A GRAPH FROM THE VIEWPOINT OF ALGEBRAIC TOPOLOGY
The conventional method of describing a graph as a pair (V,E), where V and E repectively denote the sets of vertices and edges, is simple to understand and adopted in many applications. It, however, does not provide a very rich foundation for mathematical endeavor. An alternative approach is to construct a graph in algebraic topological way. In this paper, we explore how this different perspective can help us better understand group theory and topology as well as the theory of graph.
In Wikipedia the Free Encyclopedia
The Cold War was the period of protracted conflict and competition between the United States and the Soviet Union and their allies from the late 1940s until the late 1980s. The main U.S. allies were Western Europe, Turkey, Japan and Canada. The main Soviet allies were Eastern Europe and (until the Sino-Soviet Split) China. Throughout the period, the rivalry between the two superpowers was played out in multiple arenas: military coalitions, ideology, a massive conventional and nuclear arms race, and proxy wars.
Noctilucent cloud observations over Greenland by a Rayleigh lidar
We report on the detection of noctilucent clouds (NLCs) by a Rayleigh lidar system located on the west coast of Greenland during operations in July and August 1994. The lidar detected NLCs in the zenith on three nights (July 28–29, July 31–August 1, and August 4). The lidar measurements are presented at temporal (1 minute) and spatial (192 meter) resolutions exceeding previously reported lidar measurements of NLCs and reveal significantly more structure in the clouds. Unique cloud features are observed for each night NLCs were detected. Because of the large backscatter ratio associated with NLCs, the volume backscatter coefficient for the cloud particles can be determined more accurately from the lidar signal than the backscatter ratio as the upper mesospheric molecular number density is negligible in the volume backscatter coefficient calculation. The volume backscatter coefficient values determined from the three nights of NLC observations would be classified by current models as moderate to extreme. The extreme backscatter from NLC measurements on August 4 tests the assumptions used in existing models.