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A function of more than one variable.

Given an original knot K, the knots produced by mutations together with K itself are called mutant knots. Mutant knots are often difficult to distinguish. For instance, ...

A normal extension is the splitting field for a collection of polynomials. In the case of a finite algebraic extension, only one polynomial is necessary.

Two functions f(x) and g(x) are orthogonal over the interval a<=x<=b with weighting function w(x) if <f(x)|g(x)>=int_a^bf(x)g(x)w(x)dx=0. (1) If, in addition, ...

A pair of functions phi_i(x) and phi_j(x) are orthonormal if they are orthogonal and each normalized so that int_a^b[phi_i(x)]^2w(x)dx = 1 (1) int_a^b[phi_j(x)]^2w(x)dx = 1. ...

A curve obtained by fitting polynomials to each ordinate of an ordered sequence of points. The above plots show polynomial curves where the order of the fitting polynomial ...

There exist numbers y_1<y_2<...<y_(n-1), a<y_(n-1), y_(n-1)<b, such that lambda_nu=alpha(y_nu)-alpha(y_(nu-1)), (1) where nu=1, 2, ..., n, y_0=a and y_n=b. Furthermore, the ...

A relationship between knot polynomials for links in different orientations (denoted below as L_+, L_0, and L_-). J. H. Conway was the first to realize that the Alexander ...

cos(pi/(32)) = 1/2sqrt(2+sqrt(2+sqrt(2+sqrt(2)))) (1) cos((3pi)/(32)) = 1/2sqrt(2+sqrt(2+sqrt(2-sqrt(2)))) (2) cos((5pi)/(32)) = 1/2sqrt(2+sqrt(2-sqrt(2-sqrt(2)))) (3) ...

The algebra structure of linear functionals on polynomials of a single variable (Roman 1984, pp. 2-3).