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

THE PROVISION OF RAIL SERVICE: THE IMPACT OF COMPETITION

Grain transportation is one of the most important economic issues for grain producers in the Northern Plains. The reliance on export markets and the long distances to port position means that transportation costs have a significant effect on the price received by farmers. In the prairie region of Canada, rail transportation is undergoing a major transformation that will affect the competitive positions of agriculture in both the United States and Canada and influence the direction of grain flows between the two countries. Rail rates are no longer legislated although a cap is still in place), restrictions on branch line abandonment have been lifted, and further deregulation of price and car allocation is being considered. Some parties, including the railways, argue that a completely deregulated system, similar to the U.S. system, is the only way to achieve transportation efficiencies. Other groups, supporting the status quo, argue that the regulation of rates is essential to control the monopoly power of the railways. There has been very little discussion of other policy options, with the exception of a limited discussion of nationalized railbeds. The U.S. experience provides a stark view of the likely outcome of deregulation. When railways are not faced with competition from other railways or from other forms of transportation such as barges, the evidence suggests railways will price freight services at or near truck competitive rates. Freight rates in Montana, where no effective rail and/or barge competition exists, are approximately twice those at Kansas City and Denver/Commerce City, where such competition exists. The current cost-based regulated rates in Western Canada are similar to those at Kansas City and Denver/Commerce City. Given similar distances to port and the existence of only two railways (and no likelihood of new entrants), deregulation in Western Canada is likely to result in freight rates closer to those in Montana than to the current regulated level. The increase in freight costs will result in transfers from producers to the railways, distort production incentives, and create losses elsewhere in the economy. While maintenance of a regulated freight rate structure would address the freight rate issue, other problems would result. The lack of price signals reduces incentives for industry participants to perform. Branch lines are less likely to be maintained in a regulated environment because railways may be unable to charge the extra amount necessary to make them viable. Railways may also disrupt the system - as a form of bargaining - to create pressure for deregulation. This report explores the option of the government encouraging entry into rail service provision. Just as telecommunication companies are required to allow competitors to use their phone lines, existing railways could be required to make their track and switching equipment available to rail operators who wish to run train service on a line, on the condition that the access price covers the infrastructure cost. The paper examines the case of the British railway system where the ownership of the track has been separated from the operation of the rail equipment and the provision of service, and explores the applicability of this model to grain transportation on the Great Plains. In Britain, ownership of the track rests with a company called Railtrack (although Railtrack was government-owned, it has been privatized). Railtrack leases access to thirty train operators for fees that are regulated by the Office of the Rail Regulator to cover maintenance costs and provide a return on investment. The thirty rail operators then compete to provide service to customers. This model and others similar to it need to be developed and articulated before they can be considered in the public policy forum. Nevertheless, given the importance of rail transportation to the grain industry in the Northern Plains, it is imperative that options such as these be investigated to address the very thorny issue of freight rate and entry regulation.barriers to entry, competition, grain handling, grain transportation, monopoly, railroads, regulation, Public Economics, K2, L1, L9, L5,

User's manual for the ALS base heating prediction code, volume 2

The Advanced Launch System (ALS) Base Heating Prediction Code is based on a generalization of first principles in the prediction of plume induced base convective heating and plume radiation. It should be considered to be an approximate method for evaluating trends as a function of configuration variables because the processes being modeled are too complex to allow an accurate generalization. The convective methodology is based upon generalizing trends from four nozzle configurations, so an extension to use the code with strap-on boosters, multiple nozzle sizes, and variations in the propellants and chamber pressure histories cannot be precisely treated. The plume radiation is more amenable to precise computer prediction, but simplified assumptions are required to model the various aspects of the candidate configurations. Perhaps the most difficult area to characterize is the variation of radiation with altitude. The theory in the radiation predictions is described in more detail. This report is intended to familiarize a user with the interface operation and options, to summarize the limitations and restrictions of the code, and to provide information to assist in installing the code

Hook-content formulae for symplectic and orthogonal tableaux

By considering the specialisation $s_{\lambda}(1,q,q^2,...,q^{n-1})$ of the Schur function, Stanley was able to describe a formula for the number of semistandard Young tableaux of shape $\lambda$ in terms of two properties of the boxes in the diagram for $\lambda$. Using specialisations of symplectic and orthogonal Schur functions, we derive corresponding formulae, first given by El Samra and King, for the number of semistandard symplectic and orthogonal $\lambda$-tableaux.Comment: Withdrawn; paper is outdate

Integral Grothendieck-Riemann-Roch theorem

We show that, in characteristic zero, the obvious integral version of the Grothendieck-Riemann-Roch formula obtained by clearing the denominators of the Todd and Chern characters is true (without having to divide the Chow groups by their torsion subgroups). The proof introduces an alternative to Grothendieck's strategy: we use resolution of singularities and the weak factorization theorem for birational maps.Comment: 24 page

Trends in life cycle greenhouse gas emissions of future light duty electric vehicles

The majority of previous studies examining life cycle greenhouse gas (LCGHG) emissions of battery electric vehicles (BEVs) have focused on efficiency-oriented vehicle designs with limited battery capacities. However, two dominant trends in the US BEV market make these studies increasingly obsolete: sales show significant increases in battery capacity and attendant range and are increasingly dominated by large luxury or high-performance vehicles. In addition, an era of new use and ownership models may mean significant changes to vehicle utilization, and the carbon intensity of electricity is expected to decrease. Thus, the question is whether these trends significantly alter our expectations of future BEV LCGHG emissions. To answer this question, three archetypal vehicle designs for the year 2025 along with scenarios for increased range and different use models are simulated in an LCGHG model: an efficiency-oriented compact vehicle; a high performance luxury sedan; and a luxury sport utility vehicle. While production emissions are less than 10% of LCGHG emissions for today's gasoline vehicles, they account for about 40% for a BEV, and as much as two-thirds of a future BEV operated on a primarily renewable grid. Larger battery systems and low utilization do not outweigh expected reductions in emissions from electricity used for vehicle charging. These trends could be exacerbated by increasing BEV market shares for larger vehicles. However, larger battery systems could reduce per-mile emissions of BEVs in high mileage applications, like on-demand ride sharing or shared vehicle fleets, meaning that trends in use patterns may countervail those in BEV design

The diffusion of artillery terminology in the early Thirteenth Century: the case of Henry of Livonia

As medieval mechanical artillery developed, variants of a new term for identifying the heaviest engines spread across Latin Europe. First appearing in northern Italy at the end of the twelfth century, early forms of the word ‘trebuchet’ found their way into French, German, English and crusader sources by the second decade of the thirteenth century. Although the terms appear to have been used to refer exclusively to counterweight trebuchets by the time they were adopted north of the Alps, the invention of this engine-type would appear to predate the vocabulary with which it came to be associated. Writing on the fringe of Latin Europe in the 1220s, Henry of Livonia did not employ any of these new terms in his account of the Christian campaigns in the Baltic. Whether Henry was ignorant of the new terminology or avoided it deliberately, he appears to have employed traditional terms to identify what may have been engines of this newer and heavier type. While sources appear to have used pre-existing vocabulary to refer to the earliest counterweight trebuchets in the twelfth century, some, like Henry, continued to employ such terms in the early thirteenth century, avoiding the new vocabulary embraced by others

Particle-wave duality: a dichotomy between symmetry and asymmetry

Symmetry plays a central role in many areas of modern physics. Here we show that it also underpins the dual particle and wave nature of quantum systems. We begin by noting that a classical point particle breaks translational symmetry whereas a wave with uniform amplitude does not. This provides a basis for associating particle nature with asymmetry and wave nature with symmetry. We derive expressions for the maximum amount of classical information we can have about the symmetry and asymmetry of a quantum system with respect to an arbitrary group. We find that the sum of the information about the symmetry (wave nature) and the asymmetry (particle nature) is bounded by log(D) where D is the dimension of the Hilbert space. The combination of multiple systems is shown to exhibit greater symmetry and thus more wavelike character. In particular, a class of entangled systems is shown to be capable of exhibiting wave-like symmetry as a whole while exhibiting particle-like asymmetry internally. We also show that superdense coding can be viewed as being essentially an interference phenomenon involving wave-like symmetry with respect to the group of Pauli operators.Comment: 20 pages, 3 figure

Construction, standardisation, validations and factorial and other analyses of a group picture-test

The principal conclusions reached as a result of the entire Draft C project may now be assembled, and indications given of further work which could be carried out.It seems from all the evidence that Draft C is not, after all (although a timed test) e test where results are based mainly on speed. The factor analyses failed to locate a clear speed - factor, the non -completion data in the error -analyses provided evidence that speed plays a pert (though not necessarily a significant pert), and the interviews showed that scores, while affected by quickness or slowness of response, probably do not in feet depend on a speed- factor as a crucial component in performance. The writer considers that while speed clearly enters into the matter, these tests are not so severely timed as to make speed the principal element.Nor can it be said that Draft C is essentially a power - test, in the same sense as the American P.M.A. test, for it was found in the course of the 65 interviews, and in the individual testing, that it was a relatively rare occurrence for a child to fail irrevocably in any of the items, given leisure, due encouragement, and re- iteration of the instructions. This could hardly be said of the P.M.A. test, which, covering as it does a two -year age -span, contains items which inevitably prove to be beyond the maturational stage of many of the children. It might be considered that the "power" aspect of Draft C is simply masked by the fact that it deals with a narrower age -range, maturational demands being less obvious in items appropriate to a single year of age- range. This might indeed have been a valid supposition, were it not for the writer's testimony that virtually all the children can in fact eventually solve and deal with all the items.Again, it appears from the factor- analyses, the validation against school performance, and the interviews, that Draft C is not primarily measuring school attainment in verbal and number skills to the same extent as the P.M.A. test. There are in it no specific Parts designed to test classroom skills, as are present in the P.M.A. (particularly the verbal and number parts). The result of this is demonstrated clearly enough by Draft C's lower correlation with a school attainment that was assessed mainly on reading and number.It appears that although no "age" factor was clearly disclosed by the factor analyses, the evidence afforded by the standardisation, the error -analyses and the interviews makes it fairly obvious that age is indeed of some importance in the Draft C test -performance, but undoubtedly less than if the test had been testing school attainment in verbal and number skills. The interviews in particular show that while the older child is likely to have an advantage in vocabulary, and consequently some advantage conferred by recognition and naming of pictures, this does not seem to be the crucial element in success.The Draft C test emerges from all these processes of investigation as a more homespun, less sophisticated test than the P.M.A. test. It is appropriate to a much narrower range of age, as was shown by the results of the extensive re -test with 7 -yearolds and the error -patterns based thereon. rlithin the agerange to which it is directed, it appears to measure adequacy of comprehension of oral instructions (which may be termed the "reception" aspect of mental activity) and also a general "reason - ing" ability (which concerns more the "production" aspect of this activity). The test has also been seen to measure a spatial/ perceptual ability, more rudimentary perhaps and not so specific as that tested by the P.L.A. identities and space tests. There is less demand made on either acuity or speed, but it is none the less an ability emphasising a "physical' element of perception.With regard to boy -girl differences, the factor analyses seemed to indicate greater reliance by the girls on both verbal/ naming and verbal /reasoning ability, while the boys appear to show dependence on perceptual ability, and in a wider spread of tests. (The P.L.A. identities and space tests showed the most nearly significant means in favour of boys) . The Draft C Parts 7 and 8 (particularly the lengthier items of the latter) have repeatedly shown some such distinction as this in the course of the interviews and individual tests - the girls tend to verbalise, describe and "debate'? the shapes and the patterns in these Parts, while the boys are making much more use of an ability to "see" and "spot" (quite noticeably in the longer items of Part 8 mentioned above), as indeed they also seem to do in some of the earlier Parts of the test, where again the girls were more likely to verbalise and "reason ". This tendency on the boys' part credits the boys with greater perceptual quickness and acuity with regard to present and (as in the P.M.A.) complex perceptual material, while the girls may show some tendency towards successful "imaginal" handling of rather less complex perceptual data: a tendency which need not be unrelated to a verbal ability...The interviews with the 65 children corroborated the findings of the factor analyses by underlining the special importance of verbal /reasoning rather than verbal /naming as the deciding factor in the Draft C test, and in distinguishing also a perceptual and spatial element. The girls interviewed and tested individually appeared to use e verbal approach even to the more "spatial" Parts of the test, with conspicuous success in Part 8, where their mean score was higher than that of the boys (giving a "t" ratio of 1.36)