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A bounded operator T:V->W between two Banach spaces satisfies the inequality ||Tv||<=C||v||, (1) where C is a constant independent of the choice of v in V. The inequality is ...

The Cesàro means of a function f are the arithmetic means sigma_n=1/n(s_0+...+s_(n-1)), (1) n=1, 2, ..., where the addend s_k is the kth partial sum ...

The functions describing the horizontal and vertical positions of a point on a circle as a function of angle (cosine and sine) and those functions derived from them: cotx = ...

Pairs of partitions for a single number whose Ferrers diagrams transform into each other when reflected about the line y=-x, with the coordinates of the upper left dot taken ...

A planar polygon is convex if it contains all the line segments connecting any pair of its points. Thus, for example, a regular pentagon is convex (left figure), while an ...

Geometric objects lying in a common plane are said to be coplanar. Three noncollinear points determine a plane and so are trivially coplanar. Four points are coplanar iff the ...

The Dirichlet lambda function lambda(x) is the Dirichlet L-series defined by lambda(x) = sum_(n=0)^(infty)1/((2n+1)^x) (1) = (1-2^(-x))zeta(x), (2) where zeta(x) is the ...

The elliptic hyperboloid is the generalization of the hyperboloid to three distinct semimajor axes. The elliptic hyperboloid of one sheet is a ruled surface and has Cartesian ...

The elongated pentagonal gyrobicupola is a convex equilateral solid that is Johnson solid J_(39). The unit elongated pentagonal gyrobicupola has volume ...

The elongated pentagonal orthobicupola is a convex equilateral solid that is Johnson solid J_(38). The unit elongated pentagonal orthobicupola has volume ...