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A technique for computing eigenfunctions and eigenvalues. It proceeds by requiring J=int_a^b[p(x)y_x^2-q(x)y^2]dx (1) to have a stationary value subject to the normalization ...

The term "real line" has a number of different meanings in mathematics. Most commonly, "real line" is used to mean real axis, i.e., a line with a fixed scale so that every ...

Partial differential equation boundary conditions which, for an elliptic partial differential equation in a region Omega, specify that the sum of alphau and the normal ...

Let sum_(k=1)^(infty)u_k be a series with positive terms, and let rho=lim_(k->infty)u_k^(1/k). 1. If rho<1, the series converges. 2. If rho>1 or rho=infty, the series ...

In statistics, sampling is the selection and implementation of statistical observations in order to estimate properties of an underlying population. Sampling is a vital part ...

For a diagonal metric tensor g_(ij)=g_(ii)delta_(ij), where delta_(ij) is the Kronecker delta, the scale factor for a parametrization x_1=f_1(q_1,q_2,...,q_n), ...

Consider a second-order differential operator L^~u(x)=p_0(d^2u)/(dx^2)+p_1(du)/(dx)+p_2u, (1) where u=u(x) and p_i=p_i(x) are real functions of x on the region of interest ...

The set of all planes through a line. The line is sometimes called the axis of the sheaf, and the sheaf itself is sometimes called a pencil (Altshiller-Court 1979, p. 12; ...

A singular integral is an integral whose integrand reaches an infinite value at one or more points in the domain of integration. Even so, such integrals can converge, in ...

Let (x_1,x_2) and (y_1,y_2,y_3) be two sets of complex numbers linearly independent over the rationals. Then at least one of ...