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Since every unit vector can be thought of as a point on a unit sphere, and since a versor can be thought of as the quotient of two vectors, a versor has a representative great circle arc, called a vector arc, connecting these two points, drawn from the divisor or lower part of quotient, to the dividend or upper part of the quotient. [20] [21]
A common compactness measure is the isoperimetric quotient, the ratio of the area of the shape to the area of a circle (the most compact shape) having the same perimeter. . In the plane, this is equivalent to the Polsby–Popper t
The quotient C / Z; A quotient C / (Z + τZ), where τ ∈ C with Im(τ) > 0. Topologically there are only three types: the plane, the cylinder and the torus. But while in the two former case the (parabolic) Riemann surface structure is unique, varying the parameter τ in the third case gives non-isomorphic Riemann surfaces.
For each dimensional k, the boundary maps d k : δD k → RP k−1 /RP k−2 is the map that collapses the equator on S k−1 and then identifies antipodal points. In odd (resp. even) dimensions, this has degree 0 (resp. 2):
For example, (,) = / is a meromorphic function on the two-dimensional complex affine space. Here it is no longer true that every meromorphic function can be regarded as a holomorphic function with values in the Riemann sphere : There is a set of "indeterminacy" of codimension two (in the given example this set consists of the origin ( 0 , 0 ...
The complex structure of an annulus depends only on the ratio r / R . Each annulus ann(a; r, R) can be holomorphically mapped to a standard one centered at the origin and with outer radius 1 by the map . The inner radius is then r / R < 1.
In algebraic geometry, the Quot scheme is a scheme parametrizing sheaves on a projective scheme.More specifically, if X is a projective scheme over a Noetherian scheme S and if F is a coherent sheaf on X, then there is a scheme whose set of T-points () = (, ()) is the set of isomorphism classes of the quotients of that are flat over T.
The Helmholtz decomposition in three dimensions was first described in 1849 [9] by George Gabriel Stokes for a theory of diffraction. Hermann von Helmholtz published his paper on some hydrodynamic basic equations in 1858, [10] [11] which was part of his research on the Helmholtz's theorems describing the motion of fluid in the vicinity of vortex lines. [11]
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