262 research outputs found
A simple proof of the Markoff conjecture for prime powers
We give a simple and independent proof of the result of Jack Button and Paul
Schmutz that the Markoff conjecture on the uniqueness of the Markoff triples
(a,b,c), where a, b, and c are in increasing order, holds whenever is a
prime power.Comment: 5 pages, no figure
A Combination Theorem for Metric Bundles
We define metric bundles/metric graph bundles which provide a purely
topological/coarse-geometric generalization of the notion of trees of metric
spaces a la Bestvina-Feighn in the special case that the inclusions of the edge
spaces into the vertex spaces are uniform coarsely surjective quasi-isometries.
We prove the existence of quasi-isometric sections in this generality. Then we
prove a combination theorem for metric (graph) bundles (including exact
sequences of groups) that establishes sufficient conditions, particularly
flaring, under which the metric bundles are hyperbolic. We use this to give
examples of surface bundles over hyperbolic disks, whose universal cover is
Gromov-hyperbolic. We also show that in typical situations, flaring is also a
necessary condition.Comment: v3: Major revision: 56 pages 5 figures. Many details added.
Characterization of convex cocompact subgroups of mapping class groups of
surfaces with punctures in terms of relative hyperbolicity given v4: Final
version incorporating referee comments: 63 pages 5 figures. To appear in
Geom. Funct. Ana
Centerscope
Centerscope, formerly Scope, was published by the Boston University Medical Center "to communicate the concern of the Medical Center for the development and maintenance of improved health care in contemporary society.
Dirichlet fundamental domains and complex-projective varieties
We prove that for every finitely-presented group G there exists a
2-dimensional irreducible complex-projective variety W with the fundamental
group G, so that all singularities of W are normal crossings and Whitney
umbrellas.Comment: 1 figur
The longitude problem from the 1700s to today: An international and general education physics course
For instructors wishing to use physics as part of an international or general education course, the framework for a course based on the “longitude problem” from the 1700s is described. The longitude problem is teeming with basic principles of physics and astronomy, which makes it ideal for a non-science-major-based college-level course. This paper summarizes the longitude problem in the context of conceptual physics and astronomy and outlines an appropriate curriculum. Specifics on teaching such a course in London, as part of an international studies program, are discussed
Systematic mechanical assessment of consolidants for canvas reinforcement under controlled environment
In conservation, adhesives are commonly used for the consolidation of canvases, yet their impact upon the canvas longevity has raised some concerns amongst conservators. As such, this study presents a testing protocol developed to assess the performance of commonly-used adhesives (natural animal glue and synthetic Beva® 371) and a newly developed nanocellulose consolidant, nanofibrillated nanocellulose (CNF). This includes their effect on the visual appearance, consolidation, and response of the mechanical properties of the treated canvases to programmed changes in relative humidity (RH). Scanning electron microscopy (SEM) images of animal glue- and Beva® 371-treated canvases revealed the presence of adhesive and consolidant on and in-between cotton fibres. The consolidants form bridges linking and connecting the cotton fibres and holding them together, whereas the CNF treatment, formed a visible continuous and dense surface coating. None of the treatments induced any discernible colour change. Controlled environment mechanical testing was performed in two ways: by applying a linearly increasing static force at fixed RH (Young’s modulus) and by applying a dynamic force together with a programmed RH cycling between 20 and 80% (RH dependent viscoelastic properties). CNF gave a higher value of Young’s modulus than either of the two commonly-used materials. Measurements at different values of RH (20 and 80%) demonstrated for all the treated canvases that at the lower value (RH 20%) Young’s modulus values were higher than at the higher value (RH 80%). Besides, the dynamic mode showed that the rate of response in all cases was rapid and reversible and that the nanofibrillated cellulose treated sample showed the highest variation in storage (or elastic) modulus measured at the end of RH plateaux (20 and 80% RH). Thus CNF appears to be a promising material given its higher mechanical performance. The protocol developed in this study has enabled us to examine and compare candidate materials for the consolidation of canvases systematically, using testing parameters that remained relevant to the field of canvas conservation
Anosov representations: Domains of discontinuity and applications
The notion of Anosov representations has been introduced by Labourie in his
study of the Hitchin component for SL(n,R). Subsequently, Anosov
representations have been studied mainly for surface groups, in particular in
the context of higher Teichmueller spaces, and for lattices in SO(1,n). In this
article we extend the notion of Anosov representations to representations of
arbitrary word hyperbolic groups and start the systematic study of their
geometric properties. In particular, given an Anosov representation of
into G we explicitly construct open subsets of compact G-spaces, on which
acts properly discontinuously and with compact quotient.
As a consequence we show that higher Teichmueller spaces parametrize locally
homogeneous geometric structures on compact manifolds. We also obtain
applications regarding (non-standard) compact Clifford-Klein forms and
compactifications of locally symmetric spaces of infinite volume.Comment: 63 pages, accepted for publication in Inventiones Mathematica
Rate-dependent Ca2+ signalling underlying the force-frequency response in rat ventricular myocytes: A coupled electromechanical modeling study
Rate-dependent effects on the Ca2+ sub-system in a rat ventricular myocyte are investigated. Here,
we employ a deterministic mathematical model describing various Ca2+ signalling pathways under
voltage clamp (VC) conditions, to better understand the important role of calmodulin (CaM) in modulating
the key control variables Ca2+/calmodulin-dependent protein kinase-II (CaMKII), calcineurin
(CaN), and cyclic adenosine monophosphate (cAMP) as they affect various intracellular targets. In
particular, we study the frequency dependence of the peak force generated by the myofilaments, the
force-frequency response (FFR). Our cell model incorporates frequency-dependent CaM-mediated spatially heterogenous interaction
of CaMKII and CaN with their principal targets (dihydropyridine (DHPR) and ryanodine (RyR) receptors
and the SERCA pump). It also accounts for the rate-dependent effects of phospholamban
(PLB) on the SERCA pump; the rate-dependent role of cAMP in up-regulation of the L-type Ca2+
channel (ICa;L); and the enhancement in SERCA pump activity via phosphorylation of PLB.Our model reproduces positive peak FFR observed in rat ventricular myocytes during voltage-clamp
studies both in the presence/absence of cAMP mediated -adrenergic stimulation. This study provides
quantitative insight into the rate-dependence of Ca2+-induced Ca2+-release (CICR) by investigating
the frequency-dependence of the trigger current (ICa;L) and RyR-release. It also highlights the relative
role of the sodium-calcium exchanger (NCX) and the SERCA pump at higher frequencies, as well
as the rate-dependence of sarcoplasmic reticulum (SR) Ca2+ content. A rigorous Ca2+ balance
imposed on our investigation of these Ca2+ signalling pathways clarifies their individual roles. Here,
we present a coupled electromechanical study emphasizing the rate-dependence of isometric force
developed and also investigate the temperature-dependence of FFR. Our model provides mechanistic biophysically based explanations for the rate-dependence of CICR,
generating useful and testable hypotheses. Although rat ventricular myocytes exhibit a positive peak
FFR in the presence/absence of beta-adrenergic stimulation, they show a characteristic increase in the
positive slope in FFR due to the presence of Norepinephrine or Isoproterenol. Our study identifies
cAMP-mediated stimulation, and rate-dependent CaMKII-mediated up-regulation of ICa;L as the key
mechanisms underlying the aforementioned positive FFR
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