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The engineering terminology for one use of Fourier transforms. By breaking up a wave pulse into its frequency spectrum f_nu=F(nu)e^(2piinut), (1) the entire signal can be ...

A vector is formally defined as an element of a vector space. In the commonly encountered vector space R^n (i.e., Euclidean n-space), a vector is given by n coordinates and ...

Let J_nu(z) be a Bessel function of the first kind, Y_nu(z) a Bessel function of the second kind, and K_nu(z) a modified Bessel function of the first kind. Also let R[z]>0 ...

The integer sequence beginning with a single digit in which the next term is obtained by describing the previous term. Starting with 1, the sequence would be defined by "1, ...

The characteristic equation is the equation which is solved to find a matrix's eigenvalues, also called the characteristic polynomial. For a general k×k matrix A, the ...

The set of terms of first-order logic (also known as first-order predicate calculus) is defined by the following rules: 1. A variable is a term. 2. If f is an n-place ...

The maximum number of pieces into which a cylinder can be divided by n oblique cuts is given by f(n) = (n+1; 3)+n+1 (1) = 1/6(n+1)(n^2-n+6) (2) = 1/6(n^3+5n+6), (3) where (a; ...

A sequence of real numbers {x_n} is equidistributed on an interval [a,b] if the probability of finding x_n in any subinterval is proportional to the subinterval length. The ...

Let C_(L,M) be a Padé approximant. Then C_((L+1)/M)S_((L-1)/M)-C_(L/(M+1))S_(L/(M+1)) = C_(L/M)S_(L/M) (1) C_(L/(M+1))S_((L+1)/M)-C_((L+1)/M)S_(L/(M+1)) = ...

If a subgroup H of G has a group representation phi:H×W->W, then there is a unique induced representation of G on a vector space V. The original space W is contained in V, ...