Rotation Numbers Of Invariant Manifolds Around Unstable Periodic Orbits For The Diamagnetic Kepler Problem

In this paper, a method to construct topological template in terms of symbolic dynamics for the diamagnetic Kepler problem is proposed. To confirm the topological template, rotation numbers of invariant manifolds around unstable periodic orbits in a phase space are taken as an object of comparison. The rotation numbers are determined from the definition and connected with symbolic sequences encoding the periodic orbits in a reduced Poincare section. Only symbolic codes with inverse ordering in the forward mapping can contribute to the rotation of invariant manifolds around the periodic orbits. By using symbolic ordering, the reduced Poincare section is constricted along stable manifolds and a topological template, which preserves the ordering of forward sequences and can be used to extract the rotation numbers, is established. The rotation numbers computed from the topological template are the same as those computed from their original definition.

Numbers of migratory waterbirds at Lake Lashihai, China

Between October 1999 and April 2000, WC surveyed the waterbirds at Lake Lashihai, China. A total of 52 species were recorded, of which one species was a resident, 34 were winter visitors, and 17 were passage migrants. Species richness was highest in November. Passage migrants mainly occurred in October, November, and April, and they stayed longer at the lake during their autumn migration than during the spring migration. The seasonal distribution pattern of total numbers of all waterbirds was bimodal. One peak occurred between late December and early January, and the other in middle March. The seasonal distribution patterns of 15 common species have been classified a. bimodal, unimodal, or irregular. The numbers of five common species were variable in middle winter, and their numerical Change in contiguous weeks were more than 30%, suggesting that local movements might be frequent.

Developing molecular identification numbers by an all-paths method

A new topological index is devised from an all-paths method. This molecular topological index has highly discriminating power for various kinds of organic compounds such as alkane trees, complex cyclic or polycyclic graphs, and structures containing heteroatoms and thus can be used as a Molecular IDentification number (MID) for chemical documentation. Some published MIDs derived from an all-paths method and their structural selectivity for alkane trees are also reviewed.