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The operator partial^_ is defined on a complex manifold, and is called the 'del bar operator.' The exterior derivative d takes a function and yields a one-form. It decomposes ...

A dyadic, also known as a vector direct product, is a linear polynomial of dyads AB+CD+... consisting of nine components A_(ij) which transform as (A_(ij))^' = ...

Given collinear points W, X, Y, and Z, Y and Z are harmonic conjugates with respect to W and X if (|WY|)/(|YX|)=(|WZ|)/(|XZ|). (1) W and X are also harmonic conjugates with ...

The latitude of a point on a sphere is the elevation of the point from the plane of the equator. The latitude delta is related to the colatitude (the polar angle in spherical ...

The equation of a line ax+by+c=0 in slope-intercept form is given by y=-a/bx-c/b, (1) so the line has slope -a/b. Now consider the distance from a point (x_0,y_0) to the ...

Let P and U be points, neither of which lies on a sideline of DeltaABC, given in barycentric coordinates by P=p:q:r and U=u:v:w. The P-reciprocal conjugate of U is then the ...

Take the Helmholtz differential equation del ^2F+k^2F=0 (1) in spherical coordinates. This is just Laplace's equation in spherical coordinates with an additional term, (2) ...

A tetraview is a visualization technique for bivariate complex functions. In the simplest case, the graph of a complex-valued function w=w(z) can be considered as a ...

The third Brocard point has triangle center function alpha=a^(-3) and is Kimberling center X_(76) (Kimberling 1998, p. 78). The point may have received its name since its ...

Toroidal functions are a class of functions also called ring functions that appear in systems having toroidal symmetry. Toroidal functions can be expressed in terms of the ...