Colouring of plane graphs with unique maximal colours on faces

The Four Colour Theorem asserts that the vertices of every plane graph can be properly coloured with four colors. Fabrici and G\"oring conjectured the following stronger statement to also hold: the vertices of every plane graph can be properly coloured with the numbers 1,...,4 in such a way that every face contains a unique vertex coloured with the maximal color appearing on that face. They proved that every plane graph has such a colouring with the numbers 1,...,6. We prove that every plane graph has such a colouring with the numbers 1,...,5 and we also prove the list variant of the statement for lists of sizes seven.Comment: 10 pages, 10 figure

[Review of] E. San Juan, Jr., Racism and Cultural Studies: Critiques of Multiculturalist Ideology and the Politics of Difference

Have academically fashionable cultural studies methodologies replaced mass social movements as political activity? This question is raised in E. San Juan, Jr.\u27s most recent study, Racism and Cultural Studies. Contemporary postmodern and postcolonial intellectual movements, because they valorize individualized discourses and relativist pluralism, have indeed displaced the centrality of mass social movements in the project of group liberation in San Juan\u27s judgment

How Polycentric is a Monocentric City? The Role of Agglomeration Economies

Can the demise of the monocentric economy across cities during the 20th century be explained by decreasing transport costs to the city center or are other fundamental forces at work? Taking a hybrid perspective of classical bid-rent theory and a world where clustering of economic activity is driven by (knowledge) spillovers, Berlin, Germany, from 1890 to 1936 serves as a case in point. We assess the extent to which firms in an environment of decreasing transport costs and industrial transformation face a trade-off between distance to the CBD and land rents and how agglomeration economies come into play in shaping their location decisions. Our results suggest that an observable flattening of the traditional distance to the CBD gradient may mask the emergence of significant agglomeration economies, especially within predominantly service-based inner city districts.

Mirror Symmetry on Kummer Type K3 Surfaces

We investigate both geometric and conformal field theoretic aspects of mirror symmetry on N=(4,4) superconformal field theories with central charge c=6. Our approach enables us to determine the action of mirror symmetry on (non-stable) singular fibers in elliptic fibrations of Z_N orbifold limits of K3. The resulting map gives an automorphism of order 4,8, or 12, respectively, on the smooth universal cover of the moduli space. We explicitly derive the geometric counterparts of the twist fields in our orbifold conformal field theories. The classical McKay correspondence allows for a natural interpretation of our results.Comment: 27 pages, no figures; references added, typos and equation (28) correcte

Integral Fluxes, Day-Night, and Spectrum Results from SNO's 391-Day Salt Phase

The Sudbury Neutrino Observatory is a 1000t heavy water Cherenkov detector observing neutrinos from the Sun and other astrophysical sources. Measurements of the integral solar neutrino fluxes of charged current, neutral current and elastic scattering events are reported for 391 days of live data from the salt phase of SNO operation. In this phase 2t of salt were dissolved in the heavy water, which enhanced and differentiated the detection of neutral current events. Day-night asymmetries in these fluxes were also determined. The measured electron spectrum from the charged-current channel is compatible with the undistorted spectrum of the solar 8B neutrino flux.Comment: 5 pages, 2 figures, to appear in the Proceedings of Lake Louise Winter Institute: Fundamental Interactions, Lake Louise, Alberta, Canada, Feb 20-26 200