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A convex planar domain in which the minimal generalized diameter is >1 always contains a circle of radius 1/3.

A linear operator A:D(A)->H from its domain D(A) into a Hilbert space H is closed if for any sequence of vectors v_n in D(A) such that v_n->v and Av_n->x as n->infty, it ...

For an atomic integral domain R (i.e., one in which every nonzero nonunit can be factored as a product of irreducible elements) with I(R) the set of irreducible elements, the ...

A function f is said to have a upper bound C if f(x)<=C for all x in its domain. The least upper bound is called the supremum. A set is said to be bounded from above if it ...

A convex body in Euclidean space that is centrally symmetric with center at the origin is determined among all such bodies by its brightness function (the volume of each ...

The plane spanned by two coordinate axes in the three-dimensional Euclidean space. The coordinate plane spanned by the x- and the y-axis is called xy-plane.

A polytope in n-dimensional Euclidean space R^n whose vertices are integer lattice points but which does not contain any other lattice points in its interior or on its ...

The ring of fractions of an integral domain. The field of fractions of the ring of integers Z is the rational field Q, and the field of fractions of the polynomial ring ...

A polynomial admitting a multiplicative inverse. In the polynomial ring R[x], where R is an integral domain, the invertible polynomials are precisely the constant polynomials ...

Let f be analytic on a domain U subset= C, and assume that f never vanishes. Then if there is a point z_0 in U such that |f(z_0)|<=|f(z)| for all z in U, then f is constant. ...