In this paper, we establish a new second main theorem for meromorphic mappings of [Formula: see text] into [Formula: see text] and moving hypersurfaces with truncated counting functions in the case, where the meromorphic mappings may be algebraically degenerate. A version of the second main theorem with weighted counting functions is also given. Our results improve the recent results on this topic. As an application, an algebraic dependence theorem for meromorphic mappings sharing moving hypersurfaces is given.

中文翻译：

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具有截断计数函数和应用的亚纯映射和移动超曲面的退化第二主定理

在本文中，我们建立了一个新的第二个主要定理，用于将 [Formula: see text] 亚纯映射到 [Formula: see text] 以及在亚纯映射可能是代数退化的情况下使用截断计数函数移动超曲面。还给出了具有加权计数函数的第二个主要定理的一个版本。我们的结果改进了最近关于该主题的结果。作为一个应用，给出了共享移动超曲面的亚纯映射的代数依赖定理。