11,043 research outputs found
Tight contact structures and genus one fibered knots
We study contact structures compatible with genus one open book
decompositions with one boundary component. Any monodromy for such an open book
can be written as a product of Dehn twists around dual non-separating curves in
the once-punctured torus. Given such a product, we supply an algorithm to
determine whether the corresponding contact structure is tight or overtwisted.
We rely on Ozsv{\'a}th-Szab{\'o} Heegaard Floer homology in our construction
and, in particular, we completely identify the -spaces with genus one, one
boundary component, pseudo-Anosov open book decompositions. Lastly, we reveal a
new infinite family of hyperbolic three-manifolds with no co-orientable taut
foliations, extending the family discovered in \cite{RSS}.Comment: 30 pages, 10 figures. Added figures, extended result to all
monodromies, and added sections 5 and
Symmetries and reversing symmetries of polynomial automorphisms of the plane
The polynomial automorphisms of the affine plane over a field K form a group
which has the structure of an amalgamated free product. This well-known
algebraic structure can be used to determine some key results about the
symmetry and reversing symmetry groups of a given polynomial automorphism.Comment: 27 pages, AMS-Late
The structure of reversing symmetry groups
We present some of the group theoretic properties of reversing symmetry
groups, and classify their structure in simple cases that occur frequently in
several well-known groups of dynamical systems.Comment: 12 page
Linear degree growth in lattice equations
We conjecture recurrence relations satisfied by the degrees of some
linearizable lattice equations. This helps to prove linear growth of these
equations. We then use these recurrences to search for lattice equations that
have linear growth and hence are linearizable
The Design of Mechanically Compatible Fasteners for Human Mandible Reconstruction
Mechanically compatible fasteners for use with thin or weakened bone sections in the human mandible are being developed to help reduce large strain discontinuities across the bone/implant interface. Materials being considered for these fasteners are a polyetherertherketone (PEEK) resin with continuous quartz or carbon fiber for the screw. The screws were designed to have a shear strength equivalent to that of compact/trabecular bone and to be used with a conventional nut, nut plate, or an expandable shank/blind nut made of a ceramic filled polymer. Physical and finite element models of the mandible were developed in order to help select the best material fastener design. The models replicate the softer inner core of trabecular bone and the hard outer shell of compact bone. The inner core of the physical model consisted of an expanding foam and the hard outer shell consisted of ceramic particles in an epoxy matrix. This model has some of the cutting and drilling attributes of bone and may be appropriate as an educational tool for surgeons and medical students. The finite element model was exercised to establish boundary conditions consistent with the stress profiles associated with mandible bite forces and muscle loads. Work is continuing to compare stress/strain profiles of a reconstructed mandible with the results from the finite element model. When optimized, these design and fastening techniques may be applicable, not only to other skeletal structures, but to any composite structure
Rethinking Justice in Massachusetts: Public Attitudes Toward Crime and Punishment
Presents results from a public opinion survey about the sharp increase in the incarcerated population in Massachusetts and about current strategies for reintegrating ex-offenders who have been released into the community
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