Longevity factors for short and extra-short implants: An eight-year retrospective observational clinical study. [PDF]
Leite SJ +5 more
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Using Thue Morse structure and magnified defect resonance as cancer sensor. [PDF]
Zaky ZA +3 more
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Surface chemistry governs sex-dependent responses to PEG and zwitterionic siRNA nanocarriers in primary macrophages. [PDF]
Lanier OL +7 more
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Peritectic engineering enhanced thermoelectrics for smart thermal messaging devices. [PDF]
Xin J +14 more
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Morse Theory for the <i>k</i>-NN Distance Function. [PDF]
Reani Y, Bobrowski O.
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Atrial Secondary Mitral Regurgitation Outcomes Following Mitral Transcatheter Edge-to-Edge Repair: Results From the EXPANDed Studies. [PDF]
Ricciardi MJ +19 more
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Oscillator-qubit generalized quantum signal processing: a case study of the uracil cation vibronic model. [PDF]
Hong J, Kim SH, Min SK, Huh J.
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Moduli Spaces of Morse Functions for Persistence [PDF]
30 pages, 16 figures. Amended with reviewer suggestions, text is as in published version.
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Intrinsic harmonicily of Morse functions
Mathematika, 2003Let \(M\) be a \(C^2\) closed connected \(n\)-dimensional manifold. A \(C^2\) function \(f:M\rightarrow{\mathbb R}\) is called a Morse function, if all its critical points are non-degenerate. The index of a critical point \(x\) of \(f\) is by definition the maximal subspace of the tangent space of \(M\) at \(x\), on which the Hessian of \(f\) is ...
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