Search results

by introducing coordinates on the resulting space. In this context, the term "modulus" is used synonymously with "parameter"; moduli spaces were first...

"geodesic convexity" and the coordinates are called normal coordinates. The explicit calculation of normal coordinates can be accomplished by considering...

homeomorphisms from S {\displaystyle S} to itself. It can be viewed as a moduli space for marked hyperbolic structure on the surface, and this endows it...

more easily in polar coordinates: the magnitude or modulus of the product is the product of the two absolute values, or moduli, and the angle or argument...

The coordinates a 1 , b 1 , a 2 , b 2 , … {\displaystyle a_{1},b_{1},a_{2},b_{2},\ldots } serve as coordinates for the moduli space of twisted...

surfaces into pairs of pants are used to construct the Fenchel-Nielsen coordinates on Teichmüller space, and in topological quantum field theory where they...

{C} /\Lambda } to the projective elliptic curve defined in homogeneous coordinates by E = { ( x : y : z ) ∈ C 3 ∣ y 2 z = 4 x 3 − g 2 x z 2 − g 3 z 3 }...

latter space has a distinguished system of homogeneous coordinates, given by the Plücker coordinates. An effective algebraic cycle in P n − 1 {\displaystyle...

triangle use trigonometry, side lengths (Heron's formula), vectors, coordinates, line integrals, Pick's theorem, or other properties. Heron of Alexandria...

"projective coordinates" to refer to what is commonly called Jacobian coordinates. An additional speed-up is possible if mixed coordinates are used. Reduction...

triangle have a simple characterization in barycentric coordinates. If a point has barycentric coordinates ( 0. u 1 u 2 u 3 … , 0. v 1 v 2 v 3 … , 0. w 1 w...

}\\z(\theta ,\varphi )&=r\cos \theta \\\end{aligned}}} using angular coordinates θ, φ ∈ [0, 2π), representing rotation around the tube and rotation around...

different parabola. That is, they specify coordinates on the 'space of parabolas': this is known as a moduli space of parabolas. Lambda calculus Observable...

leaves of the Lagrangian foliation are tori, and the natural linear coordinates on these are called "angle" variables. The cycles of the canonical 1...

Eddington showed that the singularity disappeared after a change of coordinates. In 1933, Georges Lemaître realised that this meant the singularity at...

about thousands of proteins can be obtained in the form of Cartesian coordinates for each atom in the protein. Many more gene sequences are known than...

introducing in particular the use of what are now generally called Chow coordinates (which were in some form familiar to Arthur Cayley). He married Margot...

lower-dimensional subset. Concretely, a rational map can be written in coordinates using rational functions. A birational map from X to Y is a rational...

four coordinates: (x, y, z, t). Cosmologists often work with space-like slices of spacetime that are surfaces of constant time in comoving coordinates. The...

freedom), of which the kinetic part coincides with the Kähler potential of the moduli space of vacua. Before taking the low-energy effective action, the theory...