Abstract In this paper, we decorate leaves and edges of planar rooted forests simultaneously and use a part of them to construct free nonunitary Rota-Baxter family algebras. As a corollary, we obtain the construction of free nonunitary Rota-Baxter algebras.

中文翻译：

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免费的非酉 Rota-Baxter 族代数和类型化叶间隔装饰平面根森林

摘要 在本文中，我们同时装饰平面有根森林的叶子和边缘，并使用它们的一部分构造自由的非酉 Rota-Baxter 家族代数。作为推论，我们获得了自由非酉 Rota-Baxter 代数的构造。