Search Results for ""

The system of partial differential equations del ^2s-(|a|^2+1)s = 0 (1) del ^2a-del (del ·a)-s^2a = a. (2)

An algebraically soluble equation of odd prime degree which is irreducible in the natural field possesses either 1. Only a single real root, or 2. All real roots.

The partial differential equation u_t=u_(xxxxx)+5/2u_(xxx)u+(25)/4u_(xx)u_x+5/4u^2u_x.

A self-adjoint elliptic differential operator defined somewhat technically as Delta=ddelta+deltad, where d is the exterior derivative and d and delta are adjoint to each ...

The inverse curve of a lemniscate in a circle centered at the origin and touching the lemniscate where it crosses the x-axis produces a rectangular hyperbola (Wells 1991).

A method for testing nested hypotheses. To apply the procedure, given a specific model, calculate the likelihood of observing the actual data. Then compare this likelihood to ...

A triangular matrix L of the form L_(ij)={a_(ij) for i>=j; 0 for i<j. (1) Written explicitly, L=[a_(11) 0 ... 0; a_(21) a_(22) ... 0; | | ... 0; a_(n1) a_(n2) ... a_(nn)]. ...

Let f be analytic on a domain U subset= C, and assume that f never vanishes. Then if there is a point z_0 in U such that |f(z_0)|<=|f(z)| for all z in U, then f is constant. ...

For all x, y, a in an alternative algebra A, (xax)y = x[a(xy)] (1) y(xax) = [(yx)a]x (2) (xy)(ax) = x(ya)x (3) (Schafer 1996, p. 28).

The natural parametric equations of a curve are parametric equations that represent the curve in terms of a coordinate-independent parameter, generally arc length s, instead ...