We investigate k-colorings of the rational n-space, Q, such that any two points at distance one get distinct colors. Two types of colorings are considered: patch colorings where the colors occupy open sets with parts of their boundary, and rigid colorings which uniquely extend from any open subset of Q. We prove that the existence of a patch k-coloring of Q implies the existence of a k-coloring...

abstract background: unstable pelvic fracture, a result of high energy antero-posterior compression injury, has been managed based on internal fixation and open reduction. the mode of fixation in unstable pelvic fracture has, however, been a subject of controversy and some authors have proposed a need to address the issue of partial breach of the pelvic ring elements in these injuries. this stu...

We consider the motion of a rigid body immersed in an incompressible perfect fluid which occupies a threedimensional bounded domain. For such a system the Cauchy problem is well-posed locally in time if the initial velocity of the fluid is in the Hölder space C. In this paper we prove that the smoothness of the motion of the rigid body may be only limited by the smoothness of the boundaries (of...

Using the lamination theory developed by Colding and Minicozzi for sequences of embedded, finite genus minimal surfaces with boundaries going to infinity [5], we show that the space of genus-one helicoids is compact (modulo rigid motions and homotheties). This generalizes a result of Hoffman and White [12].

The quantum interference between ‘pure’ electron–phonon and electron-boundary/impurity scattering drastically changes the electron–phonon relaxation rate. If impurities and boundaries vibrate in the same way as the host lattice, the electron–phonon relaxation rate is significantly decreased. In the presence of the scattering potential that does not vibrate with phonons (e.g. rigid boundaries, i...

This paper gives a method to construct rigid spaces, which is similar to the method used to construct toric schemes.