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Geometry index. In coordination chemistry and crystallography, the geometry index or structural parameter (τ) is a number ranging from 0 to 1 that indicates what the geometry of the coordination center is. The first such parameter for 5-coordinate compounds was developed in 1984. [1] Later, parameters for 4-coordinate compounds were developed. [2]
In mathematics, specifically group theory, the index of a subgroup H in a group G is the number of left cosets of H in G, or equivalently, the number of right cosets of H in G. The index is denoted or or . Because G is the disjoint union of the left cosets and because each left coset has the same size as H, the index is related to the orders of ...
The geometric mean of a data set {,, …,} is given by: (=) =. [3]The above figure uses capital pi notation to show a series of multiplications. Each side of the equal sign shows that a set of values is multiplied in succession (the number of values is represented by "n") to give a total product of the set, and then the nth root of the total product is taken to give the geometric mean of the ...
Raising and lowering indices. In mathematics and mathematical physics, raising and lowering indices are operations on tensors which change their type. Raising and lowering indices are a form of index manipulation in tensor expressions.
e. In mathematics, the winding number or winding index of a closed curve in the plane around a given point is an integer representing the total number of times that the curve travels counterclockwise around the point, i.e., the curve's number of turns. For certain open plane curves, the number of turns may be a non-integer.
Optical path length. In optics, optical path length (OPL, denoted Λ in equations), also known as optical length or optical distance, is the length that light needs to travel through a vacuum to create the same phase difference as it would have when traveling through a given medium. It is calculated by taking the product of the geometric length ...
In mathematics, and especially in algebraic geometry, the intersection number generalizes the intuitive notion of counting the number of times two curves intersect to higher dimensions, multiple (more than 2) curves, and accounting properly for tangency. One needs a definition of intersection number in order to state results like Bézout's ...
In mathematics, the cross product or vector product (occasionally directed area product, to emphasize its geometric significance) is a binary operation on two vectors in a three-dimensional oriented Euclidean vector space (named here ), and is denoted by the symbol . Given two linearly independent vectors a and b, the cross product, a × b ...