Visible-light-induced,autopromoted nickel-catalyzed three-component arylsulfonation of 1,3-enynes and mechanistic insights

Science China Chemistry - A light-induced, nickel-catalyzed three-component arylsulfonation of 1,3-enynes in the absence of photocatalyst is reported. This methodology exhibited mild conditions,...     

Generalized Toda Mechanics Associated with Loop Algebras (L)(Cr) and (L)(Dr) and Their Reductions

We construct a class of integrable generalization of Toda mechanics with long-range interactions. These systems are associated with the loop algebras L(C_r) and L(D_r) in the sense that their Lax matrices can be realized in terms of the c=0 representations of the affine Lie algebras C⁽¹⁾_r and D⁽¹⁾_r and the interactions pattern involved bears the typical characters of the corresponding root systems. We present the equations of motion and the Hamiltonian structure. These generalized systems can be identified unambiguously by specifying the underlying loop algebra together with an ordered pair of integers (n,m). It turns out that different systems associated with the same underlying loop algebra but with different pairs of integers (n₁,m₁) and (n₂,m₂) with n₂<n₁ and m₂<m₁ can be related by a nested Hamiltonian reduction procedure. For all nontrivial generalizations, the extra coordinates besides the standard Toda variables are Poisson non-commute, and when either $n$ or m≥3, the Poisson structure for the extra coordinate variables becomes some Lie algebra (i.e. the extra variables appear linearly on the right-hand side of the Poisson brackets). In the quantum case, such generalizations will become systems with noncommutative variables without spoiling the integrability.     

Non-commutative Chiral QCD2 Model

The effective action of chiral QCD₂ was studied in two-dimensional non-commutative space-time by using path integral approach. It is shown that vector boson has a mass generation and the effective Lagrangian contains a term corresponding to a Wess-Zumino-Witten-like term.     

Solution of Reflection Equation

We give some general results concerning solutions of reflection equation associated with the Z_n symmetry Belavin model. The complete solution for the eight-vertex model is obtained.     

The Unitarity of the W(3) Algebra from SU(3) Parafermion

We express the vacuum expectation value of the SU(3)k parafermion fields by that of two bosons and SU(3)_k current algebra. When k = 1,2,3, the SU(3)_k current algebra becomes an inner product of a unitary representation, and T(z), W⁽³⁾(z) are equivalent to "quasiself-adjoint" operators in this represen tation.     

Domain wall partition function of the eight-vertex model with a non-diagonal reflecting end

With the help of the Drinfeld twist or factorizing F-matrix for the eight-vertex SOS model, we derive the recursion relations of the partition function for the eight-vertex model with a generic non-diagonal reflecting end and domain wall boundary condition. Solving the recursion relations, we obtain the explicit determinant expression of the partition function. Our result shows that, contrary to the eight-vertex model without a reflecting end, the partition function can be expressed as a single determinant.     

Integrability and Gauge Fixing for Bosonic String on AdS3 × S^3

The integrability and the TST transformation of the bosonic string on AdS3× S^3 are studied. The Lax connection for gauge fixed theory is constructed and proved to be fiat.     

Loop代数上一种Toda力学系统的求解问题

研究Loop代数上的一种Toda系统L=[L,M], 其Lax Pair中的M是反对称矩阵,而L=L⁺+M, L⁺是准上三角矩阵(包含对角部分), 证明这种系统的Lax方程的求解问题与相关的正则Riemann-Hilbert问题等价. 按此方法, 发现在某些特定的初值条件下系统是可积的. 并给出实例求解这一问题, 得到了精确解.     

非对易torus上的新孤子解

利用在非对易可积torus(环)上的算子都有约化矩阵这一特点, 孤子解的求解问题可以化为求满足代数方程Q(M)=0的有限维矩阵解问题. 本文研究了当 矩阵M不可对角化时的情形, 分析这种情形,得到当势函数V(\phi)具有三阶以上的极值点时, 有限维矩阵方程V′(M)=0存在不可对角化的矩阵解. 研究了这种解的一般形式, 并通过kq表象, 构造了非对易整环上以上述矩阵解为约化矩阵 的新孤子解. 根据这种构造方法, 可以得到非对易orbifold上的新孤子解.     

AdS3×S3 弦的可积性

从Rahmfeld和Rajaraman构造的在AdS₃×S³背景中具有κ对称的GS弦的作用量出发, 推导出AdS₃×S³弦的运动方程, 然后利用连续的扭曲对偶变换构造了带有自由参数λ的平联络, 利用这些平联络可进一步得到无穷多守恒量, 说明此系统是可积的.