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Roughly speaking, the metric tensor g_(ij) is a function which tells how to compute the distance between any two points in a given space. Its components can be viewed as ...

Taking a connected graph or network with a high graph diameter and adding a very small number of edges randomly, the diameter tends to drop drastically. This is known as the ...

A finite group G has a finite number of conjugacy classes and a finite number of distinct irreducible representations. The group character of a group representation is ...

The study of the nature and properties of bifurcations.

One of the numbers ..., -2, -1, 0, 1, 2, .... The set of integers forms a ring that is denoted Z. A given integer n may be negative (n in Z^-), nonnegative (n in Z^*), zero ...

A linear equation is an algebraic equation of the form y=mx+b involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept. The ...

A number of attractive 12-compounds of the regular tetrahedron can be constructed. The compounds illustrated above will be implemented in a future version of the Wolfram ...

The supremum is the least upper bound of a set S, defined as a quantity M such that no member of the set exceeds M, but if epsilon is any positive quantity, however small, ...

A normal distribution in a variate X with mean mu and variance sigma^2 is a statistic distribution with probability density function ...

A lattice L is said to be oriented if there exists a rule which assigns a specified direction to any edge connecting arbitrary lattice points x_i,x_j in L. In that way, an ...