14 research outputs found
The exterior degree of a pair of finite groups
The exterior degree of a pair of finite groups , which is a
generalization of the exterior degree of finite groups, is the probability for
two elements in such that . In the present paper,
we state some relations between this concept and the relative commutatively
degree, capability and the Schur multiplier of a pair of groups.Comment: To appear in Mediterr. J. Mat
Analytic models of plausible gravitational lens potentials
Gravitational lenses on galaxy scales are plausibly modelled as having
ellipsoidal symmetry and a universal dark matter density profile, with a Sersic
profile to describe the distribution of baryonic matter. Predicting all lensing
effects requires knowledge of the total lens potential: in this work we give
analytic forms for that of the above hybrid model. Emphasising that complex
lens potentials can be constructed from simpler components in linear
combination, we provide a recipe for attaining elliptical symmetry in either
projected mass or lens potential. We also provide analytic formulae for the
lens potentials of Sersic profiles for integer and half-integer index. We then
present formulae describing the gravitational lensing effects due to
smoothly-truncated universal density profiles in cold dark matter model. For
our isolated haloes the density profile falls off as radius to the minus fifth
or seventh power beyond the tidal radius, functional forms that allow all
orders of lens potential derivatives to be calculated analytically, while
ensuring a non-divergent total mass. We show how the observables predicted by
this profile differ from that of the original infinite-mass NFW profile.
Expressions for the gravitational flexion are highlighted. We show how
decreasing the tidal radius allows stripped haloes to be modelled, providing a
framework for a fuller investigation of dark matter substructure in galaxies
and clusters. Finally we remark on the need for finite mass halo profiles when
doing cosmological ray-tracing simulations, and the need for readily-calculable
higher order derivatives of the lens potential when studying catastrophes in
strong lenses.Comment: 24 pages, 10 figures, matches published versio
Constraints on cosmological models from strong gravitational lensing systems
Strong lensing has developed into an important astrophysical tool for probing
both cosmology and galaxies (their structure, formation, and evolution). Using
the gravitational lensing theory and cluster mass distribution model, we try to
collect a relatively complete observational data concerning the Hubble constant
independent ratio between two angular diameter distances from
various large systematic gravitational lens surveys and lensing by galaxy
clusters combined with X-ray observations, and check the possibility to use it
in the future as complementary to other cosmological probes. On one hand,
strongly gravitationally lensed quasar-galaxy systems create such a new
opportunity by combining stellar kinematics (central velocity dispersion
measurements) with lensing geometry (Einstein radius determination from
position of images). We apply such a method to a combined gravitational lens
data set including 70 data points from Sloan Lens ACS (SLACS) and Lens
Structure and Dynamics survey (LSD). On the other hand, a new sample of 10
lensing galaxy clusters with redshifts ranging from 0.1 to 0.6 carefully
selected from strong gravitational lensing systems with both X-ray satellite
observations and optical giant luminous arcs, is also used to constrain three
dark energy models (CDM, constant and CPL) under a flat universe
assumption. For the full sample () and the restricted sample ()
including 36 two-image lenses and 10 strong lensing arcs, we obtain relatively
good fitting values of basic cosmological parameters, which generally agree
with the results already known in the literature. This results encourages
further development of this method and its use on larger samples obtained in
the future.Comment: 22 pages, 5 figures, 2 tables; accepted by JCA
Transmission of SARS and MERS coronaviruses and influenza virus in healthcare settings: the possible role of dry surface contamination
Viruses with pandemic potential including H1N1, H5N1, and H5N7 influenza viruses, and severe acute respiratory syndrome (SARS)/Middle East respiratory syndrome (MERS) coronaviruses (CoV) have emerged in recent years. SARS-CoV, MERS-CoV, and influenza virus can survive on surfaces for extended periods, sometimes up to months. Factors influencing the survival of these viruses on surfaces include: strain variation, titre, surface type, suspending medium, mode of deposition, temperature and relative humidity, and the method used to determine the viability of the virus. Environmental sampling has identified contamination in field-settings with SARS-CoV and influenza virus, although the frequent use of molecular detection methods may not necessarily represent the presence of viable virus. The importance of indirect contact transmission (involving contamination of inanimate surfaces) is uncertain compared with other transmission routes, principally direct contact transmission (independent of surface contamination), droplet, and airborne routes. However, influenza virus and SARS-CoV may be shed into the environment and be transferred from environmental surfaces to hands of patients and healthcare providers. Emerging data suggest that MERS-CoV also shares these properties. Once contaminated from the environment, hands can then initiate self-inoculation of mucous membranes of the nose, eyes or mouth. Mathematical and animal models, and intervention studies suggest that contact transmission is the most important route in some scenarios. Infection prevention and control implications include the need for hand hygiene and personal protective equipment to minimize self-contamination and to protect against inoculation of mucosal surfaces and the respiratory tract, and enhanced surface cleaning and disinfection in healthcare settings