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Every smooth manifold M has a tangent bundle TM, which consists of the tangent space TM_p at all points p in M. Since a tangent space TM_p is the set of all tangent vectors ...

Isomorphism is a very general concept that appears in several areas of mathematics. The word derives from the Greek iso, meaning "equal," and morphosis, meaning "to form" or ...

The singleton set {0}, with respect to the trivial group structure defined by the addition 0+0=0. The element 0 is the additive identity element of the group, and also the ...

The Gini coefficient (or Gini ratio) G is a summary statistic of the Lorenz curve and a measure of inequality in a population. The Gini coefficient is most easily calculated ...

The Lorenz curve is used in economics and ecology to describe inequality in wealth or size. The Lorenz curve is a function of the cumulative proportion of ordered individuals ...

One of the four divisions of observations which have been grouped into four equal-sized sets based on their statistical rank. The quartile including the top statistically ...

The median of a statistical distribution with distribution function D(x) is the value x such D(x)=1/2. For a symmetric distribution, it is therefore equal to the mean. Given ...

A function that can be defined as a Dirichlet series, i.e., is computed as an infinite sum of powers, F(n)=sum_(k=1)^infty[f(k)]^n, where f(k) can be interpreted as the set ...

A complete bipartite graph, sometimes also called a complete bicolored graph (Erdős et al. 1965) or complete bigraph, is a bipartite graph (i.e., a set of graph vertices ...

A coordinate chart is a way of expressing the points of a small neighborhood, usually on a manifold M, as coordinates in Euclidean space. An example from geography is the ...