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pro vyhledávání: '"Lei, Fengchun"'
Many structures in science, engineering, and art can be viewed as curves in 3-space. The entanglement of these curves plays a crucial role in determining the functionality and physical properties of materials. Many concepts in knot theory provide the
Externí odkaz:
http://arxiv.org/abs/2411.17331
This is a summary of mathematical tools we used in research of analyzing the structure of proteins with amyloid form \cite{xi2024Top}. We defined several geometry indicators on the discrete curve namely the hop distance, the discrete curvature and th
Externí odkaz:
http://arxiv.org/abs/2405.14370
Persistent homology theory is a relatively new but powerful method in data analysis. Using simplicial complexes, classical persistent homology is able to reveal high dimensional geometric structures of datasets, and represent them as persistent barco
Externí odkaz:
http://arxiv.org/abs/2311.15755
In the past decade, topological data analysis (TDA) has emerged as a powerful approach in data science. The main technique in TDA is persistent homology, which tracks topological invariants over the filtration of point cloud data using algebraic topo
Externí odkaz:
http://arxiv.org/abs/2311.12834
Autor:
Lin, Wei, Lei, Fengchun
Applying Morse theory, we give a standard form for a class of surfaces which includes all the properly embedded incompressible surfaces in 3-dimensional handlebodies. We also give a necessary and sufficient condition to determine the incompressibilit
Externí odkaz:
http://arxiv.org/abs/2212.05769
The main results of the paper is that we give a characteristics for an annulus sum and a once-punctured torus sum of two handlebodies to be a handlebody as follows: 1. The annulus sum $H=H_1\cup_A H_2$ of two handlebodies $H_1$ and $H_2$ is a handleb
Externí odkaz:
http://arxiv.org/abs/1908.10113
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We survey the construction and properties of the Yamada polynomial of spatial graphs and present the Yamada polynomial formulae for some classes of graphs. Then we construct an infinite family of spatial graphs for which roots of Yamada polynomials a
Externí odkaz:
http://arxiv.org/abs/1810.12749
Publikováno v:
In Topology and its Applications 1 November 2022 321
We present formulae for computing the Yamada polynomial of spatial graphs obtained by replacing edges of plane graphs, such as cycle-graphs, theta-graphs, and bouquet-graphs, by spatial parts. As a corollary, it is shown that zeros of Yamada polynomi
Externí odkaz:
http://arxiv.org/abs/1801.09075