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Let alpha(x) be a monotone increasing function and define an interval I=(x_1,x_2). Then define the nonnegative function U(I)=alpha(x_2)-alpha(x_1). The Lebesgue integral with ...

Any complex measure lambda decomposes into an absolutely continuous measure lambda_a and a singular measure lambda_c, with respect to some positive measure mu. This is the ...

The inverse curve of a lemniscate in a circle centered at the origin and touching the lemniscate where it crosses the x-axis produces a rectangular hyperbola (Wells 1991).

A function giving the distribution of the interpoint distances of a curve. It is defined by p(r)=1/Nsum_(ij)delta_(r_(ij)=r).

D^*Dpsi=del ^*del psi+1/4Rpsi, where D is the Dirac operator D:Gamma(S^+)->Gamma(S^-), del is the covariant derivative on spinors, and R is the scalar curvature.

A sphere is rigid.

A limb of a tree at a vertex v is the union of one or more branches at v in the tree. v is then called the base of the limb.

The line bisecting a given line segment P_1P_2 can be constructed geometrically, as illustrated above.

product_(i)dp_idq_i, where p_i and q_i are momenta and positions of particles.

A member of the smallest algebraically closed subfield L of C which is closed under the exponentiation and logarithm operations.