Search results
Results from the WOW.Com Content Network
In mathematics, the cone condition is a property which may be satisfied by a subset of a Euclidean space. Informally, it requires that for each point in the subset a cone with vertex in that point must be contained in the subset itself, and so the subset is "non-flat".
A right circular cone and an oblique circular cone A double cone (not shown infinitely extended) 3D model of a cone. A cone is a three-dimensional geometric shape that tapers smoothly from a flat base (frequently, though not necessarily, circular) to a point called the apex or vertex that is not contained in the base.
A subset of a vector space over an ordered field is a cone (or sometimes called a linear cone) if for each in and positive scalar in , the product is in . [2] Note that some authors define cone with the scalar ranging over all non-negative scalars (rather than all positive scalars, which does not include 0). [3]
In mathematics, specifically in order theory and functional analysis, if is a cone at the origin in a topological vector space such that and if is the neighborhood filter at the origin, then is called normal if = [], where []:= {[]:} and where for any subset , []:= (+) is the -saturatation of . [1]
A second-order cone program (SOCP) is a convex optimization problem of the form minimize subject to ‖ + ‖ +, =, …, = where the ...
The cone over a closed interval I of the real line is a filled-in triangle (with one of the edges being I), otherwise known as a 2-simplex (see the final example). The cone over a polygon P is a pyramid with base P. The cone over a disk is the solid cone of classical geometry (hence the concept's name). The cone over a circle given by
The normal cone C X Y or / of an embedding i: X → Y, defined by some sheaf of ideals I is defined as the relative Spec (= / +).. When the embedding i is regular the normal cone is the normal bundle, the vector bundle on X corresponding to the dual of the sheaf I/I 2.
The cone of curves is defined to be the convex cone of linear combinations of curves with nonnegative real coefficients in the real vector space () of 1-cycles modulo numerical equivalence. The vector spaces N 1 ( X ) {\displaystyle N^{1}(X)} and N 1 ( X ) {\displaystyle N_{1}(X)} are dual to each other by the intersection pairing, and the nef ...