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Differential Equations

Let f*g denote the cross-correlation of functions f(t) and g(t). Then f*g = int_(-infty)^inftyf^_(tau)g(t+tau)dtau (1) = ...

The trilinear pole of the orthotransversal of a point P is called its orthocorrespondent. The orthocorrespondent of a point P=p:q:r is given by where S_A, S_B, and S_C is ...

A function f in C^infty(R^n) is called a Schwartz function if it goes to zero as |x|->infty faster than any inverse power of x, as do all its derivatives. That is, a function ...

A unit circle is a circle of unit radius, i.e., of radius 1. The unit circle plays a significant role in a number of different areas of mathematics. For example, the ...

The interesting function defined by the definite integral G(x)=int_0^xsin(tsint)dt, illustrated above (Glasser 1990). The integral cannot be done in closed form, but has a ...

Bracewell's term for the delta function.

A wavelet used in multiresolution representation to analyze the information content of images. The wavelet is defined by ...

The important property of Fourier transforms that F_x[cos(2pik_0x)f(x)](k) can be expressed in terms of F[f(x)]=F(k) as follows, ...

The geometry of the Lie group consisting of real matrices of the form [1 x y; 0 1 z; 0 0 1], i.e., the Heisenberg group.