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An ultrametric is a metric which satisfies the following strengthened version of the triangle inequality, d(x,z)<=max(d(x,y),d(y,z)) for all x,y,z. At least two of d(x,y), ...

A sequence of numbers alpha_n is said to be uncorrelated if it satisfies lim_(n->infty)1/(2n)sum_(m=-n)^nalpha_m^2=1 lim_(n->infty)1/(2n)sum_(m=-n)^nalpha_malpha_(k+m)=0 for ...

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 ...

Define q=e^(2piitau) (cf. the usual nome), where tau is in the upper half-plane. Then the modular discriminant is defined by ...

A system of curvilinear coordinates in which two sets of coordinate surfaces are obtained by revolving the curves of the elliptic cylindrical coordinates about the x-axis, ...

A quantity which changes sign when indices are reversed. For example, A_(ij)=a_i-a_j is antisymmetric since A_(ij)=-A_(ji).

A topological space.

Let |sum_(n=1)^pa_n|<K, (1) where K is independent of p. Then if f_n>=f_(n+1)>0 and lim_(n->infty)f_n=0, (2) it follows that sum_(n=1)^inftya_nf_n (3) converges.

A space endowed with a non-Euclidean elliptic geometry.

dtau^2=-eta_(alphabeta)dxi^alphadxi^beta, or (d^2xi^alpha)/(dtau^2)=0.