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Let four lines in a plane represent four roads in general position, and let one traveler T_i be walking along each road at a constant (but not necessarily equal to any other ...

The integral closure of a commutative unit ring R in an extension ring S is the set of all elements of S which are integral over R. It is a subring of S containing R.

A proper ideal of a ring that is not the intersection of two ideals which properly contain it. In a principal ideal domain, the ideal I=<a> is irreducible iff a=0 or a is an ...

The Jacobian group of a one-dimensional linear series is given by intersections of the base curve with the Jacobian curve of itself and two curves cutting the series.

If Omega subset= C is a domain and phi:Omega->C is a one-to-one analytic function, then phi(Omega) is a domain, and area(phi(Omega))=int_Omega|phi^'(z)|^2dxdy (Krantz 1999, ...

A polycube composed of 5 cubes. There are 29 distinct three-dimensional pentacubes (Bouwkamp 1981). Of these, the 12 planar pentacubes (corresponding to solid pentominoes), ...

A Radon measure is a Borel measure that is finite on compact sets.

An automorphism which interchanges the two vertices of a regular map at each edge without interchanging the vertices.

Assemble six 1×2×2 blocks and three 1×1×1 blocks into a 3×3×3 cube.

f_p=f_0+1/2p(p+1)delta_(1/2)-1/2(p-1)pdelta_(-1/2) +(S_3+S_4)delta_(1/2)^3+(S_3-S_4)delta_(-1/2)^3+..., (1) for p in [-1/2,1/2], where delta is the central difference and ...