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A point traced out twice as a closed curve is traversed. The maximum number of double points for a nondegenerate quartic curve is three. An ordinary double point is also ...

Gomoku, also called go-moku (Japanese for "five points") is a tic-tac-toe-like game in which two players alternately place pieces, with each player using pieces of a fixed ...

Let l(x) be an nth degree polynomial with zeros at x_1, ..., x_n. Then the fundamental Hermite interpolating polynomials of the first and second kinds are defined by ...

Let Pi be a permutation of n elements, and let alpha_i be the number of permutation cycles of length i in this permutation. Picking Pi at random, it turns out that ...

A matrix whose elements may contain complex numbers. The matrix product of two 2×2 complex matrices is given by (1) where R_(11) = ...

The asymptotic form of the n-step Bernoulli distribution with parameters p and q=1-p is given by P_n(k) = (n; k)p^kq^(n-k) (1) ∼ 1/(sqrt(2pinpq))e^(-(k-np)^2/(2npq)) (2) ...

A real-valued stochastic process {B(t):t>=0} is a Brownian motion which starts at x in R if the following properties are satisfied: 1. B(0)=x. 2. For all times ...

Cluster analysis is a technique used for classification of data in which data elements are partitioned into groups called clusters that represent collections of data elements ...

The margin of error is an estimate of a confidence interval for a given measurement, result, etc. and is frequently cited in statistics. While phrases such as, "The poll has ...

A random variable is a measurable function from a probability space (S,S,P) into a measurable space (S^',S^') known as the state space (Doob 1996). Papoulis (1984, p. 88) ...