2,649 research outputs found
The absence of efficient dual pairs of spanning trees in planar graphs
A spanning tree T in a finite planar connected graph G determines a dual
spanning tree T* in the dual graph G such that T and T* do not intersect. We
show that it is not always possible to find T in G, such that the diameters of
T and T* are both within a uniform multiplicative constant (independent of G)
of the diameters of their ambient graphs.Comment: 7 pages, 3 figure
A Note on Real Tunneling Geometries
In the Hartle-Hawking ``no boundary'' approach to quantum cosmology, a real
tunneling geometry is a configuration that represents a transition from a
compact Riemannian spacetime to a Lorentzian universe. I complete an earlier
proof that in three spacetime dimensions, such a transition is ``probable,'' in
the sense that the required Riemannian geometry yields a genuine maximum of the
semiclassical wave function.Comment: 5 page
Homologous non-isotopic symplectic tori in a K3-surface
For each member of an infinite family of homology classes in the K3-surface
E(2), we construct infinitely many non-isotopic symplectic tori representing
this homology class. This family has an infinite subset of primitive classes.
We also explain how these tori can be non-isotopically embedded as homologous
symplectic submanifolds in many other symplectic 4-manifolds including the
elliptic surfaces E(n) for n>2.Comment: 15 pages, 9 figures; v2: extended the main theorem, gave a second
construction of symplectic tori, added a figure, added/updated references,
minor changes in figure
3-manifolds with(out) metrics of nonpositive curvature
In the context of Thurstons geometrisation program we address the question
which compact aspherical 3-manifolds admit Riemannian metrics of nonpositive
curvature. We show that non-geometric Haken manifolds generically, but not
always, admit such metrics. More precisely, we prove that a Haken manifold
with, possibly empty, boundary of zero Euler characteristic admits metrics of
nonpositive curvature if the boundary is non-empty or if at least one atoroidal
component occurs in its canonical topological decomposition. Our arguments are
based on Thurstons Hyperbolisation Theorem. We give examples of closed
graph-manifolds with linear gluing graph and arbitrarily many Seifert
components which do not admit metrics of nonpositive curvature.Comment: 16 page
Limits of corporal punishment in public schools
A review of the U.S. Supreme Court decision in Ingraham v. Wright: The Limits of Corporal Punishment in Public Schools
Compassion : the inward journey to love
https://place.asburyseminary.edu/ecommonsatsdissertations/1893/thumbnail.jp
Reconstructing the global topology of the universe from the cosmic microwave background
If the universe is multiply-connected and sufficiently small, then the last
scattering surface wraps around the universe and intersects itself. Each circle
of intersection appears as two distinct circles on the microwave sky. The
present article shows how to use the matched circles to explicitly reconstruct
the global topology of space.Comment: 6 pages, 2 figures, IOP format. To be published in the proceedings of
the Cleveland Cosmology and Topology Workshop 17-19 Oct 1997. Submitted to
Class. Quant. Gra
Spherical structures on torus knots and links
The present paper considers two infinite families of cone-manifolds endowed
with spherical metric. The singular strata is either the torus knot or the torus link . Domains of existence for a
spherical metric are found in terms of cone angles and volume formul{\ae} are
presented.Comment: 17 pages, 5 figures; typo
All flat manifolds are cusps of hyperbolic orbifolds
We show that all closed flat n-manifolds are diffeomorphic to a cusp
cross-section in a finite volume hyperbolic (n+1)-orbifold.Comment: Published by Algebraic and Geometric Topology at
http://www.maths.warwick.ac.uk/agt/AGTVol2/agt-2-13.abs.htm
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Ionising radiation exposure from medical imaging – A review of Patient's (un) awareness
Introduction: Medical imaging is the main source of artificial radiation exposure. Evidence, however, suggests that patients are poorly informed about radiation exposure when attending diagnostic scans. This review provides an overview of published literature with a focus on nuclear medicine patients on the level of awareness of radiation exposure from diagnostic imaging. Methods: A review of available literature on awareness, knowledge and perception of ionising radiation in medical imaging was conducted. Articles that met the inclusion criteria were subjected to critical appraisal using the Mixed Methods Appraisal Tool. Results: 140 articles identified and screened for eligibility, 24 critically assessed and 4 studies included in synthesis. All studies demonstrated that patients were generally lacking awareness about radiation exposure and highlighted a lack of communication between healthcare professionals and patients with respect to radiation exposure. Conclusion: Studies demonstrate a need to better inform patients about their radiation exposure, and further studies focusing on nuclear medicine patients are particularly warranted. Implications for practice: Adequate and accurate information is crucial to ensure the principle of informed consent is present
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