Deep coal seam mining floor strata water bursting is a complicate nonlinear system, whose factors are coupling and influencing themselves. It built the analytic structure model for deep coal seam mining floor strata w...Deep coal seam mining floor strata water bursting is a complicate nonlinear system, whose factors are coupling and influencing themselves. It built the analytic structure model for deep coal seam mining floor strata water bursting, the judgment matrix was found by the expert scoring method, the contribution weights of the influenced factors were given out by the equation analytic process. The thirteen controlling factors and five main controlling factors were put award by analyzing weights, so the result was basically conform to the field practice. The expert scoring method and analytic process can convert the objective fact to the subjective cognition, so it is a method that can turn the qualitative into the quantitative. This can be relative objectively and precisely to study the question of many factors and grey box.展开更多
In this article, we will derive an equality, where the Taylor series expansion around ε= 0 for any asymptotical analytical solution of the perturbed partial differential equation （PDE） with perturbing parameter e m...In this article, we will derive an equality, where the Taylor series expansion around ε= 0 for any asymptotical analytical solution of the perturbed partial differential equation （PDE） with perturbing parameter e must be admitted. By making use of the equality, we may obtain a transformation, which directly map the analytical solutions of a given unperturbed PDE to the asymptotical analytical solutions of the corresponding perturbed one. The notion of Lie-Bgcklund symmetries is introduced in order to obtain more transformations. Hence, we can directly create more transformations in virtue of known Lie-Bgcklund symmetries and recursion operators of corresponding unperturbed equation. The perturbed Burgers equation and the perturbed Korteweg-de Vries （KdV） equation are used as examples.展开更多
文摘Deep coal seam mining floor strata water bursting is a complicate nonlinear system, whose factors are coupling and influencing themselves. It built the analytic structure model for deep coal seam mining floor strata water bursting, the judgment matrix was found by the expert scoring method, the contribution weights of the influenced factors were given out by the equation analytic process. The thirteen controlling factors and five main controlling factors were put award by analyzing weights, so the result was basically conform to the field practice. The expert scoring method and analytic process can convert the objective fact to the subjective cognition, so it is a method that can turn the qualitative into the quantitative. This can be relative objectively and precisely to study the question of many factors and grey box.
基金0ne of the authors （H.Z. Liu） would like to express his sincere thanks to Dr. Shou-Feng Shen for his continuous encouragement and warm-hearted help.
文摘In this article, we will derive an equality, where the Taylor series expansion around ε= 0 for any asymptotical analytical solution of the perturbed partial differential equation （PDE） with perturbing parameter e must be admitted. By making use of the equality, we may obtain a transformation, which directly map the analytical solutions of a given unperturbed PDE to the asymptotical analytical solutions of the corresponding perturbed one. The notion of Lie-Bgcklund symmetries is introduced in order to obtain more transformations. Hence, we can directly create more transformations in virtue of known Lie-Bgcklund symmetries and recursion operators of corresponding unperturbed equation. The perturbed Burgers equation and the perturbed Korteweg-de Vries （KdV） equation are used as examples.
