论文标题
通过非共同的Picard-vessiot理论在通用微分方程的解决方案上
On the solutions of universal differential equation by noncommutative Picard-Vessiot theory
论文作者
论文摘要
基于非共同微分方程方程和代数组合学的Picard-vessiot理论，在非共同形式序列上具有带有圆锥形系数的形式序列，提出了各种杂种序列序列序列的递归结构，这些序列融合到通用微分方程的溶液中。基于单体因素化，这些结构强烈地使用对角线序列和二元性的各对碱基，在串联shuffle bialgebra和loday的广义bialgebra中。作为应用，dévissage提供了knizhnik-zamolodchikov方程的独特解决方案，令人满意的渐近条件。
Basing on Picard-Vessiot theory of noncommutative differential equations and algebraic combinatorics on noncommutative formal series with holomorphic coefficients, various recursive constructions of sequences of grouplike series converging to solutions of universal differential equation are proposed. Basing on monoidal factorizations, these constructions intensively use diagonal series and various pairs of bases in duality, in concatenation-shuffle bialgebra and in a Loday's generalized bialgebra. As applications, the unique solution, satisfying asymptotic conditions, of Knizhnik-Zamolodchikov equations is provided by dévissage.
