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An expression occurring in existential sentences. "For some x" is the same as " exists x." Unlike in everyday language, it is does not necessarily refer to a plurality of ...

Let f(x) be a positive definite, measurable function on the interval (-infty,infty). Then there exists a monotone increasing, real-valued bounded function alpha(t) such that ...

A one-dimensional map whose increments are distributed according to a normal distribution. Let y(t-Deltat) and y(t+Deltat) be values, then their correlation is given by the ...

Frequency representation is the notation (1^(a_1)2^(a_2)...) used to abbreviate a partition {1,...,1_()_(a_1),2,...,2_()_(a_2),...} (Andrews 1998, p. 1).

rho_(n+1)(x)=intrho_n(y)delta[x-M(y)]dy, where delta(x) is a delta function, M(x) is a map, and rho is the natural invariant.

Let A=a_(ij) be a matrix with positive coefficients so that a_(ij)>0 for all i,j=1, 2, ..., n, then A has a positive eigenvalue lambda_0, and all its eigenvalues lie on 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 f^'(x) is continuous and the integral converges, int_0^infty(f(ax)-f(bx))/xdx=[f(0)-f(infty)]ln(b/a).

At least one power series solution will be obtained when applying the Frobenius method if the expansion point is an ordinary, or regular, singular point. The number of roots ...

Two unit-speed plane curves which have the same curvature differ only by a Euclidean motion.