Search Results for ""

Let u_1<=u_2<=... be harmonic functions on a connected open set U subset= C. Then either u_j->infty uniformly on compact sets or there is a finite-values harmonic function u ...

The partial differential equation u_t=u_(xxx)u^3.

Let X be a metric space, A be a subset of X, and d a number >=0. The d-dimensional Hausdorff measure of A, H^d(A), is the infimum of positive numbers y such that for every ...

For n>=3, there exist no additive finite and invariant measures for the group of displacements in R^n.

The havercosine, also called the haversed cosine, is a little-used trigonometric function defined by havercosz = vercosz (1) = 1/2(1+cosz), (2) where vercosz is the vercosine ...

A metric on a bunch of segments with a common endpoint O, which defines the distance between two points P_1 and P_2 as the length of the shortest path connecting them inside ...

The second-order ordinary differential equation (Moon and Spencer 1961, p. 157; Zwillinger 1997, p. 166).

The system of partial differential equations S_t=SxS_(xx).

In bipolar coordinates, the Helmholtz differential equation is not separable, but Laplace's equation is.

The Helmholtz differential equation is not separable in bispherical coordinates.