Search Results for ""

The pathological function f_a(x)=sum_(k=1)^infty(sin(pik^ax))/(pik^a) (originally defined for a=2) that is continuous but differentiable only on a set of points of measure ...

A version of set theory which is a formal system expressed in first-order predicate logic. Zermelo-Fraenkel set theory is based on the Zermelo-Fraenkel axioms. ...

Given a real number q>1, the series x=sum_(n=0)^inftya_nq^(-n) is called the q-expansion, or beta-expansion (Parry 1957), of the positive real number x if, for all n>=0, ...

A number of interesting graphs are associated with the work of van Cleemput and Zamfirescu (2018). Two 13- and 15-node graphs, denoted alpha and beta respectively, were used ...

The Jacobi theta functions are the elliptic analogs of the exponential function, and may be used to express the Jacobi elliptic functions. The theta functions are ...

P(n), sometimes also denoted p(n) (Abramowitz and Stegun 1972, p. 825; Comtet 1974, p. 94; Hardy and Wright 1979, p. 273; Conway and Guy 1996, p. 94; Andrews 1998, p. 1), ...

An alternating knot is a knot which possesses a knot diagram in which crossings alternate between under- and overpasses. Not all knot diagrams of alternating knots need be ...

In most modern literature, a Boolean model is a probabilistic model of continuum percolation theory characterized by the existence of a stationary point process X and a ...

A Moore graph of type (v,g) is a regular graph of vertex degree v>2 and girth g that contains the maximum possible number of nodes, namely ...

An n-polyhedral graph (sometimes called a c-net) is a 3-connected simple planar graph on n nodes. Every convex polyhedron can be represented in the plane or on the surface of ...