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Article
Discrete Differential Calculus on Simplicial Complexes and Constrained Homology
Let V be a finite set. Let \({\cal K}\) K be a simplicial complex with its ...
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Article
A Künneth Formula for Finite Sets
In this paper, the authors define the homology of sets, which comes from and contains the ideas of path homology and embedded homology. Moreover, A Künneth formula for sets associated to the homology of sets i...
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Article
Computational Tools in Weighted Persistent Homology
In this paper, the authors study further properties and applications of weighted homology and persistent homology. The Mayer-Vietoris sequence and generalized Bockstein spectral sequence for weighted homology ...
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Article
Weighted Fundamental Group
In this paper, we develop and study the theory of weighted fundamental groups of weighted simplicial complexes. When all weights are 1, the weighted fundamental group reduces to the usual fundamental group as ...
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Article
Real hypersurfaces in a complex space form with a condition on the structure Jacobi operator
In this paper we classify the real hypersurfaces in a non-flat complex space form with its structure Jacobi operator R ξ satisfying (∇ X ...