hypersphere

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hy·per·sphere

 (hī′pər-sfîr′)
n.
Any of a set of objects resulting from the generalization of a two-dimensional circle and a three-dimensional sphere to n dimensions. In n-dimensional space, a hypersphere is the set of all points that are a given distance, called the radius, from a given point, called the center.
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Transportation noise was modelled by well-established noise propagation models (sonRoad, sonRAIL and FLULA 2) by Empa and n-sphere. The air pollution and the transportation noise models were applied for each address of the 4.4 million Swiss adult citizen (aged 30 years and above).
The boundary Bd([I.sup.n+1]) of an (n + 1)-cube [I.sup.n+1] is homeomorphic to n-sphere [S.sup.n].
We define the discrete n-sphere as [s.sup.n] = S ([S.sup.n-1]) starting with the circle [S.sup.1] = [S.sup.1.sub.4].
Let [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] be a Lipschitz continuous objective function, I [subset] D is an n-simplex, [R.sub.2](I) denotes the radius of circumscribed n-sphere and V(I) denotes the set of vertices.
In [C] Cheng proved that d(M) = [Pi] if and only if M is isometric to the unit n-sphere Sn in [R.sup.n+l].