Superposition of special non-abelian potentials

The superposition of the non-abelian potentials of the formA′^μ=Aα^μ+aβ ^μ andB′^μ=Bγ^μ+bη^μ are considered and the necessary as well as the sufficient conditions are obtained. The significance of the conditions is discussed and the constrained isotopic spins of the perturbation potentials (aβ ^μ,bη^μ) are shown to be necessary for the superposition of these potenitals. Work under the projecthcs/dst/1081/81     

Twistor correspondences for the soliton hierarchies

In this article we propose a new overview on the theory of integrable systems based on symmetry reduction of the anti-self-dual Yang—Mills equations and its twistor correspondence. First, the non-linear Schrödinger (NS) equations and the Korteweg de Vries (KdV) equations are shown to be symmetry reductions of the anti-self-dual Yang—Mills (ASDYM) equation with real forms of SL (2, ) as gauge groups.

We obtain a twistor correspondence between solutions of the NS and KdV equations and certain holomorphic vector bundles with a symmetry on the total space of the complex line bundle of Chern class two on the Riemann sphere. Remarkably, when the Chern class is increased, the correspondence extends to the NS and KdV hierarchies. If the symmetry condition is dropped we obtain a twistor correspondence for a hierarchy for the Bogomolny equations, which yields the KdV and NS hierarchies when the symmetry is imposed.

The inverse scattering transform is shown to be a coordinate realization of the twistor correspondence. Both the pure solitons and the solitonless cases are treated. The k-soliton solutions arise from the kth “Ward ansatze” in an analogous fashion to the monopole solutions.     

Self-dual connections,hyperbolic metrics and harmonic mappings on Riemann surfaces

The Sampson-Wolf model of Teichmüller space (using harmonic mappings) is shown to be exactly the same as the more recent Hitchin model (utilizing self-dual connections). Indeed, it is noted how the self-duality equations become the harmonicity equations. An interpretation of the modular group action in this model is mentioned.     

On Hitchin's connection

The aim of the paper is to give an explicit expression for Hitchin's connection in the case of stable rank 2 bundles on genus 2 curves. Some general theory (in the algebraic geometric setting) concerning heat operators is developed. In particular the notion of compatibility of a heat operator with respect to a closed subvariety is introduced. This is used to compare the heat operator in the nonabelian rank 2 genus 2 case to the abelian heat operator (on theta functions) for abelian surfaces. This relation allows one to perform the computation; the resulting differential equations are similar to the Knizhnik-Zalmolodshikov equations.

     

Gauge-invariant discrete models of Yang-Mills equations

Two discrete models of Yang-Mill equations are constructed in the space ℝⁿ for some matrix-valued Lie group. A gauge-invariant discrete model is examined. Translated fromMatematicheskie Zametki, Vol. 61, No. 5, pp. 742–754, May, 1997. Translated by O. V. Sipacheva     

The Yang-Mills functional and Laplace's equation on quantum Heisenberg manifolds

In this paper, we discuss the Yang-Mills functional and a certain family of its critical points on quantum Heisenberg manifolds using noncommutative geometrical methods developed by A. Connes and M. Rieffel. In our main result, we construct a certain family of connections on a projective module over a quantum Heisenberg manifold that gives rise to critical points of the Yang-Mills functional. Moreover, we show that there is a relationship between this particular family of critical points of the Yang-Mills functional and Laplace's equation on multiplication-type, skew-symmetric elements of quantum Heisenberg manifolds; recall that Laplacian is the leading term for the coupled set of equations making up the Yang-Mills equation.     

基于Fuzzy-Grey关联分析的信息资源聚焦的数学模型

本文运用饱和信息维的增减技术对信息获取子空间进行结构上的剖分,用饱和信息维列作为因子列来构造灰色关联空间,将灰色理论中的关联分析用于模糊综合评判模型,用灰色关联系数来替代隶属度,用关联序来描述信息之间的相关联程度,得到信息资源聚焦的一种新的数学模型。     

Correspondences of Coclosed Submodules

We establish an order-preserving bijective correspondence between the sets of coclosed elements of some bounded lattices related by suitable Galois connections. As an application, we deduce that if M is a finitely generated quasi-projective left R-module with S = End _R (M) and N is an M-generated left R-module, then there exists an order-preserving bijective correspondence between the sets of coclosed left R-submodules of N and coclosed left S-submodules of Hom _R (M, N).