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The metric g can take up to two vectors or vector fields X, Y as arguments. In the former case the output is a number, the (pseudo-)inner product of X and Y. In the latter case, the inner product of X p, Y p is taken at all points p on the manifold so that g(X, Y) defines a smooth function on M. Vector fields act (by definition) as differential ...
[4] Other biologically important polymers that can be effectively modeled as worm-like chains include: double-stranded DNA (persistence length 40-50 nm) and RNA (persistence length 64 nm) [3] [5] single-stranded DNA (persistence length 4 nm) [6] unstructured RNA (persistence length 2 nm) [7] unstructured proteins (persistence length 0.6-0.7 nm) [8]
6.4 Scalar curvature. 6.5 Traceless Ricci tensor. 6.6 ... Download as PDF; Printable version; In other projects ... The defining formula is ...
In two dimensions, the Levi-Civita symbol is defined by: = {+ (,) = (,) (,) = (,) = The values can be arranged into a 2 × 2 antisymmetric matrix: = (). Use of the two-dimensional symbol is common in condensed matter, and in certain specialized high-energy topics like supersymmetry [1] and twistor theory, [2] where it appears in the context of 2-spinors.
In mathematics, a versor is a quaternion of norm one (a unit quaternion).Each versor has the form = = + , =, [,], where the r 2 = −1 condition means that r is a unit-length vector quaternion (or that the first component of r is zero, and the last three components of r are a unit vector in 3 dimensions).
Sylvester's theorem or Sylvester's formula describes a particular interpretation of the sum of three pairwise distinct vectors of equal length in the context of triangle geometry. It is also referred to as Sylvester's (triangle) problem in literature, when it is given as a problem rather than a theorem.
As the name implies, the divergence is a (local) measure of the degree to which vectors in the field diverge. The divergence of a tensor field T {\displaystyle \mathbf {T} } of non-zero order k is written as div ( T ) = ∇ ⋅ T {\displaystyle \operatorname {div} (\mathbf {T} )=\nabla \cdot \mathbf {T} } , a contraction of a tensor field ...
The first two steps of the Gram–Schmidt process. In mathematics, particularly linear algebra and numerical analysis, the Gram–Schmidt process or Gram-Schmidt algorithm is a way of finding a set of two or more vectors that are perpendicular to each other.