Search Results for ""

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, ...

Consider a horse rider who wishes to feed his horse at a field, gather water from a river, and then return to his tent, all in the smallest overall distance possible. The ...

If W is a simply connected, compact manifold with a boundary that has two components, M_1 and M_2, such that inclusion of each is a homotopy equivalence, then W is ...

The area moment of inertia is a property of a two-dimensional plane shape which characterizes its deflection under loading. It is also known as the second moment of area or ...

Green's theorem is a vector identity which is equivalent to the curl theorem in the plane. Over a region D in the plane with boundary partialD, Green's theorem states ...

A sutured manifold is a tool in geometric topology which was first introduced by David Gabai in order to study taut foliations on 3-manifolds. Roughly, a sutured manifold is ...

A theorem outlined by Kolmogorov (1954) which was subsequently proved in the 1960s by Arnol'd (1963) and Moser (1962; Tabor 1989, p. 105). It gives conditions under which ...

Let L=<L, v , ^ > and K=<K, v , ^ > be lattices, and let h:L->K. Then h is a lattice homomorphism if and only if for any a,b in L, h(a v b)=h(a) v h(b) and h(a ^ b)=h(a) ^ ...

The Lyapunov characteristic exponent [LCE] gives the rate of exponential divergence from perturbed initial conditions. To examine the behavior of an orbit around a point ...

Alexandrov's theorem addresses conditions under which a polygon will fold into a convex polyhedron (Malkevitch).