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A generalized Vandermonde matrix of two sequences a and b where a is an increasing sequence of positive integers and b is an increasing sequence of nonnegative integers of ...

The gnomonic projection is a nonconformal map projection obtained by projecting points P_1 (or P_2) on the surface of sphere from a sphere's center O to point P in a plane ...

A general quartic surface defined by x^4+y^4+z^4+a(x^2+y^2+z^2)^2+b(x^2+y^2+z^2)+c=0 (1) (Gray 1997, p. 314). The above two images correspond to (a,b,c)=(0,0,-1), and ...

The inhomogeneous Helmholtz differential equation is del ^2psi(r)+k^2psi(r)=rho(r), (1) where the Helmholtz operator is defined as L^~=del ^2+k^2. The Green's function is ...

The group algebra K[G], where K is a field and G a group with the operation *, is the set of all linear combinations of finitely many elements of G with coefficients in K, ...

The number of elements in a group G, denoted |G|. If the order of a group is a finite number, the group is said to be a finite group. The order of an element g of a finite ...

Let n be an integer such that n>=lambda_1, where lambda=(lambda_1,lambda_2,...) is a partition of n=|lambda| if lambda_1>=lambda_2>=...>=0, where lambda_i are a sequence of ...

An apodization function chosen to minimize the height of the highest sidelobe (Hamming and Tukey 1949, Blackman and Tukey 1959). The Hamming function is given by ...

It is always possible to write a sum of sinusoidal functions f(theta)=acostheta+bsintheta (1) as a single sinusoid the form f(theta)=ccos(theta+delta). (2) This can be done ...

A device consisting of two coupled pendula, usually oscillating at right angles to each other, which are attached to a pen. The resulting motion can produce beautiful, ...