On generalized Kneser hypergraph colorings

In Ziegler (2002), the second author presented a lower bound for the chromatic numbers of hypergraphs \KG{r}{\pmb s}{\calS}, "generalized $r$-uniform Kneser hypergraphs with intersection multiplicities $\pmb s$." It generalized previous lower bounds by Kriz (1992/2000) for the case ${\pmb s}=(1,...,1)$ without intersection multiplicities, and by Sarkaria (1990) for \calS=\tbinom{[n]}k. Here we discuss subtleties and difficulties that arise for intersection multiplicities $s_i>1$: 1. In the presence of intersection multiplicities, there are two different versions of a "Kneser hypergraph," depending on whether one admits hypergraph edges that are multisets rather than sets. We show that the chromatic numbers are substantially different for the two concepts of hypergraphs. The lower bounds of Sarkaria (1990) and Ziegler (2002) apply only to the multiset version. 2. The reductions to the case of prime $r$ in the proofs Sarkaria and by Ziegler work only if the intersection multiplicities are strictly smaller than the largest prime factor of $r$. Currently we have no valid proof for the lower bound result in the other cases. We also show that all uniform hypergraphs without multiset edges can be represented as generalized Kneser hypergraphs.Comment: 9 pages; added examples in Section 2; added reference ([11]), corrected minor typos; to appear in J. Combinatorial Theory, Series

All Abelian Quotient C.I.-Singularities Admit Projective Crepant Resolutions in All Dimensions

For Gorenstein quotient spaces $C^d/G$, a direct generalization of the classical McKay correspondence in dimensions $d\geq 4$ would primarily demand the existence of projective, crepant desingularizations. Since this turned out to be not always possible, Reid asked about special classes of such quotient spaces which would satisfy the above property. We prove that the underlying spaces of all Gorenstein abelian quotient singularities, which are embeddable as complete intersections of hypersurfaces in an affine space, have torus-equivariant projective crepant resolutions in all dimensions. We use techniques from toric and discrete geometry.Comment: revised version of MPI-preprint 97/4, 35 pages, 13 figures, latex2e-file (preprint.tex), macro packages and eps-file

Vertex-Facet Incidences of Unbounded Polyhedra

How much of the combinatorial structure of a pointed polyhedron is contained in its vertex-facet incidences? Not too much, in general, as we demonstrate by examples. However, one can tell from the incidence data whether the polyhedron is bounded. In the case of a polyhedron that is simple and "simplicial," i.e., a d-dimensional polyhedron that has d facets through each vertex and d vertices on each facet, we derive from the structure of the vertex-facet incidence matrix that the polyhedron is necessarily bounded. In particular, this yields a characterization of those polyhedra that have circulants as vertex-facet incidence matrices.Comment: LaTeX2e, 14 pages with 4 figure

Discutindo a educação ambiental no cotidiano escolar: desenvolvimento de projetos na escola formação inicial e continuada de professores

A presente pesquisa buscou discutir como a Educação Ambiental (EA) vem sendo trabalhada, no Ensino Fundamental e como os docentes desta escola compreendem e vem inserindo a EA no cotidiano escolar., em uma escola estadual do município de Tangará da Serra/MT, Brasil. Para tanto, realizou-se entrevistas com os professores que fazem parte de um projeto interdisciplinar de EA na escola pesquisada. Verificou-se que o projeto da escola não vem conseguindo alcançar os objetivos propostos por: desconhecimento do mesmo, pelos professores; formação deficiente dos professores, não entendimento da EA como processo de ensino-aprendizagem, falta de recursos didáticos, planejamento inadequado das atividades. A partir dessa constatação, procurou-se debater a impossibilidade de tratar do tema fora do trabalho interdisciplinar, bem como, e principalmente, a importância de um estudo mais aprofundado de EA, vinculando teoria e prática, tanto na formação docente, como em projetos escolares, a fim de fugir do tradicional vínculo “EA e ecologia, lixo e horta”.Facultad de Humanidades y Ciencias de la Educació

Proceedings From FDA/A.S.P.E.N. Public Workshop:Clinical Trial Design for Intravenous Fat Emulsion Products, October 29, 2013

The development of intravenous fat emulsion (IVFE) is the culmination of physiological, biochemical, nutritional, and medical scientific advancements. IVFEs have the ability to deliver critical nutritional substrates to the patient. Recent literature purports that they may also play roles in modulation of immune functionality and pulmonary physiology, but data supporting these potential benefits are limited. While soybean-based IVFEs have comprised the dominant fat in U.S. markets, a number of other novel IVFEs may prove to optimize the care of children and adults in both hospitalized and home settings. The October 2013 U.S. Food and Drug Administration (FDA)/American Society for Parenteral and Enteral Nutrition (A.S.P.E.N.) Public Workshop brought together scientists, researchers, and clinical experts to present updated clinical perspectives of IVFEs, including historical development, current state of usage throughout the world, and considerations for the regulatory approval of new IVFEs in the United States.SCOPUS: cp.jinfo:eu-repo/semantics/publishe