In mathematics, an invariant convex cone is a closed convex cone in a Lie algebra of a connected Lie group that is invariant under inner automorphisms...

[0, 1]. This implies that convexity is invariant under affine transformations. Further, it implies that a convex set in a real or complex topological vector...

analysis and related areas of mathematics, locally convex topological vector spaces (LCTVS) or locally convex spaces are examples of topological vector spaces...

(X_{P},L_{P})} is given by a convex function f {\displaystyle f} on P {\displaystyle P} , then the Donaldson-Futaki invariant can be written as DF ⁡ ( X...

the Shilov boundary S being equal to the complex dimension of D. Invariant convex cone Knapp 1972 Wolf 2010 See: Helgason 1978 Wolf 2010 Kobayashi & Nomizu...

mathematics, the cone of curves (sometimes the Kleiman-Mori cone) of an algebraic variety X {\displaystyle X} is a combinatorial invariant of importance...

concept is named, introduced it for convex polyhedra more generally but failed to rigorously prove that it is an invariant. In modern mathematics, the Euler...

Geons are the simple 2D or 3D forms such as cylinders, bricks, wedges, cones, circles and rectangles corresponding to the simple parts of an object in...

self-concordant function, that is also a barrier function for a particular convex set. Self-concordant barriers are important ingredients in interior point...

The positive cone of ≤ P {\displaystyle \leq _{P}} is P {\displaystyle P} . The left-invariant order ≤ {\displaystyle \leq } is bi-invariant if and only...

In geometry, a Platonic solid is a convex, regular polyhedron in three-dimensional Euclidean space. Being a regular polyhedron means that the faces are...

0 {\displaystyle x\geq 0} forms a positive cone of F . {\displaystyle F.} Conversely, given a positive cone P {\displaystyle P} of F {\displaystyle F}...

hence they are members of the convex cone of nonnegative real numbers (whose nonzero members have reciprocals in this same cone). For several parameters,...

construction arises for a closed convex cone K in a Banach space V (possibly, infinite-dimensional). In addition, the cone K is assumed to be pointed, i...

equivalent to one taking only the values ±1. Metaplectic group Invariant convex cone Folland 1989 Hilgert & Neeb 1993, pp. 59–60 Hilgert & Neeb 1993...

algebras without identity. A convex cone C in a finite-dimensional real inner product space V is a convex set invariant under multiplication by positive...

X} be a Banach space, and let K ⊂ X {\displaystyle K\subset X} be a convex cone such that K ∩ − K = { 0 } {\displaystyle K\cap -K=\{0\}} , and K − K...

light is directly related to the radii of curvature of the wavefronts. A convex lens or concave mirror will cause parallel rays to focus, converging toward...

caveat: many terms in Riemannian and metric geometry, such as convex function, convex set and others, do not have exactly the same meaning as in general...

algebra invariant convex cone An invariant convex cone is a closed convex cone in the Lie algebra of a connected Lie group that is invariant under inner...

PT-invariance is needed. Equilibrium may be not T- or PT-invariant even if the laws of motion are invariant. This non-invariance may be caused by the spontaneous...

the shape of a set of points is all the geometrical information that is invariant to translations, rotations, and size changes. Having the same shape is...

combinations with nonnegative coefficients of points in (P,1). Then C(P) is a convex cone, C ( P ) = { λ 1 ( x 1 , 1 ) + ⋯ + λ n ( x n , 1 ) ∣ x i ∈ P ,   λ i...

intersection of two given solids Cone algorithm: identify surface points Convex hull algorithms: determining the convex hull of a set of points Chan's algorithm...

friction cones are convex cones (as they typically are), the support polygon is always a convex region. It is also invariant to the mass of the object...

lens is an optical lens in the shape of a sphere. Formally, it is a bi-convex spherical lens with the same radius of curvature on both sides, and diameter...

groups are sometimes regarded as strongly geometric as well. Convex geometry investigates convex shapes in the Euclidean space and its more abstract analogues...

are the convex bodies in R n {\displaystyle \mathbb {R} ^{n}} compact convex polytopes in R n {\displaystyle \mathbb {R} ^{n}} convex cones smooth compact...

define a convex cone, which contains all non-negative linear combinations of its vectors. Corresponding concept in an affine space is a convex set, which...

in the six-dimensional space of stresses. The yield surface is usually convex and the state of stress of inside the yield surface is elastic. When the...