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If we expand the determinant of a matrix A using determinant expansion by minors, first in terms of the minors of order r formed from any r rows, with their complementaries, ...

A subgroup is a subset H of group elements of a group G that satisfies the four group requirements. It must therefore contain the identity element. "H is a subgroup of G" is ...

The second-order ordinary differential equation y^('')+(y^')/x+(1-(nu^2)/(x^2))y=(x-nu)/(pix^2)sin(pinu) whose solutions are Anger functions.

A finite, increasing sequence of integers {a_1,...,a_m} such that (a_i-1)|(a_1...a_(m-1)) for i=1, ..., m, where m|n indicates that m divides n. A Carmichael sequence has ...

If a one-parameter family of curves has index N and class M, the number tangent to a curve of order n_1 and class m_1 in general position is m_1N+n_1M.

A surface of revolution of the form r(phi)=a[1-esin^2phi-(3/8e^2+k)sin^2(2phi)], where k is a second-order correction to the figure of a rotating fluid.

The order-n dipole graph D_n is a multigraph consisting of two vertices and n multiple edges joining them. The dipole graph D_2 is a multigraph that can be considered to ...

A functional differential equation is a differential equation in which the derivative y^'(t) of an unknown function y has a value at t that is related to y as a function of ...

A function f(x) satisfies the Lipschitz condition of order beta at x=0 if |f(h)-f(0)|<=B|h|^beta for all |h|<epsilon, where B and beta are independent of h, beta>0, and alpha ...

A quintic curve is an algebraic curve of order five. Examples of quintic curves include the Burnside curve, butterfly catastrophe curve, and stirrup curve.