Combinatorial modulus and type of graphs

Let a $A$ be the 1-skeleton of a triangulated topological annulus. We establish bounds on the combinatorial modulus of a refinement $A'$, formed by attaching new vertices and edges to $A$, that depend only on the refinement and not on the structure of $A$ itself. This immediately applies to showing that a disk triangulation graph may be refined without changing its combinatorial type, provided the refinement is not too wild. We also explore the type problem in terms of disk growth, proving a parabolicity condition based on a superlinear growth rate, which we also prove optimal. We prove our results with no degree restrictions in both the EEL and VEL settings and examine type problems for more general complexes and dual graphs.Comment: 24 pages, 12 figure

ROLE OF SMALL FARMS IN AMERICAN AGRICULTURE AND RURAL SOCIETY

Agricultural and Food Policy,

Space environment robot vision system

A prototype twin-camera stereo vision system for autonomous robots has been developed at Goddard Space Flight Center. Standard charge coupled device (CCD) imagers are interfaced with commercial frame buffers and direct memory access to a computer. The overlapping portions of the images are analyzed using photogrammetric techniques to obtain information about the position and orientation of objects in the scene. The camera head consists of two 510 x 492 x 8-bit CCD cameras mounted on individually adjustable mounts. The 16 mm efl lenses are designed for minimum geometric distortion. The cameras can be rotated in the pitch, roll, and yaw (pan angle) directions with respect to their optical axes. Calibration routines have been developed which automatically determine the lens focal lengths and pan angle between the two cameras. The calibration utilizes observations of a calibration structure with known geometry. Test results show the precision attainable is plus or minus 0.8 mm in range at 2 m distance using a camera separation of 171 mm. To demonstrate a task needed on Space Station Freedom, a target structure with a movable I beam was built. The camera head can autonomously direct actuators to dock the I-beam to another one so that they could be bolted together