27,558 research outputs found
Groups whose locally maximal product-free sets are complete
Let G be a finite group and S a subset of G. Then S is product-free if S â© SS = â
, and complete if Gâ â S âȘ SS. A product-free set is locally maximal if it is not contained in a strictly larger product-free set. If S is product-free and complete then S is locally maximal, but the converse does not necessarily hold. Street and Whitehead [J. Combin. Theory Ser. A 17 (1974), 219â226] defined a group G as filled if every locally maximal product-free set S in G is complete (the term comes from their use of the phrase âS fills Gâ to mean S is complete). They classified all abelian filled groups, and conjectured that the finite dihedral group of order 2n is not filled when n = 6k +1 (k â„ 1). The conjecture was disproved by two of the current authors [C.S. Anabanti and S.B. Hart, Australas. J. Combin. 63 (3) (2015), 385â398], where we also classified the filled groups of odd order.
In this paper we classify filled dihedral groups, filled nilpotent groups and filled groups of order 2n p where p is an odd prime. We use these results to determine all filled groups of order up to 2000
Involution products in Coxeter groups
For W a Coxeter group, let
= {w â W | w = xy where x, y â W and x 2 = 1 = y 2}.
It is well known that if W is finite then W = . Suppose that w â . Then the minimum value of â(x) + â(y) â â(w), where x, y â W with w = xy and x 2 = 1 = y 2, is called the excess of w (â is the length function of W). The main result established here is that w is always W-conjugate to an element with excess equal to zero
On the Shapley-like Payoff Mechanisms in Peer-Assisted Services with Multiple Content Providers
This paper studies an incentive structure for cooperation and its stability
in peer-assisted services when there exist multiple content providers, using a
coalition game theoretic approach. We first consider a generalized coalition
structure consisting of multiple providers with many assisting peers, where
peers assist providers to reduce the operational cost in content distribution.
To distribute the profit from cost reduction to players (i.e., providers and
peers), we then establish a generalized formula for individual payoffs when a
"Shapley-like" payoff mechanism is adopted. We show that the grand coalition is
unstable, even when the operational cost functions are concave, which is in
sharp contrast to the recently studied case of a single provider where the
grand coalition is stable. We also show that irrespective of stability of the
grand coalition, there always exist coalition structures which are not
convergent to the grand coalition. Our results give us an important insight
that a provider does not tend to cooperate with other providers in
peer-assisted services, and be separated from them. To further study the case
of the separated providers, three examples are presented; (i) underpaid peers,
(ii) service monopoly, and (iii) oscillatory coalition structure. Our study
opens many new questions such as realistic and efficient incentive structures
and the tradeoffs between fairness and individual providers' competition in
peer-assisted services.Comment: 13 pages, 4 figures, an extended version of the paper to be presented
in ICST GameNets 2011, Shanghai, China, April 201
Study protocol: Delayed intervention randomised controlled trial within the Medical Research Council (MRC) Framework to assess the effectiveness of a new palliative care service
Background: Palliative care has been proposed to help meet the needs of patients who suffer
progressive non-cancer conditions but there have been few evaluations of service development
initiatives. We report here a novel protocol for the evaluation of a new palliative care service in
this context.
Methods/Design: Using the MRC Framework for the Evaluation of Complex Interventions we
modelled a new palliative care and neurology service for patients severely affected by Multiple
Sclerosis (MS). We conducted qualitative interviews with patients, families and staff, plus a
literature review to model and pilot the service. Then we designed a delayed intervention
randomised controlled trial to test its effectiveness as part of phase II of the MRC framework.
Inclusion criteria for the trial were patients identified by referring clinicians as having unresolved
symptoms or psychological concerns. Referrers were advised to use a score of greater than 8 on
the Expanded Disability Scale was a benchmark. Consenting patients newly referred to the new
service were randomised to either receive the palliative care service immediately (fast-track) or
after a 12-week wait (standard best practice). Face to face interviews were conducted at baseline
(before intervention), and at 4â6, 10â12 (before intervention for the standard-practice group), 16â
18 and 22â24 weeks with patients and their carers using standard questionnaires to assess
symptoms, palliative care outcomes, function, service use and open comments. Ethics committee
approval was granted separately for the qualitative phase and then for the trial.
Discussion: We publish the protocol trial here, to allow methods to be reviewed in advance of
publication of the results. The MRC Framework for the Evaluation of Complex Interventions was
helpful in both the design of the service, methods for evaluation in convincing staff and the ethics
committee to accept the trial. The research will provide valuable information on the effects of
palliative care among non-cancer patients and a method to evaluate palliative care in this context
A synopsis of recent North American microtine rodents
http://deepblue.lib.umich.edu/bitstream/2027.42/56364/1/MP120.pd
Beginning of stability theory for Polish Spaces
We consider stability theory for Polish spaces and more generally for
definable structures. We succeed to prove existence of indiscernibles under
reasonable conditions
Ground-layer wavefront reconstruction from multiple natural guide stars
Observational tests of ground layer wavefront recovery have been made in open
loop using a constellation of four natural guide stars at the 1.55 m Kuiper
telescope in Arizona. Such tests explore the effectiveness of wide-field seeing
improvement by correction of low-lying atmospheric turbulence with ground-layer
adaptive optics (GLAO). The wavefronts from the four stars were measured
simultaneously on a Shack-Hartmann wavefront sensor (WFS). The WFS placed a 5 x
5 array of square subapertures across the pupil of the telescope, allowing for
wavefront reconstruction up to the fifth radial Zernike order. We find that the
wavefront aberration in each star can be roughly halved by subtracting the
average of the wavefronts from the other three stars. Wavefront correction on
this basis leads to a reduction in width of the seeing-limited stellar image by
up to a factor of 3, with image sharpening effective from the visible to near
infrared wavelengths over a field of at least 2 arc minutes. We conclude that
GLAO correction will be a valuable tool that can increase resolution and
spectrographic throughput across a broad range of seeing-limited observations.Comment: 25 pages, 8 figures, to be published in Astrophys.
The monopole mass in the three-dimensional Georgi-Glashow model
We study the three-dimensional Georgi-Glashow model to demonstrate how
magnetic monopoles can be studied fully non-perturbatively in lattice Monte
Carlo simulations, without any assumptions about the smoothness of the field
configurations. We examine the apparent contradiction between the conjectured
analytic connection of the `broken' and `symmetric' phases, and the
interpretation of the mass (i.e., the free energy) of the fully quantised 't
Hooft-Polyakov monopole as an order parameter to distinguish the phases. We use
Monte Carlo simulations to measure the monopole free energy and its first
derivative with respect to the scalar mass. On small volumes we compare this to
semi-classical predictions for the monopole. On large volumes we show that the
free energy is screened to zero, signalling the formation of a confining
monopole condensate. This screening does not allow the monopole mass to be
interpreted as an order parameter, resolving the paradox.Comment: 12 pages, 7 figures, uses revtex. Minor changes made to the text to
match with the published version at
http://link.aps.org/abstract/PRD/v65/e12500
The wootton bassett mud spings (Wiltshire, U.K.): an unusual Largerstatten for jurassic foraminifera
Abstrac
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