137 research outputs found
Critical points of Wang-Yau quasi-local energy
In this paper, we prove the following theorem regarding the Wang-Yau
quasi-local energy of a spacelike two-surface in a spacetime: Let be a
boundary component of some compact, time-symmetric, spacelike hypersurface
in a time-oriented spacetime satisfying the dominant energy
condition. Suppose the induced metric on has positive Gaussian
curvature and all boundary components of have positive mean curvature.
Suppose where is the mean curvature of in and
is the mean curvature of when isometrically embedded in .
If is not isometric to a domain in , then 1. the Brown-York mass
of in is a strict local minimum of the Wang-Yau quasi-local
energy of , 2. on a small perturbation of in
, there exists a critical point of the Wang-Yau quasi-local energy of
.Comment: substantially revised, main theorem replaced, Section 3 adde
A Reilly formula and eigenvalue estimates for differential forms
We derive a Reilly-type formula for differential p-forms on a compact
manifold with boundary and apply it to give a sharp lower bound of the spectrum
of the Hodge Laplacian acting on differential forms of an embedded hypersurface
of a Riemannian manifold. The equality case of our inequality gives rise to a
number of rigidity results, when the geometry of the boundary has special
properties and the domain is non-negatively curved. Finally we also obtain, as
a by-product of our calculations, an upper bound of the first eigenvalue of the
Hodge Laplacian when the ambient manifold supports non-trivial parallel forms.Comment: 22 page
Rigidity of compact Riemannian spin Manifolds with Boundary
In this article, we prove new rigidity results for compact Riemannian spin
manifolds with boundary whose scalar curvature is bounded from below by a
non-positive constant. In particular, we obtain generalizations of a result of
Hang-Wang \cite{hangwang1} based on a conjecture of Schroeder and Strake
\cite{schroeder}.Comment: English version of "G\'eom\'etrie spinorielle extrins\`eque et
rigidit\'es", Corollary 6 in Section 3 added, to appear in Letters Math. Phy
Characterization of plant-based protein sources for use in canine and feline nutrition
The objective of this study was to determine the macronutrient composition and standardized amino acid digestibility of 14 novel, plant-based, protein sources. The 14 protein sources are comprised of protein concentrates (pea, potato, faba bean, yeast, and soy concentrates), pulses (garbanzo beans, navy beans, black beans, lentils, and peas), and byproducts (corn gluten meal, peanut flour, soybean meal, and soy flakes). Macronutrient compositions and a complete amino acid profile were analyzed for all 14 protein sources. Cecectomized roosters (n=4/treatment) were utilized in a precision-fed rooster assay to measure standardized amino acid digestibility and true metabolizable energy corrected for nitrogen (TMEn). The roosters were precision-fed 30g of a 1:1 ratio of an ingredient and corn mixture. Excreta was collected after 48h, freeze-dried, and analyzed for a complete amino acid profile. Due to the high amino acid digestibility and well-balanced essential amino acid profiles, these plant-based proteins have the potential to become viable protein sources in canine and feline diets
-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
Electronic structure of rectangular quantum dots
We study the ground state properties of rectangular quantum dots by using the
spin-density-functional theory and quantum Monte Carlo methods. The dot
geometry is determined by an infinite hard-wall potential to enable comparison
to manufactured, rectangular-shaped quantum dots. We show that the electronic
structure is very sensitive to the deformation, and at realistic sizes the
non-interacting picture determines the general behavior. However, close to the
degenerate points where Hund's rule applies, we find spin-density-wave-like
solutions bracketing the partially polarized states. In the
quasi-one-dimensional limit we find permanent charge-density waves, and at a
sufficiently large deformation or low density, there are strongly localized
stable states with a broken spin-symmetry.Comment: 8 pages, 9 figures, submitted to PR
Mutation of a single residue, β-glutamate-20, alters protein–lipid interactions of light harvesting complex II
It is well established that assembly of the peripheral antenna complex, LH2, is required for proper photosynthetic membrane biogenesis in the purple bacterium Rhodobacter sphaeroides. The underlying interactions are, as yet, not understood. Here we examined the relationship between the morphology of the photosynthetic membrane and the lipid–protein interactions at the LH2–lipid interface. The non-bilayer lipid, phosphatidylethanolamine, is shown to be highly enriched in the boundary lipid phase of LH2. Sequence alignments indicate a putative lipid binding site, which includes β-glutamate-20 and the adjacent carotenoid end group. Replacement of β-glutamate-20 with alanine results in significant reduction of phosphatidylethanolamine and concomitant raise in phosphatidylcholine in the boundary lipid phase of LH2 without altering the lipid composition of the bulk phase. The morphology of the LH2 housing membrane is, however, unaffected by the amino acid replacement. In contrast, simultaneous modification of glutamate-20 and exchange of the carotenoid sphaeroidenone with neurosporene results in significant enlargement of the vesicular membrane invaginations. These findings suggest that the LH2 complex, specifically β-glutamate-20 and the carotenoids' polar head group, contribute to the shaping of the photosynthetic membrane by specific interactions with surrounding lipid molecules
The Cholecystectomy As A Day Case (CAAD) Score: A Validated Score of Preoperative Predictors of Successful Day-Case Cholecystectomy Using the CholeS Data Set
Background
Day-case surgery is associated with significant patient and cost benefits. However, only 43% of cholecystectomy patients are discharged home the same day. One hypothesis is day-case cholecystectomy rates, defined as patients discharged the same day as their operation, may be improved by better assessment of patients using standard preoperative variables.
Methods
Data were extracted from a prospectively collected data set of cholecystectomy patients from 166 UK and Irish hospitals (CholeS). Cholecystectomies performed as elective procedures were divided into main (75%) and validation (25%) data sets. Preoperative predictors were identified, and a risk score of failed day case was devised using multivariate logistic regression. Receiver operating curve analysis was used to validate the score in the validation data set.
Results
Of the 7426 elective cholecystectomies performed, 49% of these were discharged home the same day. Same-day discharge following cholecystectomy was less likely with older patients (OR 0.18, 95% CI 0.15–0.23), higher ASA scores (OR 0.19, 95% CI 0.15–0.23), complicated cholelithiasis (OR 0.38, 95% CI 0.31 to 0.48), male gender (OR 0.66, 95% CI 0.58–0.74), previous acute gallstone-related admissions (OR 0.54, 95% CI 0.48–0.60) and preoperative endoscopic intervention (OR 0.40, 95% CI 0.34–0.47). The CAAD score was developed using these variables. When applied to the validation subgroup, a CAAD score of ≤5 was associated with 80.8% successful day-case cholecystectomy compared with 19.2% associated with a CAAD score >5 (p < 0.001).
Conclusions
The CAAD score which utilises data readily available from clinic letters and electronic sources can predict same-day discharges following cholecystectomy
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