Stirling numbers of the first kindIn mathematics, especially in combinatorics, Stirling numbers of the first kind arise in the study of permutations. In particular, the Stirling numbers of the first kind count permutations according to their number of cycles (counting fixed points as cycles of length one). The Stirling numbers of the first and second kind can be understood as inverses of one another when viewed as triangular matrices. This article is devoted to specifics of Stirling numbers of the first kind.
Four-dimensional spaceFour-dimensional space (4D) is the mathematical extension of the concept of three-dimensional space (3D). Three-dimensional space is the simplest possible abstraction of the observation that one needs only three numbers, called dimensions, to describe the sizes or locations of objects in the everyday world. For example, the volume of a rectangular box is found by measuring and multiplying its length, width, and height (often labeled x, y, and z).
Stirling numbers of the second kindIn mathematics, particularly in combinatorics, a Stirling number of the second kind (or Stirling partition number) is the number of ways to partition a set of n objects into k non-empty subsets and is denoted by or . Stirling numbers of the second kind occur in the field of mathematics called combinatorics and the study of partitions. They are named after James Stirling. The Stirling numbers of the first and second kind can be understood as inverses of one another when viewed as triangular matrices.
Animal migration trackingAnimal migration tracking is used in wildlife biology, conservation biology, ecology, and wildlife management to study animals' behavior in the wild. One of the first techniques was bird banding, placing passive ID tags on birds legs, to identify the bird in a future catch-and-release. Radio tracking involves attaching a small radio transmitter to the animal and following the signal with a RDF receiver. Sophisticated modern techniques use satellites to track tagged animals, and GPS tags which keep a log of the animal's location.
