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Defined for a vector field A by (A·del ), where del is the gradient operator. Applied in arbitrary orthogonal three-dimensional coordinates to a vector field B, the ...

The double sphere is the degenerate quartic surface (x^2+y^2+z^2-r^2)^2=0 obtained by squaring the left-hand side of the equation of a usual sphere x^2+y^2+z^2-r^2=0.

Given a differential operator D on the space of differential forms, an eigenform is a form alpha such that Dalpha=lambdaalpha (1) for some constant lambda. For example, on ...

An endomorphism is called ergodic if it is true that T^(-1)A=A implies m(A)=0 or 1, where T^(-1)A={x in X:T(x) in A}. Examples of ergodic endomorphisms include the map X->2x ...

Factor analysis allows the determination of common axes influencing sets of independent measured sets. It is "the granddaddy of multivariate techniques (Gould 1996, pp. ...

A number x is said to have "n figures" if it takes n digits to express it. The number of figures is therefore equal to one more than the power of 10 in the scientific ...

A group acts freely if there are no group fixed points. A point which is fixed by every group element would not be free to move.

The G-transform of a function f(x) is defined by the integral (Gf)(x)=(G_(pq)^(mn)|(a_p); (b_q)|f(t))(x) (1) =1/(2pii)int_sigmaGamma[(b_m)+s, 1-(a_n)-s; (a_p^(n+1))+s, ...

The Diophantine equation x^2+y^2=p can be solved for p a prime iff p=1 (mod 4) or p=2. The representation is unique except for changes of sign or rearrangements of x and y. ...

A product of a reflection in a line and translation along the same line.