9,057 research outputs found

    It\u27s Fun, But Is It Science? Goals and Strategies in a Problem-Based Learning Course

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    All students at Hampshire College must complete a science requirement in which they demonstrate their understanding of how science is done, examine the work of science in larger contexts, and communicate their ideas effectively. Human Biology: Selected Topics in Medicine is one of 18-20 freshman seminars designed to move students toward completing this requirement. Students work in cooperative groups of 4-6 people to solve actual medical cases about which they receive information progressively. Students assign themselves homework tasks to bring information back for group deliberation. The goal is for case teams to work cooperatively to develop a differential diagnosis and recommend treatment. Students write detailed individual final case reports. Changes observed in student work over six years of developing this course include: increased motivation to pursue work in depth, more effective participation on case teams, increase in critical examination of evidence, and more fully developed arguments in final written reports. As part of a larger study of eighteen introductory science courses in two institutions, several types of pre- and post-course assessments were used to evaluate how teaching approaches might have influenced students’ attitudes about science, their ability to learn science, and their understanding of how scientific knowledge is developed [1]. Preliminary results from interviews and Likert-scale measures suggest improvements in the development of some students’ views of epistemology and in the importance of cooperative group work in facilitating that development

    Plethystic Vertex Operators and Boson-Fermion Correspondences

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    We study the algebraic properties of plethystic vertex operators, introduced in J. Phys. A: Math. Theor. 43 405202 (2010), underlying the structure of symmetric functions associated with certain generalized universal character rings of subgroups of the general linear group, defined to stabilize tensors of Young symmetry type characterized by a partition of arbitrary shape \pi. Here we establish an extension of the well-known boson-fermion correspondence involving Schur functions and their associated (Bernstein) vertex operators: for each \pi, the modes generated by the plethystic vertex operators and their suitably constructed duals, satisfy the anticommutation relations of a complex Clifford algebra. The combinatorial manipulations underlying the results involve exchange identities exploiting the Hopf-algebraic structure of certain symmetric function series and their plethysms.Comment: 21 pages, LaTeX. Minor typos corrected. Added brief survey of related work and new reference

    The Hopf Algebra Structure of the Character Rings of Classical Groups

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    The character ring \CGL of covariant irreducible tensor representations of the general linear group admits a Hopf algebra structure isomorphic to the Hopf algebra \Sym$ of symmetric functions. Here we study the character rings \CO and \CSp of the orthogonal and symplectic subgroups of the general linear group within the same framework of symmetric functions. We show that \CO and \CSp also admit natural Hopf algebra structures that are isomorphic to that of \CGL, and hence to \Sym. The isomorphisms are determined explicitly, along with the specification of standard bases for \CO and \CSp analogous to those used for \Sym. A major structural change arising from the adoption of these bases is the introduction of new orthogonal and symplectic Schur-Hall scalar products. Significantly, the adjoint with respect to multiplication no longer coincides, as it does in the \CGL case, with a Foulkes derivative or skew operation. The adjoint and Foulkes derivative now require separate definitions, and their properties are explored here in the orthogonal and symplectic cases. Moreover, the Hopf algebras \CO and \CSp are not self-dual. The dual Hopf algebras \CO^* and \CSp^* are identified. Finally, the Hopf algebra of the universal rational character ring \CGLrat of mixed irreducible tensor representations of the general linear group is introduced and its structure maps identified.Comment: 38 pages, uses pstricks; new version is a major update, new title, new material on rational character

    A complete distribution of redshifts for sub-millimetre galaxies in the SCUBA-2 Cosmology Legacy Survey UDS field

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    This is a pre-copyedited, author-produced PDF of an article accepted for publication in Monthly Notices of the Royal Astronomical Society following peer review. Available online at https://doi.org/10.1093/mnras/stx1689. © 2017 The Author(s). Published by Oxford University Press on behalf of the Royal Astronomical Society. All rights reserved.Sub-milllimetre galaxies (SMGs) are some of the most luminous star-forming galaxies in the Universe, however their properties remain hard to determine due to the difficulty of identifying their optical\slash near-infrared counterparts. One of the key steps to determining the nature of SMGs is measuring a redshift distribution representative of the whole population. We do this by applying statistical techniques to a sample of 761 850μ\mum sources from the SCUBA-2 Cosmology Legacy Survey observations of the UKIDSS Ultra-Deep Survey (UDS) Field. We detect excess galaxies around >98.4> 98.4 per cent of the 850μ\mum positions in the deep UDS catalogue, giving us the first 850μ\mum selected sample to have virtually complete optical\slash near-infrared redshift information. Under the reasonable assumption that the redshifts of the excess galaxies are representative of the SMGs themselves, we derive a median SMG redshift of z=2.05±0.03z = 2.05 \pm 0.03, with 68 per cent of SMGs residing between $1.07Peer reviewedFinal Accepted Versio

    Chord diagrams and BPHZ subtractions

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    The combinatorics of the BPHZ subtraction scheme for a class of ladder graphs for the three point vertex in Ď•3\phi^3 theory is transcribed into certain connectivity relations for marked chord diagrams (knots with transversal intersections). The resolution of the singular crossings using the equivalence relations in these examples provides confirmation of a proposed fundamental relationship between knot theory and renormalization in perturbative quantum field theory.Comment: 12 pages, 5 Postscript figures, LaTex 2

    Transportation noise pollution - Control and abatement

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    Control and abatement of transportation noise pollutio
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