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A "pointwise-bounded" family of continuous linear operators from a Banach space to a normed space is "uniformly bounded." Symbolically, if sup||T_i(x)|| is finite for each x ...

For every positive integer n, there exists a circle which contains exactly n lattice points in its interior. H. Steinhaus proved that for every positive integer n, there ...

Multiple series generalizations of basic hypergeometric series over the unitary groups U(n+1). The fundamental theorem of U(n) series takes c_1, ..., c_n and x_1, ..., x_n as ...

Linnik's constant L is the constant appearing in Linnik's theorem. Heath-Brown (1992) has shown that L<=5.5, and Schinzel, Sierpiński, and Kanold (Ribenboim 1989) have ...

In 1891, Chebyshev and Sylvester showed that for sufficiently large x, there exists at least one prime number p satisfying x<p<(1+alpha)x, where alpha=0.092.... Since the ...

A manifold possessing a metric tensor. For a complete Riemannian manifold, the metric d(x,y) is defined as the length of the shortest curve (geodesic) between x and y. Every ...

Three circles packed inside a triangle such that each is tangent to the other two and to two sides of the triangle are known as Malfatti circles. The Malfatti configuration ...

An ordinary double point of a plane curve is point where a curve intersects itself such that two branches of the curve have distinct tangent lines. Ordinary double points of ...

A "beam detector" for a given curve C is defined as a curve (or set of curves) through which every line tangent to or intersecting C passes. The shortest 1-arc beam detector, ...

A plot in the complex plane of the points B(t)=S(t)+iC(t), (1) where S(t) and C(t) are the Fresnel integrals (von Seggern 2007, p. 210; Gray 1997, p. 65). The Cornu spiral is ...