2 problems

Let $R\colon \mathbb{R}[x]\to\mathbb{R}[x]$ be an injective Rota–Baxter operator of weight zero. A formal integration at some point is the corresponding formal integration operator…

Let $(\mathcal{G},\varint)$ be a separated Rota–Baxter hierarchy over a field $K$. Consider the reduction system induced by the rules in Table, or a slight variation of those rules…