state of the quantum entity, but its interaction with the measuring system. According to this modelization, a quantum measurement is to be understood, in general, as a tripartite process, formed by an initial deterministic decoherence-like process, a subsequent indeterministic collapse-like process, and a final deterministic purification-like process. We also show that quantum probabilities can be generally interpreted as the probabilities of a first-order non-classical theory, describing situations of maximal lack of knowledge regarding the process of actualization of potential interactions, during a measurement.     

Analytic solutions for a three-level system in a time-dependent field

This paper generalizes some known solitary solutions of a time-dependent Hamiltonian in two ways: The time-dependent field can be an elliptic function, and the time evolution is obtained for a complete set of basis vectors. The latter makes it feasible to consider arbitrary initial conditions. The former makes it possible to observe a beating caused by the non-harmonicity of the driving field.     

Spherical T-duality II: An infinity of spherical T-duals for non-principal SU(2)-bundles

Recently we initiated the study of spherical T-duality for spacetimes that are principal $\mathrm{SU}\left(2\right)$-bundles (Bouwknegt et al., to appear). In this paper, we extend spherical T-duality to spacetimes that are oriented non-principal $\mathrm{SU}\left(2\right)$-bundles. There are several interesting new examples in this case and a new phenomenon appearing in the non-principal case is the existence of infinitely many spherical T-duals.     

Common methods for the chiral determination of amphetamine and related compounds I. Gas, liquid and thin-layer chromatography

This article reviews the most common, useful methods for the chiral determination of amphetamine (AM) and AM-derived designer drugs in different of matrix, including blood, hair, urine, medicaments or standard solutions, taking into consideration articles published in the past 15 years. We consider chromatographic methods (e.g., gas, liquid, high-performance liquid, and thin layer). We describe several types of chiral derivatization reagent, mobile-phase additive and chiral stationary phase commonly used in the chromatographic methods. Tables summarize basic information about conditions (e.g., type of column and mobile phase), detection mode and reference data for each procedure.     

习近平与中国传统文化

习近平总书记对历史悠久、博大精深的中国传统文化有深厚的感情、深入的了解、深刻的研究和科学的评价。习近平总书记继承和弘扬了中国优秀传统文化的道统。从习近平总书记的思想和事功中,我们看到了中国文化、中国国家、中国共产党的光辉前景。