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For a measurable function mu, the Beltrami differential equation is given by f_(z^_)=muf_z, where f_z is a partial derivative and z^_ denotes the complex conjugate of z.

Let M be a compact n-dimensional manifold with injectivity radius inj(M). Then Vol(M)>=(c_ninj(M))/pi, with equality iff M is isometric to the standard round sphere S^n with ...

If a minimal surface is given by the equation z=f(x,y) and f has continuous first and second partial derivatives for all real x and y, then f is a plane.

A convergence test also called "de Morgan's and Bertrand's test." If the ratio of terms of a series {a_n}_(n=1)^infty can be written in the form ...

The free part of the homology group with a domain of coefficients in the group of integers (if this homology group is finitely generated).

If a and b are integers not both equal to 0, then there exist integers u and v such that GCD(a,b)=au+bv, where GCD(a,b) is the greatest common divisor of a and b.

A maximal subgraph of an undirected graph such that any two edges in the subgraph lie on a common simple cycle.

Johnson solid J_(50).

The study of the nature and properties of bifurcations.

The ordinary differential equation (y^')^m=f(x,y) (Hille 1969, p. 675; Zwillinger 1997, p. 120).