Chern class formulas for quiver varieties

In this paper a formula is proved for the general degeneracy locus associated to an oriented quiver of type A_n. Given a finite sequence of vector bundles with maps between them, these loci are described by putting rank conditions on arbitrary composites of the maps. Our answer is a polynomial in Chern classes of the bundles involved, depending on the given rank conditions. It can be expressed as a linear combination of products of Schur polynomials in the differences of the bundles. The coefficients are interesting generalizations of Littlewood-Richardson numbers. These polynomials specialize to give new formulas for Schubert polynomials.Comment: 17 pages, 20 figures. The document is available as a .tar.gz file containing one LaTeX2e file and 20 (included) postscript files. Packages xypic and psfrag are used. Note that when viewed with xdvi, the text in figures looks bad, but it comes out right when printed. The paper is also available as one postscript file at http://www.math.uchicago.edu/~abuch/papers/quiver.ps.g

Making Cities and Counties Work in the 21st Century

Most American cities are either too big or too small to serve the people who live in them in a cost-effective manner. The system that created them has ossified over time, making change difficult if not impossible. But short of wholesale change, there are some ways cities large and small can become both more responsive and most cost-effective

Alien Registration- Fulton, William E. (Presque Isle, Aroostook County)

https://digitalmaine.com/alien_docs/33767/thumbnail.jp

The population growth and control of African elephants in Kruger National Park, South Africa:: Modeling, managing, and ethics concerning a threatened species

Elephants are hard to count. Despite the apparent implausibility of such a statement, it is true (at least in the wild). Although elephants are the world\u27s largest land animals, their size necessitates that they (as a species) are spread out over proportionately large distances, making accurate counts difficult and cost-intensive - many counts in parks with large (n \u3e 50) populations rely on statistical inferences that may or may not be accurate, based on data collected from aerial surveys conducted from helicopters or fixed-wing aircraft. Despite the difficulty of obtaining information, we have a vested interest in gathering these data about elephant populations because elephants are an endangered species (as of 2012, elephants are classified as vulnerable by the IUCN). Furthermore, as international awareness of and interest in conservation increases, so does the widespread sense that people generally and the African societies in direct contact with elephants specifically must act to not only protect the existing population but ensure the ability of the population to grow to a non-endangered threshold. This goal is complicated by the concurrent goal of maintaining biodiversity because of the unique elephant problem : There are not enough elephants in the world (in the sense that most conservationists and biologists believe that to guarantee the future of African elephants, there is a minimum necessary population threshold), and yet where elephants exist - indeed, thrive - there are too many of them. That is to say that many elephant populations in wildlife preserves currently are near or exceed the density at which elephant drastically change their landscapes through grazing, debarking of trees, and other ecological impacts. The author is developing a mathematical model to explain and predict population variations and outcomes. Part of evaluating the management decisions involves not only choosing actions which bring about acceptable consequences in the ecosystem, but are also in and of themselves acceptable actions to the concerned parties (for example, increasing the land available to wildlife preserves by demolishing or preventing the construction of buildings or farms might be beneficial to the elephant population but not be acceptable to the general public). Therefore, part of assessing the model and the management decisions and their outcomes must be to consider not only the numerical impacts but also the social ramifications for elephants and the ethical issues surrounding management. In this thesis the author discusses an approach to modeling and several possible applicable models, as well as discussing one particular model that describes and projects the population changes and constraints in Kruger National Park, South Africa. This model will include several different management options, with preference placed on projected effectiveness of implementation and ethical considerations. The ultimate goal of the modeling process is to obtain a mathematical representation of the elephant population which can accurately predict the growth or decline of elephant populations for the purpose of maintaining biodiversity