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Sedative Choice and Neurocognitive Outcomes After Critical Illness in Early Childhood.
JAMA Netw OpenCurley MAQ +8 more
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Ascending and descending regions of a discrete Morse function
Computational Geometry: Theory and Applications, 2009 We present an algorithm which produces a decomposition of a regular cellular complex with a discrete Morse function analogous to the Morse–Smale decomposition of a smooth manifold with respect to a smooth Morse function.
Jerše, Gregor, Mramor Kosta, Neža
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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 ...
Frosini P., Landi C.
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On morse theory for piecewise smooth functions
Journal of Dynamical and Control Systems, 1997zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Agrachev, A. A. +2 more
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Normal Morse Data of Two Morse Functions
1988In this chapter we analyze the normal Morse data at a critical point p∈Z of a function f1: Z → ℝ under the assumption that there exists a second function f2: Z → ℝ such that the map (f1,f2): Z → ℝ2 has a nondegenerate critical point at p (see below).
Mark Goresky, Robert MacPherson
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Morse numbers and minimal morse functions on nonsimply connected manifolds
Ukrainian Mathematical Journal, 1988See the review in Zbl 0648.58005.
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2004
In this chapter we introduce the Morse-Smale transversality condition for gradient vector fields, and we prove the Kupka-Smale Theorem (Theorem 6.6) which says that the space of smooth Morse-Smale gradient vector fields is a dense subspace of the space of all smooth gradient vector fields on a finite dimensional compact smooth Riemannian manifold (M,g)
Augustin Banyaga, David Hurtubise
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In this chapter we introduce the Morse-Smale transversality condition for gradient vector fields, and we prove the Kupka-Smale Theorem (Theorem 6.6) which says that the space of smooth Morse-Smale gradient vector fields is a dense subspace of the space of all smooth gradient vector fields on a finite dimensional compact smooth Riemannian manifold (M,g)
Augustin Banyaga, David Hurtubise
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1988
It is often necessary to consider a “Morse function” f: X → ℝ which is not proper, but which can be extended to a proper function $$ \bar{f}:Z \to \mathbb{R} $$ where Z contains X as a dense open subset. For example, Z may be a compactification of some noncompact algebraic variety X ⊂ ℂℙ n , and f may be a smooth function defined on the ambient ...
Mark Goresky, Robert MacPherson
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It is often necessary to consider a “Morse function” f: X → ℝ which is not proper, but which can be extended to a proper function $$ \bar{f}:Z \to \mathbb{R} $$ where Z contains X as a dense open subset. For example, Z may be a compactification of some noncompact algebraic variety X ⊂ ℂℙ n , and f may be a smooth function defined on the ambient ...
Mark Goresky, Robert MacPherson
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The Periodicity of Morse's Function
Physical Review, 1935The applicability of a simple modification of Morse's rule has been tested, and found generally satisfactory for simple non-hydride di-atoms and for hydrides of the $K\mathrm{H}$ period. Morse's function is shown to possess a periodic character, and to be capable of adjustment by the introduction of group numbers and period constants on the basis of ...
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