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A curve similar to the sine function but possibly shifted in phase, period, amplitude, or any combination thereof. The general sinusoid of amplitude a, angular frequency ...

A closed geometric figure on the surface of a sphere which is formed by the arcs of great circles. The spherical polygon is a generalization of the spherical triangle. If ...

Defined for samples x_i, i=1, ..., N by alpha_r=1/Nsum_(i=1)^Nz_i^r=(mu_r)/(sigma^r), (1) where z_i=(x_i-x^_)/(s_x). (2) The first few are alpha_1 = 0 (3) alpha_2 = 1 (4) ...

f_p=f_0+1/2p(p+1)delta_(1/2)-1/2(p-1)pdelta_(-1/2) +(S_3+S_4)delta_(1/2)^3+(S_3-S_4)delta_(-1/2)^3+..., (1) for p in [-1/2,1/2], where delta is the central difference and ...

A catastrophe which can occur for three control factors and one behavior axis. The swallowtail catastrophe is the universal unfolding of singularity f(x)=x^5 with codimension ...

The general function y(a,b,c,d)=csin{pi/(b-a)[((b-a)x/d+a)^2-a^2]}.

The partial differential equation u_(xx)=au_(tt)+bu_t+cu.

The function defined by T_n(x)=((-1)^(n-1))/(sqrt(n!))Z^((n-1))(x), where Z(x)=1/(sqrt(2pi))e^(-x^2/2) and Z^((k))(x) is the kth derivative of Z(x).

The partial differential equation u_(yy)=yu_(xx).

The point about which an angle is measured is called the angle's vertex, and the angle theta associated with a given vertex is called the vertex angle. In a polygon, the ...