hypersurface


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hypersurface

(mathematics)
The analog of a surface in n-dimensional Euclidean space, where n is a positive integer; the set of points, (x1, x2, …, xn ), satisfying an equation of the form ƒ(x1, …, xn ) = 0.
References in periodicals archive ?
Yamamoto, Periods of tropical K3 hypersurfaces, arXiv:1806.04239.
It is clear that both the Lagrangian densities respect both (i.e., co-BRST and anti-co-BRST) fermionic symmetry transformations on a hypersurface, where the CF-type restrictions B x C = 0 and B x [bar.C] = 0 are satisfied.
The generalized Jang equation is motivated by the need for they hypersurface [summation] to have weakly nonnegative scalar curvature.
Owing to the reason that NSGA-III-WA needs to build a hypersurface, M extreme points cannot be found in the later stage of the algorithm to construct the hypersurface, and it cannot converge to a curve well.
Kamiyama, "A hypersurface of the configuration space of a spatial robot arm," JP Journal of Geometry and Topology, vol.
Hanebeck, "Random hypersurface models for extended object tracking," in Proc.
It is known (see [1] and the references therein) that a connected real analytic hypersurface of [C.sup.n+1] which is Levi nondegenerate at every point is (k, n - k)-pseudospherical at one point if and only if it is (k, n - k)-pseudospherical at every point.
Let p be a point in [bar.M] and ((M, g): [x.sup.1] = a constant) be a timelike hypersurface of [bar.M] passing through p.
[6] Nemethi,A.: Some topological invariants of isolated hypersurface singularities, EMS summer schoolEger (Hungary), 29 July-9 August (1996).
Let M = X(u) be a Lorentzian surface in anti-de Sitter space and let N(u) be its spacelike normal vector; a hypersurface L[H.sup.[+ or -].sub.M] defined by L[H.sup.[+ or - ].sub.M](u, [mu]) = X(u) + g(X[??](u)) is called L[H.sup.[+ or -].sub.M] the lightlike hypersurface along M.
According to this approach learning is based on a quadratic programming optimization procedure which aims at the identification of a subset of important feature vectors from the training set, used for the construction of a separating hypersurface between the two classes.