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In geometry, a half-space is either of the two parts into which a plane divides the three-dimensional Euclidean space. If the space is two-dimensional...

number and defines the shift. The pair (a, b) defines a point in the right halfplane R+ × R. The projection of a function x onto the subspace of scale a then...

{1-x^{2}-y^{2}}{x^{2}+(1-y)^{2}}}\right)\,} in the halfplane model. A point (x,y) in the halfplane model maps to ( 2 x x 2 + ( 1 + y ) 2   ,   x 2 + y...

The convex layers of a point set and their intersection with a halfplane...

plane, with a single pole of order 1 at z = 1. Its zeros in the left halfplane are all the negative even integers, and the Riemann hypothesis is the...

series converges absolutely and uniformly on compact sets (in the upper halfplane), and is a modular form of weight 2k for Γ. Note that, when Γ is the full...

the power of P. In the case n = 2, the power diagram consists of two halfplanes, separated by a line called the radical axis or chordale of the two circles...

distinct halfplane, with all halfplanes having that line as their common boundary. An embedding like this in which the edges are drawn on halfplanes is called...

intersection, which may be found by intersecting the line with each of the halfplane boundary planes and choosing the intersection point that is closest to...

of the weights of the two unidentified halfplanes of that neighborhood is the weight of the identified halfplane. Branched covering Branched manifold Li...

{\displaystyle r_{e}} represents: when the circle is completely inside the halfplane a hyperbolic circle with center ⟨ x e , y e 2 − r e 2 ⟩ {\displaystyle...

of L2 boundary values of holomorphic functions on the upper and lower halfplanes. H 2 ( R ) {\displaystyle H^{2}(\mathbb {R} )} and its conjugate consist...

the lower half-plane where y < 0 and to focus on the flow in the upper halfplane. With this interpretation, the flow is that of a vertically directed jet...

is either the Riemann sphere, the complex plane or the unit disk/upper halfplane. The first important invariant of a compact Riemann surface is its genus...

of the ring lemma, showing that it is tight. The construction allows halfplanes to be considered as degenerate circles with infinite radius, and includes...

Because the points are not all in a line, at least one of the two open halfplanes bounded by this line must be non-empty. Grünbaum forms two monotone polygonal...

pair of holomorphic functions one each on the upper and lower complex halfplane modulo entire holomorphic functions. More generally one can define B (...

T} such that vertices placed on x-axis and all edges embedded in the halfplane above or below and all neighbors of a vertex lay completely on the left...

of polygons and polyhedra which can be obtained from a finite set of halfplanes (halfspaces) by Boolean operations of set intersection and set complement...

solutions of Beltrami's equation restrict to diffeomorphisms of the upper halfplane or unit disk if the coefficient μ has extra symmetry properties; since...

algorithms for testing whether the two polygons can be separated into disjoint halfplanes by a continuous linear motion, and in data structures for collision detection...

such that the two become separated by a straight line into different halfplanes) and this separation may be found in linear time. A polygon is called...

real line onto the circle, sending the point at ∞ to 1, and the upper halfplane onto the unit disk. Define the unitary operator from L2(T) onto L2(R)...

function of s that is analytic in the right halfplane (σ>0), have a positive real part in the right halfplane and take on real values on the real axis....

Euclidean plane. The edges are drawn as semicircles in one or both of the two halfplanes bounded by the line, or as smooth curves formed by sequences of semicircles...

circle with the point 1 omitted. It carries the upper halfplane onto the unit disk and the lower halfplane onto the complement of the closed unit disk. In operator...

studied for negatively curved surfaces—in particular the hyperbolic upper halfplane and unit disk—by Morse and generalised to negatively curved symmetric...

biholomorphisms of the Riemann sphere exchanging the unit disk and the upper halfplane. When the Hermitian symmetric space is of tube type the same Möbius transformations...