In this note, we reported some results of homeomorphic classification of graphlikemanifolds of which contractions are edges of pyramids, and the number of vertexes of thebase of a pyramid, equal to 6 or 7 or 8.
It is shown that K 4(i,j,l,k,m,n) is chromatically unique if three numbers among i,j,l,k,m,n have the same value and the other three numbers are not equal but larger than that value.
This paper establishes the geometric framework of manifold learning.After summarizing the requirements of the classical manifold learning methods,we construct the smooth homeomorphism between the manifold and its tang...This paper establishes the geometric framework of manifold learning.After summarizing the requirements of the classical manifold learning methods,we construct the smooth homeomorphism between the manifold and its tangent space.Then we propose a new algorithm via homeomorphic tangent space(LHTS).We also present another algorithm via compactness(CSLI)by analyzing the topological properties of manifolds.We illustrate our algorithm on the completed manifold and non-completed manifold.We also address several theoretical issues for further research and improvements.展开更多
Let X be a Jordan domain satisfying certain hyperbolic growth conditions.Assume that φ is a homeomorphism from the boundary ?X of X onto the unit circle.Denote by h the harmonic diffeomorphic extension of φ from X o...Let X be a Jordan domain satisfying certain hyperbolic growth conditions.Assume that φ is a homeomorphism from the boundary ?X of X onto the unit circle.Denote by h the harmonic diffeomorphic extension of φ from X onto the unit disk.We establish the optimal Orlicz-Sobolev regularity and weighted Sobolev estimate of h.These generalize the Sobolev regularity of h in [A.Koski,J.Onninen,Sobolev homeomorphic extensions,J.Eur.Math.Soc.23(2021) 4065-4089,Theorem 3.1].展开更多
基金Supported by the State Ethnic Affairs Commission of PRC in 2000 year
文摘In this note, we reported some results of homeomorphic classification of graphlikemanifolds of which contractions are edges of pyramids, and the number of vertexes of thebase of a pyramid, equal to 6 or 7 or 8.
文摘It is shown that K 4(i,j,l,k,m,n) is chromatically unique if three numbers among i,j,l,k,m,n have the same value and the other three numbers are not equal but larger than that value.
文摘This paper establishes the geometric framework of manifold learning.After summarizing the requirements of the classical manifold learning methods,we construct the smooth homeomorphism between the manifold and its tangent space.Then we propose a new algorithm via homeomorphic tangent space(LHTS).We also present another algorithm via compactness(CSLI)by analyzing the topological properties of manifolds.We illustrate our algorithm on the completed manifold and non-completed manifold.We also address several theoretical issues for further research and improvements.
基金partially supported by the Young Scientist Program of the Ministry of Science and Technology of China(2021YFA1002200)supported by National Natural Science Foundation of China(12101226)+1 种基金partially supported by the National Natural Science Foundation of China(12101362)supported by Shandong Provincial Natural Science Foundation(ZR2021QA032)。
文摘Let X be a Jordan domain satisfying certain hyperbolic growth conditions.Assume that φ is a homeomorphism from the boundary ?X of X onto the unit circle.Denote by h the harmonic diffeomorphic extension of φ from X onto the unit disk.We establish the optimal Orlicz-Sobolev regularity and weighted Sobolev estimate of h.These generalize the Sobolev regularity of h in [A.Koski,J.Onninen,Sobolev homeomorphic extensions,J.Eur.Math.Soc.23(2021) 4065-4089,Theorem 3.1].
