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There are several related theorems involving Hamiltonian cycles of graphs that are associated with Pósa. Let G be a simple graph with n graph vertices. 1. If, for every k in ...

The goat problem (or bull-tethering problem) considers a fenced circular field of radius a with a goat (or bull, or other animal) tied to a point on the interior or exterior ...

A connection on a vector bundle pi:E->M is a way to "differentiate" bundle sections, in a way that is analogous to the exterior derivative df of a function f. In particular, ...

For an arbitrary not identically constant polynomial, the zeros of its derivatives lie in the smallest convex polygon containing the zeros of the original polynomial.

AW, AB, and AY in the above figure are in a harmonic range.

Recall the definition of the autocorrelation function C(t) of a function E(t), C(t)=int_(-infty)^inftyE^_(tau)E(t+tau)dtau. (1) Also recall that the Fourier transform of E(t) ...

Let s_1, s_2, ... be an infinite series of real numbers lying between 0 and 1. Then corresponding to any arbitrarily large K, there exists a positive integer n and two ...

Consider a convex plane curve K with perimeter L, and the set of points P exterior to K. Further, let t_1 and t_2 be the perpendicular distances from P to K (with ...

The operator partial^_ is defined on a complex manifold, and is called the 'del bar operator.' The exterior derivative d takes a function and yields a one-form. It decomposes ...

Given a planar graph G, its geometric dual G^* is constructed by placing a vertex in each region of G (including the exterior region) and, if two regions have an edge x in ...