Search results
Results From The WOW.Com Content Network
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 ]
This process is called raising the index. Raising and then lowering the same index (or conversely) are inverse operations, which is reflected in the metric and inverse metric tensors being inverse to each other (as is suggested by the terminology): = = =
The Törnqvist or Törnqvist-Theil index is the geometric average of the n price relatives of the current to base period prices (for n goods) weighted by the arithmetic average of the value shares for the two periods. [16] [17]
A subgroup H of finite index in a group G (finite or infinite) always contains a normal subgroup N (of G), also of finite index. In fact, if H has index n, then the index of N will be some divisor of n! and a multiple of n; indeed, N can be taken to be the kernel of the natural homomorphism from G to the permutation group of the left (or right ...
The formula may also be used to calculate the genus of hyperelliptic curves. As another example, the Riemann sphere maps to itself by the function z n, which has ramification index n at 0, for any integer n > 1. There can only be other ramification at the point at infinity. In order to balance the equation
Multi-index notation is a mathematical notation that simplifies formulas used in multivariable calculus, partial differential equations and the theory of distributions, by generalising the concept of an integer index to an ordered tuple of indices.
Get AOL Mail for FREE! Manage your email like never before with travel, photo & document views. Personalize your inbox with themes & tabs. You've Got Mail!
Let X be a Riemann surface.Then the intersection number of two closed curves on X has a simple definition in terms of an integral. For every closed curve c on X (i.e., smooth function :), we can associate a differential form of compact support, the Poincaré dual of c, with the property that integrals along c can be calculated by integrals over X: