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Given a subset B of a set A, the injection f:B->A defined by f(b)=b for all b in B is called the inclusion map.

The system of ordinary differential equations (dm)/(dt) = lambdamxm+gammax1 (1) (dgamma)/(dt) = lambdagammaxm. (2)

An image of an object obtained by reflecting it in a mirror so that the signs of one of its coordinates are reversed.

The term pairwise refers to taking all unordered 2-subsets of a given set. For example, the pairwise products of the set {a,b,c} are ab, ac, and bc.

The knot move obtained by fixing disk 1 in the figure above and flipping disks 2 and 3.

Differential Geometry

Roughly speaking, isospectral manifolds are drums that sound the same, i.e., have the same eigenfrequency spectrum. Two drums with differing area, perimeter, or genus can ...

Given a general quadratic curve Ax^2+Bxy+Cy^2+Dx+Ey+F=0, (1) the quantity X is known as the discriminant, where X=B^2-4AC, (2) and is invariant under rotation. Using the ...

Two nonisomorphic graphs that have equal resistance spectra (i.e., multisets of resistance distances) are said to be resistance-equivalent. All nonisomorphic simple graphs on ...

A solitary number is a number which does not have any friends. Solitary numbers include all primes, prime powers, and numbers for which (n,sigma(n))=1, where (a,b) is the ...