Given a set of rectangular items, all of them associated with a profit, and a single bigger rectangular bin, we can ask to find a non-rotational, non-overlapping packing of a selection of these items into the bin to maximize the profit. A detailed description of the (2 + )-approximation algorithm of Jansen and Zhang [8] for the twodimensional case is given. Furthermore we derive a (16 + )-appro...

A perfect parallelepiped has edges, face diagonals, and body diagonals all of integer length. We prove the existence of an infinite family of dissimilar perfect parallelepipeds with two nonparallel rectangular faces. We also show that we can obtain perfect parallelepipeds of this form with the angle of the non-rectangular face arbitrarily close to 90◦. Finally, we discuss the implications which...

The authors present the case of a nine-year-old female patient who presented with pain in her right foot associated with physical activities. After this case was diagnosed as cuboid-navicular tarsal coalition, the patient was treated surgically with resection of the coalition, thereby resolving the symptoms. The literature was reviewed and the importance of adequate physical examination and ima...

Cavitation-based histotripsy uses high-intensity focused ultrasound at low duty factor to create bubble clouds inside tissue to liquefy a region, and provides better fidelity to planned lesion coordinates and the ability to perform real-time monitoring. The goal of this study was to identify the most important mechanical properties for predicting lesion dimensions, among these three: Young's mo...

INTRODUCTION Isolated cuboid dislocations are rare injuries Jacobson (1990). It is clinically significant and important in surgical education, as it is an injury and a source of lateral foot pain that can be misdiagnosed at the time of initial presentation and may be difficult to identify clinically or with imaging Drummond and Hastings (1969). PRESENTATION OF CASE We present a case report in...

We investigate the problem of computing a minimum volume container for the non-overlapping packing of a given set of three-dimensional convex objects. Already the simplest versions of the problem are NPhard so that we cannot expect to find exact polynomial time algorithms. We give constant ratio approximation algorithms for packing axis-parallel (rectangular) cuboids under translation into an a...

A case of isolated dorsal midtarsal (Chopart) dislocation resulting from blunt trauma is reported. The mechanism of injury, management, and long-term outcome are discussed. A 45-year-old inebriated man fell from a 4-m height and landed on his feet. He had immediate bilateral foot and back pain. Radiographs showed a burst fracture of the second lumbar vertebra, a left Pott's fracture, and an iso...

Near infrared absorption (NIR) spectra of natural morphologically cubic polycrystalline diamonds (cuboid) were obtained at room temperature, and the stretching plus bending combination band of molecular water was observed. The spectrum consisted of the main band at 5180 cm 1 due to liquid water and a shoulder at 5000 cm . The 5000 cm 1 band suggests the presence of a phase with stronger hydroge...

Optimal path planning problems for rigid and deformable (bendable) cuboid robots are considered by providing an analytic safety constraint using generalized Lp norms. For regular cuboid robots, level sets of weighted Lp norms generate implicit approximations of their surfaces. For bendable cuboid robots a weighted Lp norm in polar coordinates implicitly approximates the surface boundary through...