A novel collision cone approach is proposed as an aid to collision detection and avoidance between irregularly shaped moving objects with unknown trajectories. It is shown that the collision cone can be effectively used to determine whether collision between a robot and an obstacle (both moving in a dynamic environment) is imminent. No restrictions are placed on the shapes of either the robot o...

A cone beam circular half-scan scheme is becoming an attractive imaging method in cone beam CT since it improves the temporal resolution. Traditionally, the redundant data in the circular half-scan range is weighted by a central scanning plane-dependent weighting function; FDK algorithm is then applied on the weighted projection data for reconstruction. However, this scheme still suffers the at...

We study electromagnetic plane wave diffraction by a hollow circular cone with thin walls modelled by the so-called impedance-sheet boundary conditions. By means of Kontorovich–Lebedev integral representations for the Debye potentials and a ‘partial’ separation of variables, the problem is reduced to coupled functional difference (FD) equations for the relevant spectral functions. For a circula...

The theory of the dielectric cone antenna has been known since the early seventies. On their own, this antenna has a reasonably circular symmetric radiation pattern but exhibits an undesirably high side-lobe level. A properly designed metallic shield, which does not interfere with the field structure of the dielectric cone, may be used to reduce the side-lobe level. Although in principle this a...

A common computational approach for polynomial optimization problems (POPs) is to use (hierarchies of) semidefinite programming (SDP) relaxations. When the variables in POP are required be nonnegative – as case combinatorial problems, example these SDP typically involve matrices, i.e. they conic over doubly cone. The Jordan reduction, a symmetry reduction method optimization, was recently intro...

In single photon emission computed tomography (SPECT), a varying-focal-length cone-beam collimator can be used to reduce the truncation problem and to maintain sensitivity when imaging the organ of interest. The collimator is constructed so that the collimator holes focus to a circular symmetric, spatially varying, focal point function. The focal length increases radially from the shortest foca...

We perform an average analysis of the Grassmann condition number C (A) for the homogeneous convex feasibility problem ∃x ∈ C \ 0 : Ax = 0, where C ⊂ R may be any regular cone. This in particular includes the cases of linear programming, second-order programming, and semidefinite programming. We thus give the first average analysis of convex programming, which is not restricted to linear program...

This study investigated the effects of screwdriver handle shape, surface, and workpiece orientation on subjective discomfort, number of screw-tightening rotations, screw-insertion time, axial screwdriving force, and finger contact forces in a screwdriving task. Handles with three longitudinal cross-sectional shapes (circular, hexagonal, triangular), four lateral shapes (cylindrical, double frus...