187 research outputs found
Sharp estimates on the first eigenvalue of the p-Laplacian with negative Ricci lower bound
We complete the picture of sharp eigenvalue estimates for the p-Laplacian on
a compact manifold by providing sharp estimates on the first nonzero eigenvalue
of the nonlinear operator when the Ricci curvature is bounded from
below by a negative constant. We assume that the boundary of the manifold is
convex, and put Neumann boundary conditions on it. The proof is based on a
refined gradient comparison technique and a careful analysis of the underlying
model spaces.Comment: Sign mistake fixed in the proof of the gradient comparison theorem
(theorem 5.1 pag 10), and some minor improvements aroun
Logarithmically-concave moment measures I
We discuss a certain Riemannian metric, related to the toric Kahler-Einstein
equation, that is associated in a linearly-invariant manner with a given
log-concave measure in R^n. We use this metric in order to bound the second
derivatives of the solution to the toric Kahler-Einstein equation, and in order
to obtain spectral-gap estimates similar to those of Payne and Weinberger.Comment: 27 page
-minimal surface and manifold with positive -Bakry-\'{E}mery Ricci curvature
In this paper, we first prove a compactness theorem for the space of closed
embedded -minimal surfaces of fixed topology in a closed three-manifold with
positive Bakry-\'{E}mery Ricci curvature. Then we give a Lichnerowicz type
lower bound of the first eigenvalue of the -Laplacian on compact manifold
with positive -Bakry-\'{E}mery Ricci curvature, and prove that the lower
bound is achieved only if the manifold is isometric to the -shpere, or the
-dimensional hemisphere. Finally, for compact manifold with positive
-Bakry-\'{E}mery Ricci curvature and -mean convex boundary, we prove an
upper bound for the distance function to the boundary, and the upper bound is
achieved if only if the manifold is isometric to an Euclidean ball.Comment: 15 page
Upper bounds on the first eigenvalue for a diffusion operator via Bakry-\'{E}mery Ricci curvature II
Let be a symmetric diffusion operator
with an invariant measure on a complete Riemannian
manifold. In this paper we prove Li-Yau gradient estimates for weighted
elliptic equations on the complete manifold with
and -dimensional Bakry-\'{E}mery Ricci curvature bounded below by some
negative constant. Based on this, we give an upper bound on the first
eigenvalue of the diffusion operator on this kind manifold, and thereby
generalize a Cheng's result on the Laplacian case (Math. Z., 143 (1975)
289-297).Comment: Final version. The original proof of Theorem 2.1 using Li-Yau
gradient estimate method has been moved to the appendix. The new proof is
simple and direc
Linear broadening of the confining string in Yang-Mills theory at low temperature
The logarithmic broadening predicted by the systematic low-energy effective
field theory for the confining string has recently been verified in numerical
simulations of (2+1)-d SU(2) lattice Yang-Mills theory at zero temperature. The
same effective theory predicts linear broadening of the string at low non-zero
temperature. In this paper, we verify this prediction by comparison with very
precise Monte Carlo data. The comparison involves no additional adjustable
parameters, because the low-energy constants of the effective theory have
already been fixed at zero temperature. It yields very good agreement between
the underlying Yang-Mills theory and the effective string theory.Comment: 10 pages, 3 figures. Version published in JHEP; improved figures 1
and
A Schwarz lemma for K\"ahler affine metrics and the canonical potential of a proper convex cone
This is an account of some aspects of the geometry of K\"ahler affine metrics
based on considering them as smooth metric measure spaces and applying the
comparison geometry of Bakry-Emery Ricci tensors. Such techniques yield a
version for K\"ahler affine metrics of Yau's Schwarz lemma for volume forms. By
a theorem of Cheng and Yau there is a canonical K\"ahler affine Einstein metric
on a proper convex domain, and the Schwarz lemma gives a direct proof of its
uniqueness up to homothety. The potential for this metric is a function
canonically associated to the cone, characterized by the property that its
level sets are hyperbolic affine spheres foliating the cone. It is shown that
for an -dimensional cone a rescaling of the canonical potential is an
-normal barrier function in the sense of interior point methods for conic
programming. It is explained also how to construct from the canonical potential
Monge-Amp\`ere metrics of both Riemannian and Lorentzian signatures, and a mean
curvature zero conical Lagrangian submanifold of the flat para-K\"ahler space.Comment: Minor corrections. References adde
Recommended from our members
Impact of loading capability on optimal location of renewable energy systems distribution networks
Copyright © 2023 The Authors. A distribution system's network reconfiguration is the process of altering the open/closed status of sectionalizing and tie switches to change the topological structure of distribution feeders. For the last two decades, numerous heuristic search evolutionary algorithms have been used to tackle the problem of network reconfiguration for time-varying loads, which is a very difficult and highly non-linear efficiency challenge. This research aims to offer an ideal solution for addressing network reconfiguration difficulties in terms of a system for power distribution, to decrease energy losses, and increase the voltage profile. A hybrid Genetic Archimedes optimization technique (GAAOA) has also been developed to size and allocate three types of DGs, wind turbine, fuel cell and PV considering load variation. This approach is quite useful and may be used in many situations. This technique is evaluated for loss reduction and voltage profile on a typical 33-bus radial distribution system and a 69-bus radial distribution system. The system has been simulated using MATLAB software. The findings suggest that this approach is effective and acceptable for real-time usage
Antimicrobial resistance among migrants in Europe: a systematic review and meta-analysis
BACKGROUND: Rates of antimicrobial resistance (AMR) are rising globally and there is concern that increased migration is contributing to the burden of antibiotic resistance in Europe. However, the effect of migration on the burden of AMR in Europe has not yet been comprehensively examined. Therefore, we did a systematic review and meta-analysis to identify and synthesise data for AMR carriage or infection in migrants to Europe to examine differences in patterns of AMR across migrant groups and in different settings. METHODS: For this systematic review and meta-analysis, we searched MEDLINE, Embase, PubMed, and Scopus with no language restrictions from Jan 1, 2000, to Jan 18, 2017, for primary data from observational studies reporting antibacterial resistance in common bacterial pathogens among migrants to 21 European Union-15 and European Economic Area countries. To be eligible for inclusion, studies had to report data on carriage or infection with laboratory-confirmed antibiotic-resistant organisms in migrant populations. We extracted data from eligible studies and assessed quality using piloted, standardised forms. We did not examine drug resistance in tuberculosis and excluded articles solely reporting on this parameter. We also excluded articles in which migrant status was determined by ethnicity, country of birth of participants' parents, or was not defined, and articles in which data were not disaggregated by migrant status. Outcomes were carriage of or infection with antibiotic-resistant organisms. We used random-effects models to calculate the pooled prevalence of each outcome. The study protocol is registered with PROSPERO, number CRD42016043681. FINDINGS: We identified 2274 articles, of which 23 observational studies reporting on antibiotic resistance in 2319 migrants were included. The pooled prevalence of any AMR carriage or AMR infection in migrants was 25·4% (95% CI 19·1-31·8; I2 =98%), including meticillin-resistant Staphylococcus aureus (7·8%, 4·8-10·7; I2 =92%) and antibiotic-resistant Gram-negative bacteria (27·2%, 17·6-36·8; I2 =94%). The pooled prevalence of any AMR carriage or infection was higher in refugees and asylum seekers (33·0%, 18·3-47·6; I2 =98%) than in other migrant groups (6·6%, 1·8-11·3; I2 =92%). The pooled prevalence of antibiotic-resistant organisms was slightly higher in high-migrant community settings (33·1%, 11·1-55·1; I2 =96%) than in migrants in hospitals (24·3%, 16·1-32·6; I2 =98%). We did not find evidence of high rates of transmission of AMR from migrant to host populations. INTERPRETATION: Migrants are exposed to conditions favouring the emergence of drug resistance during transit and in host countries in Europe. Increased antibiotic resistance among refugees and asylum seekers and in high-migrant community settings (such as refugee camps and detention facilities) highlights the need for improved living conditions, access to health care, and initiatives to facilitate detection of and appropriate high-quality treatment for antibiotic-resistant infections during transit and in host countries. Protocols for the prevention and control of infection and for antibiotic surveillance need to be integrated in all aspects of health care, which should be accessible for all migrant groups, and should target determinants of AMR before, during, and after migration. FUNDING: UK National Institute for Health Research Imperial Biomedical Research Centre, Imperial College Healthcare Charity, the Wellcome Trust, and UK National Institute for Health Research Health Protection Research Unit in Healthcare-associated Infections and Antimictobial Resistance at Imperial College London
Control of mycotoxigenic fungi with microcapsules of essential oils encapsulated in chitosan
- …