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The cloacal outgrowth orchestrates co-development of the bladder and umbilical arteries. [PDF]

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Ye X   +12 more
europepmc   +1 more source
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Lines of curvature and umbilical points for implicit surfaces

Computer Aided Geometric Design, 2007
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jean-Claude Paul
exaly   +5 more sources

An Isolated Umbilical Point of the Graph of a Homogeneous Polynomial

Geometriae Dedicata, 2000
Consider a homogeneous polynomial \(f\) in two real variables \(x,y\) of degree \(k\geq 3\) whose graph \((x,y,f(x,y))\) in \(\mathbb{R}^3\) has the origin \(o\) as an isolated umbilic point. It is proved, that the index \(l\) of \(o\) belongs to the set \(\{1,0, \dots, 1-k/2\}\) if \(k\) is even or \(\{1/2,-1/2, \dots, 1-k/2\}\) if \(k\) is odd ...
Naoya Ando
exaly   +3 more sources

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