24,013 research outputs found
Reshetikhin's Formula for the Jones Polynomial of a Link: Feynman diagrams and Milnor's Linking Numbers
We use Feynman diagrams to prove a formula for the Jones polynomial of a link
derived recently by N.~Reshetikhin. This formula presents the colored Jones
polynomial as an integral over the coadjoint orbits corresponding to the
representations assigned to the link components. The large limit of the
integral can be calculated with the help of the stationary phase approximation.
The Feynman rules allow us to express the phase in terms of integrals over the
manifold and the link components. Its stationary points correspond to flat
connections in the link complement. We conjecture a relation between the
dominant part of the phase and Milnor's linking numbers. We check it explicitly
for the triple and quartic numbers by comparing their expression through the
Massey product with Feynman diagram integrals.Comment: 33 pages, 11 figure
Aberrations of radio signals traversing the auroral ionosphere Semiannual analysis report, 1 Jul. 1968 - 31 Jan. 1969
Satellite observations of aberrations of radio signals traversing auroral ionosphere indicating decreasing trend in scintillation activit
The Abundances of Light Neutron-Capture Elements in Planetary Nebulae III. The Impact of New Atomic Data on Nebular Selenium and Krypton Abundance Determinations
The detection of neutron(n)-capture elements in several planetary nebulae
(PNe) has provided a new means of investigating s-process nucleosynthesis in
low-mass stars. However, a lack of atomic data has inhibited accurate
trans-iron element abundance determinations in astrophysical nebulae. Recently,
photoionization and recombination data were determined for Se and Kr, the two
most widely detected n-capture elements in nebular spectra. We have
incorporated these new data into the photoionization code Cloudy. To test the
atomic data, numerical models were computed for 15 PNe that exhibit emission
lines from multiple Kr ions. We found systematic discrepancies between the
predicted and observed emission lines that are most likely caused by inaccurate
photoionization and recombination data. These discrepancies were removed by
adjusting the Kr--Kr photoionization cross sections within their
cited uncertainties and the dielectronic recombination rate coefficients by
slightly larger amounts. From grids of models spanning the physical conditions
encountered in PNe, we derive new, broadly applicable ionization correction
factor (ICF) formulae for calculating Se and Kr elemental abundances. The ICFs
were applied to our previous survey of near-infrared [Kr III] and [Se IV]
emission lines in 120 PNe. The revised Se and Kr abundances are 0.1-0.3 dex
lower than former estimates, with average values of [Se/(O, Ar)]=0.120.27
and [Kr/(O, Ar)]=0.820.29, but correlations previously found between their
abundances and other nebular and stellar properties are unaffected. We also
find a tendency for high-velocity PNe that can be associated with the Galactic
thick disk to exhibit larger s-process enrichments than low-velocity PNe
belonging to the thin disk population.Comment: 73 pages, 6 figures, 18 tables, accepted for publication in ApJ
Accounting for Seismic Risk in Financial Analysis of Property Investment
A methodology is presented for making property investment decisions using loss
analysis and the principles of decision analysis. It proposes that the investor choose among
competing investment alternatives on the basis of the certainty equivalent of their net asset value
which depends on the uncertain discounted future net income, uncertain discounted future
earthquake losses, initial equity and the investor’s risk tolerance. The earthquake losses are
modelled using a seismic vulnerability function, the site seismic hazard function, and an
assumption that strong shaking at a site follows a Poisson process. A building-specific
vulnerability approach, called assembly-based vulnerability, or ABV, is used. ABV involves a
simulation approach that includes dynamic structural analyses and damage analyses using
fragility functions and probability distributions on unit repair costs and downtimes for all
vulnerable structural and nonstructural components in a building. The methodology is
demonstrated using some results from a seven-storey reinforced-concrete hotel in Los Angeles
Vibrating quantum billiards on Riemannian manifolds
Quantum billiards provide an excellent forum for the analysis of quantum
chaos. Toward this end, we consider quantum billiards with time-varying
surfaces, which provide an important example of quantum chaos that does not
require the semiclassical () or high quantum-number
limits. We analyze vibrating quantum billiards using the framework of
Riemannian geometry. First, we derive a theorem detailing necessary conditions
for the existence of chaos in vibrating quantum billiards on Riemannian
manifolds. Numerical observations suggest that these conditions are also
sufficient. We prove the aforementioned theorem in full generality for one
degree-of-freedom boundary vibrations and briefly discuss a generalization to
billiards with two or more degrees-of-vibrations. The requisite conditions are
direct consequences of the separability of the Helmholtz equation in a given
orthogonal coordinate frame, and they arise from orthogonality relations
satisfied by solutions of the Helmholtz equation. We then state and prove a
second theorem that provides a general form for the coupled ordinary
differential equations that describe quantum billiards with one
degree-of-vibration boundaries. This set of equations may be used to illustrate
KAM theory and also provides a simple example of semiquantum chaos. Moreover,
vibrating quantum billiards may be used as models for quantum-well
nanostructures, so this study has both theoretical and practical applications.Comment: 23 pages, 6 figures, a few typos corrected. To appear in
International Journal of Bifurcation and Chaos (9/01
Storage tests of nitrogen tetroxide and hydrazine in aluminum containers
Nitrogen tetroxide and hydrazine compatibility with aluminum alloy storage tank
Task 6 storable propellant module environmental control technology Summary report
Thermal control concepts for space storable fluorine hydrazine propulsion modul
Severity of disease and risk of malignant change in hereditary multiple exostoses. A genotype-phenotype study
We performed a prospective genotype-phenotype study using molecular screening and clinical assessment to compare the severity of disease and the risk of sarcoma in 172 individuals (78 families) with hereditary multiple exostoses. We calculated the severity of disease including stature, number of exostoses, number of surgical procedures that were necessary, deformity and functional parameters and used molecular techniques to identify the genetic mutations in affected individuals. Each arm of the genotype-phenotype study was blind to the outcome of the other. Mutations EXT1 and EXT2 were almost equally common, and were identified in 83% of individuals. Non-parametric statistical tests were used. There was a wide variation in the severity of disease. Children under ten years of age had fewer exostoses, consistent with the known age-related penetrance of this condition. The severity of the disease did not differ significantly with gender and was very variable within any given family. The sites of mutation affected the severity of disease with patients with EXT1 mutations having a significantly worse condition than those with EXT2 mutations in three of five parameters of severity (stature, deformity and functional parameters). A single sarcoma developed in an EXT2 mutation carrier, compared with seven in EXT1 mutation carriers. There was no evidence that sarcomas arose more commonly in families in whom the disease was more severe. The sarcoma risk in EXT1 carriers is similar to the risk of breast cancer in an older population subjected to breast-screening, suggesting that a role for regular screening in patients with hereditary multiple exostoses is justifiable. ©2004 British Editorial Society of Bone and Joint Surgery
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