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A nonreflexible regular map of genus 7 with eight graph vertices, 28 graph edges, and eight heptagonal faces.

In two dimensions, the curve known as an "egg' is an oval with one end more pointed than the other.

Let (X,B,mu) be a measure space and let E be a measurable set with mu(E)<infty. Let {f_n} be a sequence of measurable functions on E such that each f_n is finite almost ...

Given a differential operator D on the space of differential forms, an eigenform is a form alpha such that Dalpha=lambdaalpha (1) for some constant lambda. For example, on ...

If L^~ is a linear operator on a function space, then f is an eigenfunction for L^~ and lambda is the associated eigenvalue whenever L^~f=lambdaf. Renteln and Dundes (2005) ...

Let ABCD be a quadrilateral with perpendicular polygon diagonals. The midpoints of the sides (a, b, c, and d) determine a parallelogram (the Varignon parallelogram) with ...

If, in the above commutative diagram of modules and module homomorphisms the columns and two upper rows are exact, then so is the bottom row.

A roll of eight on a pair of six-sided dice in the game of craps. The probability of rolling "eighter from Decatur" is 5/36, or 13.888...%.

The Eisenstein units are the Eisenstein integers +/-1, +/-omega, +/-omega^2, where omega = 1/2(-1+isqrt(3)) (1) omega^2 = 1/2(-1-isqrt(3)). (2)

For an atomic integral domain R (i.e., one in which every nonzero nonunit can be factored as a product of irreducible elements) with I(R) the set of irreducible elements, the ...