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A linear transformation of period two. Since a linear transformation has the form, lambda^'=(alphalambda+beta)/(gammalambda+delta), (1) applying the transformation a second ...

The determinant of a knot is defined as |Delta(-1)|, where Delta(z) is the Alexander polynomial (Rolfsen 1976, p. 213).

Let a^p+b^p=c^p be a solution to Fermat's last theorem. Then the corresponding Frey curve is y^2=x(x-a^p)(x+b^p). (1) Ribet (1990a) showed that such curves cannot be modular, ...

A ruled surface parameterization x(u,v)=b(u)+vg(u) is called noncylindrical if gxg^' is nowhere 0. A noncylindrical ruled surface always has a parameterization of the form ...

The triangle coefficient is function of three variables written Delta(abc)=Delta(a,b,c) and defined by Delta(abc)=((a+b-c)!(a-b+c)!(-a+b+c)!)/((a+b+c+1)!), (Shore and Menzel ...

The Feigenbaum constant delta is a universal constant for functions approaching chaos via period doubling. It was discovered by Feigenbaum in 1975 (Feigenbaum 1979) while ...

A sequence is said to be convergent if it approaches some limit (D'Angelo and West 2000, p. 259). Formally, a sequence S_n converges to the limit S lim_(n->infty)S_n=S if, ...

The inversion of a convolution equation, i.e., the solution for f of an equation of the form f*g=h+epsilon, given g and h, where epsilon is the noise and * denotes the ...

Let A, B, and C be three polar vectors, and define V_(ijk) = |A_i B_i C_i; A_j B_j C_j; A_k B_k C_k| (1) = det[A B C], (2) where det is the determinant. The V_(ijk) is a ...

Let (X,B,mu) be a measure space and let E be a measurable set with mu(E)<infty. Let {f_n} be a sequence of measurable functions on E such that each f_n is finite almost ...