supported by National Natural Science Foundation of China(Grant No.12071241);the National Key Research and Development Program of China(Grant No.2021YFA1002000).
First,we prove a decomposition formula for any multiplicative differential form on a Lie groupoid G.Next,we prove that if G is a Poisson Lie groupoid,then the spaceΩ_(mult)·(G)of multiplicative forms on G has a diff...
The big problem of Big Data is the lack of a machine learning process that scales and finds meaningful features. Humans fill in for the insufficient automation, but the complexity of the tasks outpaces the human mind...
We introduce the notions of implicative ideals and fuzzy implicative ideals of a distributive implication groupoid. Some properties of these ideals will be investigated. In particular, the necessary and sufficient con...
Let S be an inverse AG-groupoid (Abel-Grassmann groupoid) and define a relation γ on S by aγb if and only if there exist some positive integers n and m such that bm∈ (Sa)S and an∈ (Sb)S. We prove that S/γ i...
Proposed here is a new framework for the analysis of complex systems as a non-explicitly programmed mathematical hierarchy of subsystems using only the fundamental principle of causality, the mathematics of groupoid s...
National Key Basic Research Project of China under Grant No.2004CB318000;National Natural Science Foundation of China under Grant Nos.10375038 and 90403018
After introducing some of the basic definitions and results from the theory of groupoid and Lie algebroid,we investigate the discrete Lagrangian mechanics from the viewpoint of groupoid theory and give the connection ...
supported in part by Project P15691 from the Austrian Federal FWF,the national science finding body,as well as by several ongoing grants from Stadt Linz,Land Obersterreich and the Austrian Federal BKA.Kunst
A graph has the unique path property UPPn if there is a unique path of length n between any ordered pair of nodes. This paper reiterates Royle and MacKay's technique for constructing orderly algorithms. We wish to u...
Supported by the office of Graduate Studies and the Center of Excellence for Mathematics of the University of Isfahan
A notion of an irreducible representation, as well as of a square integrable representation on an arbitrary locally compact groupoid, is introduced. A generalization of a version of Schur's lemma on a locally compact...