6 citations · 8 across the 5 of their papers we have counts for
6 papers
Moerdijk Hopf algebras of decorated rooted forests: an operated algebra approach
Loic Foissy, Xiao-Song Peng, Yunzhou Xie +1
In this paper, we first endow the space of decorated planar rooted forests with a coproduct that equips it with the structure of a bialgebra and further a Moerdijk Hopf algebra. We…
Extending structures of Rota-Baxter Lie algebras
Xiao-song Peng, Yi Zhang
In this paper, we first introduce the notion of an extending datum of a Rota-Baxter Lie algebra through a vector space. We then construct a unified product for the Rota-Baxter Lie…
Reduced typed angularly decorated planar rooted trees and generalized tridendriform algebras
Loïc Foissy, Xiao-Song Peng
We introduce a generalization of tridendriform algebras, where each of the three products are replaced by a family of products indexed by a set . We study the needed structure o…
Typed angularly decorated planar rooted trees and generalized Rota-Baxter algebras
Loïc Foissy, Xiao-Song Peng
We introduce a generalization of parametrized Rota-Baxter algebras, which includes family and matching Rota-Baxter algebras. We study the structure needed on the set of paramet…
Dizygotic Conditional Variational AutoEncoder for Multi-Modal and Partial Modality Absent Few-Shot Learning
Yi Zhang, Sheng Huang, Xi Peng +1
Data augmentation is a powerful technique for improving the performance of the few-shot classification task. It generates more samples as supplements, and then this task can be tra…
Matching Hom-Setting of Rota-Baxter algebras, dendriform algebras and pre-Lie algebras
Dan Chen, Xiao-Song Peng, Chia Zargeh +1
In this paper, we introduce the Hom-algebra setting of the notions of matching Rota-Baxter algebras, matching (tri)dendriform algebras and matching (pre)Lie algebras. Moreover, we…