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A region in a knot or link projection plane surrounded by a circle such that the knot or link crosses the circle exactly four times. Two tangles are equivalent if a sequence ...

If f(omega) is square integrable over the real omega-axis, then any one of the following implies the other two: 1. The Fourier transform F(t)=F_omega[f(omega)](t) is 0 for ...

The W-transform of a function f(x) is defined by the integral where Gamma[(beta_m)+s, 1-(alpha_n)-s; (alpha_p^(n+1))+s, 1-(beta_q^(m+1))-s] =Gamma[beta_1+s, ..., beta_m+s, ...

The one-dimensional wave equation is given by (partial^2psi)/(partialx^2)=1/(v^2)(partial^2psi)/(partialt^2). (1) In order to specify a wave, the equation is subject to ...

Recall the definition of the autocorrelation function C(t) of a function E(t), C(t)=int_(-infty)^inftyE^_(tau)E(t+tau)dtau. (1) Also recall that the Fourier transform of E(t) ...

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

The partial differential equation u_t+u_(xxx)-6uu_x=0 (1) (Lamb 1980; Zwillinger 1997, p. 175), often abbreviated "KdV." This is a nondimensionalized version of the equation ...

A prime partition of a positive integer n>=2 is a set of primes p_i which sum to n. For example, there are three prime partitions of 7 since 7=7=2+5=2+2+3. The number of ...

Two square matrices A and B that are related by B=X^(-1)AX, (1) where X is a square nonsingular matrix are said to be similar. A transformation of the form X^(-1)AX is called ...

A sequence whose terms are integers. The most complete printed references for such sequences are Sloane (1973) and its update, Sloane and Plouffe (1995). Neil Sloane ...