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The exterior derivative of a function f is the one-form df=sum_(i)(partialf)/(partialx_i)dx_i (1) written in a coordinate chart (x_1,...,x_n). Thinking of a function as a ...

A module M over a unit ring R is called faithful if for all distinct elements a, b of R, there exists x in M such that ax!=bx. In other words, the multiplications by a and by ...

C_2×C_4 is one of the three Abelian groups of group order 8 (the other two being non-Abelian). Examples include the modulo multiplication groups M_(15), M_(16), M_(20), and ...

The n×n square matrix F_n with entries given by F_(jk)=e^(2piijk/n)=omega^(jk) (1) for j,k=0, 1, 2, ..., n-1, where i is the imaginary number i=sqrt(-1), and normalized by ...

The full width at half maximum (FWHM) is a parameter commonly used to describe the width of a "bump" on a curve or function. It is given by the distance between points on the ...

A 4×4 magic square in which the elements in each 2×2 corner have the same sum. Dürer's magic square, illustrated above, is an example of a gnomon magic square since the sums ...

The great stellated truncated dodecahedron, also called the quasitruncated great stellated dodecahedron is the uniform polyhedron with Maeder index 66 (Maeder 1997), ...

Given two groups G and H, there are several ways to form a new group. The simplest is the direct product, denoted G×H. As a set, the group direct product is the Cartesian ...

The Hammer-Aitoff equal-area projection, also called the Hammer projection, is a map projection that is a modification of the Lambert azimuthal equal-area projection. It ...

A (presumably autobiographical) character in one of astrophysicist Fred Hoyle's novels opined the following. "I figure that if to be totally known and totally loved is worth ...