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For K a given knot in S^3, choose a Seifert surface M^2 in S^3 for K and a bicollar M^^×[-1,1] in S^3-K. If x in H_1(M^^) is represented by a 1-cycle in M^^, let x^+ denote ...

A fractional integral of order 1/2. The semi-integral of t^lambda is given by D^(-1/2)t^lambda=(t^(lambda+1/2)Gamma(lambda+1))/(Gamma(lambda+3/2)), so the semi-integral of ...

The field of semidefinite programming (SDP) or semidefinite optimization (SDO) deals with optimization problems over symmetric positive semidefinite matrix variables with ...

A fractional derivative of order 1/2. The semiderivative of t^lambda is given by D^(1/2)t^lambda=(t^(lambda-1/2)Gamma(lambda+1))/(Gamma(lambda+1/2)), so the semiderivative of ...

Let the values of a function f(x) be tabulated at points x_i equally spaced by h=x_(i+1)-x_i, so f_1=f(x_1), f_2=f(x_2), ..., f_4=f(x_4). Then Simpson's 3/8 rule ...

In general, a singularity is a point at which an equation, surface, etc., blows up or becomes degenerate. Singularities are often also called singular points. Singularities ...

Skewness is a measure of the degree of asymmetry of a distribution. If the left tail (tail at small end of the distribution) is more pronounced than the right tail (tail at ...

A formula also known as the Legendre addition theorem which is derived by finding Green's functions for the spherical harmonic expansion and equating them to the generating ...

The sum of the absolute squares of the spherical harmonics Y_l^m(theta,phi) over all values of m is sum_(m=-l)^l|Y_l^m(theta,phi)|^2=(2l+1)/(4pi). (1) The double sum over m ...

A piecewise polynomial function that can have a locally very simple form, yet at the same time be globally flexible and smooth. Splines are very useful for modeling arbitrary ...