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Let f(x) be a finite and measurable function in (-infty,infty), and let epsilon be freely chosen. Then there is a function g(x) such that 1. g(x) is continuous in ...

A Lyndon word is an aperiodic notation for representing a necklace.

If a sphere is covered by three closed sets, then one of them must contain a pair of antipodal points.

A robust estimation based on maximum likelihood arguments.

A tree not having the complete bipartite graph K_(1,2) with base at the vertex of degree two as a limb (Lu et al. 1993, Lu 1996).

The MacBeath circle, a term coined here for the first time, is the circumcircle of the MacBeath triangle. It has a fairly complicated radius, center function, and circle ...

The MacBeath triangle DeltaX_AX_BX_C (a term coined here for the first time), is the triangle whose vertices are the contact points of the MacBeath inconic with the reference ...

In abstract topology, a machine is method for producing infinite loop spaces and spectra. In automata theory, an abstract machine that is implemented in hardware is simply ...

Let E and F be paired spaces with S a family of absolutely convex bounded sets of F such that the sets of S generate F and, if B_1,B_2 in S, there exists a B_3 in S such that ...

If f(x) is positive and decreases to 0, then an Euler constant gamma_f=lim_(n->infty)[sum_(k=1)^nf(k)-int_1^nf(x)dx] can be defined. For example, if f(x)=1/x, then ...