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Topic: Nondegenerate

	What is the vertex enumeration problem, and what is the facet enumeration problem?
		If a given polyhedron does not satisfy the assumptions, it is easy to transform the polyhedron to an isomorphic lower dimensional polyhedron satisfying the assumptions.
		There are easy (nondegenerate) cases and difficult (degenerate) cases.
		The vertex enumeration is called nondegenerate if there is no point
	www.ifor.math.ethz.ch /~fukuda/polyfaq/node15.html (175 words)

	[No title]
		Nondegenerate geometry is the metric geometry presented in terms of natural geometric objects (NGO).
		In the nondegenerate geometries the analog of the straight appears to be a hallow tube (i.e.
		Application of nondegenerate geometry where thickness of tubes is connected with the quantum constant admits to explain quantum effects without using the quantum principles.
	pavel.physics.sunysb.edu /~rylov/pref.htm (833 words)

	[No title]
		This new type of geometry (called T-geometry, or nondegenerate geometry) may be interpreted also as an alternative way of generalization of the Euclidean geometry other than the Riemannian geometry.
		If the nondegenerate geometry is considered to be the space-time geometry, the particle world lines are substituted by stochastic world tubes and the quantum constant appears to be a geometrical quantity (thickness of the tubes).
		The nondegenerate space-time geometry admits one to restrict the field of scope of quantum mechanics in the same way as the statistical physics restricts the field of scope of the axiomatic thermodynamics.
	pavel.physics.sunysb.edu /~rylov/arindg.htm (800 words)

	Symplectic spaces
		Recall that ``alternating'' means that (v,v)=0 for all v in V, from which it follows that (v,w) = -(w,v) for all v,w in V; and ``nondegenerate'' means that the only vector v such that (v,w=0) for all v in V is the zero vector.
		The first claim is clear: any nondegenerate pairing identifies V with its dual; under this identification, W is just the annihilator of H; and we know that the dimensions of a space and its annihilator add up to dim(V).
		The second claim is a consequence of the fact that the pairing on H is nondegenerate.
	www.math.harvard.edu /~elkies/M55a.99/pfaff.html (1202 words)

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