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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 ...

A polygon vertex x_i of a simple polygon P is a principal polygon vertex if the diagonal [x_(i-1),x_(i+1)] intersects the boundary of P only at x_(i-1) and x_(i+1).

The Reeb foliation of the hypersphere S^3 is a foliation constructed as the union of two solid tori with common boundary.

If f is analytic on a domain U, then a point z_0 on the boundary partialU is called regular if f extends to be an analytic function on an open set containing U and also the ...

An area-minimizing surface (rectifiable current) bounded by a smooth curve in R^3 is a smooth submanifold with boundary.

If the knot K is the boundary K=f(S^1) of a singular disk f:D->S^3 which has the property that each self-intersecting component is an arc A subset f(D^2) for which f^(-1)(A) ...

A phase curve (i.e., an invariant manifold) which meets a hyperbolic fixed point (i.e., an intersection of a stable and an unstable invariant manifold) or connects the ...

The partial differential equation del ^2u+lambda^2sinhu=0, where del ^2 is the Laplacian (Ting et al. 1987; Zwillinger 1997, p. 135).

Find the tunnel between two points A and B on a gravitating sphere which gives the shortest transit time under the force of gravity. Assume the sphere to be nonrotating, of ...

Giving a set F={f_1,f_2,...,f_n} of contracting similitudes of R^l, the closed set E is said to be subselfsimilar for F if E subset union _(i=1)^nf_i(E) (Falconer 1995, ...