3-Lie bialgebras and 3-Lie classical Yang–Baxter equations in low dimensions

In this paper, we give low-dimensional examples of local cocycle 3-Lie bialgebras and double construction 3-Lie bialgebras which were introduced in the study of the classical Yang–Baxter equation and Manin triples for 3-Lie algebras. We give an explicit and practical formula to compute the skew-symmetric solutions of the 3-Lie classical Yang–Baxter equation (CYBE). As an illustration, we obtain all skew-symmetric solutions of the 3-Lie CYBE in complex 3-Lie algebras of dimensions 3 and 4 and then the induced local cocycle 3-Lie bialgebras. On the other hand, we classify the double construction 3-Lie bialgebras for complex 3-Lie algebras in dimensions 3 and 4 and then give the corresponding eight-dimensional pseudo-metric 3-Lie algebras.     

The ‘Three-Line’ Theorem for the Vinogradov C-Spectral Sequence of the Yang–Mills Equations

The Vinogradov C-spectral sequence for the Yang–Mills equations is considered and the three-line theorem for the term E₁ of the C-spectral sequence is proved: E₁ ^p,q = 0 if p > 0 and q < n – 2, where n is the dimension of spacetime.     

磁绝缘传输线的有损线模型

 开发了一种磁绝缘传输线(MITL)的电路模拟方法。以传输线模拟方法TLCOD为基础,将MITL分成若干段有损传输线单元,每个单元由一段无损传输线及一个对地损失电阻组成。根据磁绝缘准则判断单元的磁绝缘状况并计算相关参量,推导丝阵负载条件下MITL末端界面电压的表达式,阐述模型的求解方法及步骤;用有损线模型计算阳加速器MITL得到的结果与实验结果基本吻合,表明模型正确有效。     

阳加速器水传输线及磁绝缘传输线的电路模拟

 根据阳加速器传输线的阻抗分区特性,建立电路模型,并对短路实验及丝阵内爆实验进行模拟。短路实验的模拟结果与实验测试结果非常接近;通过对丝阵具体条件的分析,合理地引入串联电阻,同样准确地模拟了丝阵内爆的传输线响应特性,并利用模型简单描述了丝阵内爆的一般特性。模拟结果表明,模拟方法正确有效、电路模型可用于变阻抗水传输线及MITL的设计分析及基本规律研究。     

Yang–Lee zeros of the Ising model on random graphs of non planar topology

We obtain in a closed form the 1/N² contribution to the free energy of the two Hermitian N×N random matrix model with nonsymmetric quartic potential. From this result, we calculate numerically the Yang–Lee zeros of the 2D Ising model on dynamical random graphs with the topology of a torus up to n=16 vertices. They are found to be located on the unit circle on the complex fugacity plane. In order to include contributions of even higher topologies we calculated analytically the nonperturbative (sum over all genus) partition function of the model for the special cases of N=1,2 and graphs with n≤20 vertices. Once again the Yang–Lee zeros are shown numerically to lie on the unit circle on the complex fugacity plane. Our results thus generalize previous numerical results on random graphs by going beyond the planar approximation and strongly indicate that there might be a generalization of the Lee–Yang circle theorem for dynamical random graphs.     

Octonionic Yang–Mills instanton on quaternionic line bundle of Spin(7) holonomy

The total space of the spinor bundle on the four-dimensional sphere S⁴ is a quaternionic line bundle that admits a metric of Spin(7) holonomy. We consider octonionic Yang–Mills instanton on this eight-dimensional gravitational instanton. This is a higher dimensional generalization of (anti-) self-dual instanton on the Eguchi-Hanson space. We propose an ansatz for Spin(7) Yang–Mills field and derive a system of non-linear ordinary differential equations. The solutions are classified according to the asymptotic behavior at infinity. We give a complete solution when the gauge group is reduced to a product of SU(2) subalgebras in Spin(7). The existence of more general Spin(7) valued solutions can be seen by making an asymptotic expansion.     

阴阳学说与化学元素的关系(人体健康和疾病的物质基础)

论述了中医的阴阳学说与化学元素的关系,揭示了人体内宏量和微量元素是其健康和疾病的物质基础,为元素医学提供了理论依据。     

Exotic Yang–Mills Dilaton Gauge Theories

An exotic class of nonlinear p-form non-Abelian gauge theories is studied, arising from the most general allowed covariant deformation of linear Abelian gauge theory for a set of massless 1-form fields and 2-form fields in four dimensions. These theories combine a Chapline–Manton type coupling of the 1-forms and 2-forms, along with a Yang–Mills coupling of the 1-forms, a Freedman–Townsend coupling of the 2-forms, and an extended Freedman–Townsend type coupling between the 1-forms and 2-forms. It is shown that the resulting theories have a geometrically interesting dual formulation that is equivalent to an exotic Yang–Mills dilaton theory involving a nonlinear sigma field. In particular, the nonlinear sigma field couples to the Yang–Mills 1-form field through a generalized Chern class 4-form term.     

Geometrical Lagrangian for a Supersymmetric Yang–Mills Theory on the Group Manifold

Perhaps one of the main features of Einstein's General Theory of Relativity is that spacetime is not flat itself but curved. Nowadays, however, many of the unifying theories like superstrings on even alternative gravity theories such as teleparalell geometric theories assume flat spacetime for their calculations. This article, an extended account of an earlier author's contribution, it is assumed a curved group manifold as a geometrical background from which a Lagrangian for a supersymmetric N=2, d=5 Yang–Mills – SYM, N=2, d=5 – is built up. The spacetime is a hypersurface embedded in this geometrical scenario, and the geometrical action here obtained can be readily coupled to the five-dimensional supergravity action. The essential idea that underlies this work has its roots in the Einstein–Cartan formulation of gravity and in the group manifold approach to gravity and supergravity theories. The group SYM, N=2, d=5, turns out to be the direct product of supergravity and a general gauge group .