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The topological completion C of a field F with respect to the absolute value |·| is the smallest field containing F for which all Cauchy sequences or rationals converge.

The trimean is defined to be TM=1/4(H_1+2M+H_2), where H_i are the hinges and M is the statistical median. Press et al. (1992) call this Tukey's trimean. It is an L-estimate.

Given a nonhomogeneous ordinary differential equation, select a differential operator which will annihilate the right side, and apply it to both sides. Find the solution to ...

A group whose left Haar measure equals its right Haar measure.

In Season 4 episode "Black Swan" of the television crime drama NUMB3RS, the character Amita Ramanujan refers to universality classes when studying a map of the Los Angeles ...

A set of three conjectures proposed by Weil in 1942 for extending Riemann hypothesis-like statements to classes of mathematical structures. The conjectures were proved by ...

The anti-self-dual Yang-Mills equation is the system of partial differential equations ...

sum_(y=0)^m(-1)^(m-y)q^((m-y; 2))[m; y]_q(1-wq^m)/(q-wq^y) ×(1-wq^y)^m(-(1-z)/(1-wq^y);q)_y=(1-z)^mq^((m; 2)), where [n; y]_q is a q-binomial coefficient.

Comprehensive encyclopedia of mathematics with 13,000 detailed entries. Continually updated, extensively illustrated, and with interactive examples.

The Bailey mod 9 identities are a set of three Rogers-Ramanujan-like identities appearing as equations (1.6), (1.8), and (1.7) on p. 422 of Bailey (1947) given by A(q) = ...