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The finite Fourier cosine transform of an apodization function, also known as an apparatus function. The instrument function I(k) corresponding to a given apodization ...

An invariant series of a group G is a normal series I=A_0<|A_1<|...<|A_r=G such that each A_i<|G, where H<|G means that H is a normal subgroup of G.

Two figures are said to be similar when all corresponding angles are equal, and are inversely similar when all corresponding angles are equal and described in the opposite ...

An involutive algebra is an algebra A together with a map a|->a^* of A into A (a so-called involution), satisfying the following properties: 1. (a^*)^*=a. 2. (ab)^*=b^*a^*. ...

An element a of a ring which is nonzero, not a unit, and whose only divisors are the trivial ones (i.e., the units and the products ua, where u is a unit). Equivalently, an ...

Given a general second tensor rank tensor A_(ij) and a metric g_(ij), define theta = A_(ij)g^(ij)=A_i^i (1) omega^i = epsilon^(ijk)A_(jk) (2) sigma_(ij) = ...

A transformation of an algebraic curve which is of the same type as its inverse. A Jonquière's transformation is always factorable.

An optical illusion, illustrated above, in which the eye perceives a white upright equilateral triangle where none is actually drawn.

In Kepler's 1619 book Harmonice Mundi on tilings, he discussed a tiling built with pentagons, pentagrams, decagons, and "fused decagon pairs." He also called them "monsters." ...

A polynomial factorization algorithm that proceeds by considering the vector of coefficients of a polynomial P, calculating b_i=P(i)/a_i, constructing the Lagrange ...