In general, not much is known about the arithmetic of K3 surfaces. Once the geometric Picard number, which is the rank of the Neron-Séveri group over an algebraic closure of the base field, is high enough, more structure is known and more can be said. However, until recently not a single K3 surface was known to have geometric Picard number one. We give explicit examples of such surfaces over th...

where v ranges over all places of Q and Qv is the completion of Q at v, denote its TateShafarevich group. As usual, L(E/Q, s) is the complex L-function of E over Q. Since E is now known to be modular, Kolyvagin’s work [11] shows that X(E/Q) is finite if L(E/Q, s) has a zero at s = 1 of order ≤ 1, and that gE/Q is equal to the order of the zero of L(E/Q, s) at s = 1. His proof relies heavily on ...

Edge-intersection graphs of paths in grids are graphs that can be represented with vertices as paths in grids and edges between the vertices of the graph exist whenever two grid paths share a grid edge. This type of graphs is motivated by applications in conflict resolution of paths in grid networks. In this paper, we continue the study of edge-intersection graphs of paths in a grid, which was ...

In this paper we continue the study of the edge intersection graphs of single bend paths on a rectangular grid (i.e., the edge intersection graphs where each vertex is represented by one of the following shapes: x, p, y, q). These graphs, called B1-EPG graphs, were first introduced by Golumbic et al (2009) [5]. We consider the natural subclasses of B1-EPG formed by the subsets of the four singl...

First we recall some standard definitions. By a d-dimensional convex body we mean a compact convex subset of Rd with non-empty interior. Two subsets of Rd with non-empty interiors are non-overlapping if they have no common interior point, and we say that they touch each other if they are non-overlapping and their intersection is non-empty. Denote by H(K) the translative kissing number of a d-di...

We measured the contact areas and contact stresses at the post-cam mechanism of a posterior-stabilised total knee arthroplasty when a posterior force of 500 N was applied to the Kirschner Performance, Scorpio Superflex, NexGen LPS Flex Fixed, and NexGen LPS Flex Mobile knee systems. Measurements were made at 90 degrees, 120 degrees, and 150 degrees of flexion both in neutral rotation and 10 deg...

Unstable fractures of the distal radius can be stabilised with Kirschner wires. The K wires need to be removed after five to six weeks. The authors surveyed 100 consecutive patients with distal radial fractures treated with percutaneous Kirschner wires that were left buried under the skin. Group A had 50 patients who had such wires removed under local anaesthetic in the orthopaedic outpatient d...

Open calcaneal fractures are high morbidity injuries and the risk of complications depends on the concomitant injuries, on the size and the position of the traumatic wound. A 53-year-old male patient with bilateral open calcaneal fractures and associated concomitant lower extremity injuries such as subtalar dislocation, talonavicular dislocation and open distal tibial metaphyseal fracture was i...

Kirschner (K) wires can easily migrate, resulting in serious complications. We report a 49-year-old woman who had a rare and late complication related to the migration of K wire. It had been used for left hip replacement 8 years ago. The patient admitted to our hospital with breathing-dependent chest pain and increasing dyspnea for ∼2 h. Chest X-ray and chest computed tomographic scans revealed...