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Let A be a unital Banach algebra. If a in A and ||1-a||<1, then a^(-1) can be represented by the series sum_(n=0)^(infty)(1-a)^n. This criterion for checking invertibility of ...

The system of partial differential equations u_t+u_x = v^2-u^2 (1) v_t-v_x = u^2-v^2. (2)

The function given by CK_n(x)=cos(nxcos^(-1)x), where n is an integer and -1<x<1.

The relationship Sq^i(x cup y)=Sigma_(j+k=i)Sq^j(x) cup Sq^k(y) encountered in the definition of the steenrod algebra.

The antisymmetric parts of the Christoffel symbol of the second kind Gamma^lambda_(munu).

A Cartesian curve is a curve specified in Cartesian coordinates. The term "Cartesian curve" is sometimes also used to refer to the Cartesian ovals.

The use of coordinates (such as Cartesian coordinates) in the study of geometry. Cartesian geometry is named after René Descartes (Bell 1986, p. 48), although Descartes may ...

An operator Gamma=sum_(i=1)^me_i^Ru^(iR) on a representation R of a Lie algebra.

A map projection defined by x = sin^(-1)[cosphisin(lambda-lambda_0)] (1) y = tan^(-1)[(tanphi)/(cos(lambda-lambda_0))]. (2) The inverse formulas are phi = sin^(-1)(sinDcosx) ...

If P(x) is an irreducible cubic polynomial all of whose roots are real, then to obtain them by radicals, you must take roots of nonreal numbers at some point.