481 research outputs found
Reconstructing the geometric structure of a Riemannian symmetric space from its Satake diagram
The local geometry of a Riemannian symmetric space is described completely by
the Riemannian metric and the Riemannian curvature tensor of the space. In the
present article I describe how to compute these tensors for any Riemannian
symmetric space from the Satake diagram, in a way that is suited for the use
with computer algebra systems. As an example application, the totally geodesic
submanifolds of the Riemannian symmetric space SU(3)/SO(3) are classified.
The submission also contains an example implementation of the algorithms and
formulas of the paper as a package for Maple 10, the technical documentation
for this implementation, and a worksheet carrying out the computations for the
space SU(3)/SO(3) used in the proof of Proposition 6.1 of the paper.Comment: 23 pages, also contains two Maple worksheets and technical
documentatio
Free Differential Algebras: Their Use in Field Theory and Dual Formulation
The gauging of free differential algebras (FDA's) produces gauge field
theories containing antisymmetric tensors. The FDA's extend the Cartan-Maurer
equations of ordinary Lie algebras by incorporating p-form potentials (). We study here the algebra of FDA transformations. To every p-form in the
FDA we associate an extended Lie derivative generating a corresponding
``gauge" transformation. The field theory based on the FDA is invariant under
these new transformations. This gives geometrical meaning to the antisymmetric
tensors. The algebra of Lie derivatives is shown to close and provides the dual
formulation of FDA's.Comment: 10 pages, latex, no figures. Talk presented at the 4-th Colloquium on
"Quantum Groups and Integrable Sysytems", Prague, June 199
Pubertal timing and body mass index gain from birth to maturity in relation with femoral neck BMD and distal tibia microstructure in healthy female subjects
Summary: Childhood body mass index (BMI) gain is linked to hip fracture risk in elderly. In healthy girls, menarcheal age is inversely related to BMI gain during childhood and to femoral neck areal bone mass density (aBMD) and distal tibia structural components at maturity. This study underscores the importance of pubertal timing in age-related fragility fracture risk. Introduction: Recent data point to a relationship between BMI change during childhood and hip fracture risk in later life. We hypothesized that BMI development is linked to variation in pubertal timing as assessed by menarcheal age (MENA) which in turn, is related to peak bone mass (PBM) and hip fracture risk in elderly. Methods: We studied in a 124 healthy female cohort the relationship between MENA and BMI from birth to maturity, and DXA-measured femoral neck (FN) aBMD at 20.4year. At this age, we also measured bone strength related microstructure components of distal tibia by HR-pQCT. Results: At 20.4â±â0.6year, FN aBMD (mg/cm2), cortical thickness (ÎŒm), and trabecular density (mgHA/cm3) of distal tibia were inversely related to MENA (Pâ=â0.023, 0.015, and 0.041, respectively) and positively to BMI changes from 1.0 to 12.4years (Pâ=â0.031, 0.089, 0.016, respectively). Significant inverse (Pâ<â0.022 to <0.001) correlations (Râ=ââ0.21 to -0.42) were found between MENA and BMI from 7.9 to 20.4years, but neither at birth nor at 1.0year. Linear regression indicated that MENA Z-score was inversely related to BMI changes not only from 1.0 to 12.4years (Râ=ââ0.35, Pâ=â0.001), but also from 1.0 to 8.9years, (Râ=ââ0.24, Pâ=â0.017), i.e., before pubertal maturation. Conclusion: BMI gain during childhood is associated with pubertal timing, which in turn, is correlated with several bone traits measured at PBM including FN aBMD, cortical thickness, and volumetric trabecular density of distal tibia. These data complement the reported relationship between childhood BMI gain and hip fracture risk in later lif
Population demography of an endangered lizard, the Blue Mountains Water Skink.
BACKGROUND: Information on the age structure within populations of an endangered species can facilitate effective management. The Blue Mountains Water Skink (Eulamprus leuraensis) is a viviparous scincid lizard that is restricted toâ<â40 isolated montane swamps in south-eastern Australia. We used skeletochronology of phalanges (corroborated by mark-recapture data) to estimate ages of 222 individuals from 13 populations.
RESULTS: These lizards grow rapidly, from neonatal size (30âmm snout-vent length) to adult size (about 70âmm SVL) within two to three years. Fecundity is low (mean 2.9 offspring per litter) and is affected by maternal body length and age. Offspring quality may decline with maternal age, based upon captive-born neonates (older females gave birth to slower offspring). In contrast to its broadly sympatric (and abundant) congener E. tympanum, E. leuraensis is short-lived (maximum 6âyears, vs 15âyears for E. tympanum). Litter size and offspring size are similar in the two species, but female E. leuraensis reproduce annually whereas many E. tympanum produce litters biennially. Thus, a low survival rate (rather than delayed maturation or low annual fecundity) is the key reason why E. leuraensis is endangered. Our 13 populations exhibited similar growth rates and population age structures despite substantial variation in elevation, geographic location and swamp size. However, larger populations (based on a genetic estimate of effective population size) contained older lizards, and thus a wider variance in ages.
CONCLUSION: Our study suggests that low adult survival rates, as well as specialisation on a rare and fragmented habitat type (montane swamps) contribute to the endangered status of the Blue Mountains Water Skink
On Proper Polynomial Maps of
Two proper polynomial maps are said to be \emph{equivalent} if there exist such that .
We investigate proper polynomial maps of arbitrary topological degree up to equivalence. Under the further assumption that the maps are Galois
coverings we also provide the complete description of equivalence classes. This
widely extends previous results obtained by Lamy in the case .Comment: 15 pages. Final version, to appear in Journal of Geometric Analysi
Cosmology, cohomology, and compactification
Ashtekar and Samuel have shown that Bianchi cosmological models with compact
spatial sections must be of Bianchi class A. Motivated by general results on
the symmetry reduction of variational principles, we show how to extend the
Ashtekar-Samuel results to the setting of weakly locally homogeneous spaces as
defined, e.g., by Singer and Thurston. In particular, it is shown that any
m-dimensional homogeneous space G/K admitting a G-invariant volume form will
allow a compact discrete quotient only if the Lie algebra cohomology of G
relative to K is non-vanishing at degree m.Comment: 6 pages, LaTe
On the embeddability of certain infinitely divisible probability measures on Lie groups
We describe certain sufficient conditions for an infinitely divisible
probability measure on a class of connected Lie groups to be embeddable in a
continuous one-parameter convolution semigroup of probability measures.
(Theorem 1.3). This enables us in particular to conclude the embeddability of
all infinitely divisible probability measures on certain Lie groups, including
the so called Walnut group (Corollary 1.5). The embeddability is concluded also
under certain other conditions (Corollary 1.4 and Theorem 1.6).Comment: 24 page
Quantum affine Cartan matrices, Poincare series of binary polyhedral groups, and reflection representations
We first review some invariant theoretic results about the finite subgroups
of SU(2) in a quick algebraic way by using the McKay correspondence and quantum
affine Cartan matrices. By the way it turns out that some parameters
(a,b,h;p,q,r) that one usually associates with such a group and hence with a
simply-laced Coxeter-Dynkin diagram have a meaningful definition for the
non-simply-laced diagrams, too, and as a byproduct we extend Saito's formula
for the determinant of the Cartan matrix to all cases. Returning to invariant
theory we show that for each irreducible representation i of a binary
tetrahedral, octahedral, or icosahedral group one can find a homomorphism into
a finite complex reflection group whose defining reflection representation
restricts to i.Comment: 19 page
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