The bisymplectomorphism group of a bounded symmetric domain

An Hermitian bounded symmetric domain in a complex vector space, given in its circled realization, is endowed with two natural symplectic forms: the flat form and the hyperbolic form. In a similar way, the ambient vector space is also endowed with two natural symplectic forms: the Fubini-Study form and the flat form. It has been shown in arXiv:math.DG/0603141 that there exists a diffeomorphism from the domain to the ambient vector space which puts in correspondence the above pair of forms. This phenomenon is called symplectic duality for Hermitian non compact symmetric spaces. In this article, we first give a different and simpler proof of this fact. Then, in order to measure the non uniqueness of this symplectic duality map, we determine the group of bisymplectomorphisms of a bounded symmetric domain, that is, the group of diffeomorphisms which preserve simultaneously the hyperbolic and the flat symplectic form. This group is the direct product of the compact Lie group of linear automorphisms with an infinite-dimensional Abelian group. This result appears as a kind of Schwarz lemma.Comment: 19 pages. Version 2: minor correction

Vacuum Energy: Cosmological Constant or Quintessence?

For a flat universe presently dominated by smooth energy, either cosmological constant (LCDM) or quintessence (QCDM), we calculate the asymptotic collapsed mass fraction as function of the present ratio of smooth energy to matter energy $\mathcal R_0$. Identifying the normalized collapsed fraction as a conditional probability for habitable galaxies, we observe that the observed present ratio $\mathcal R_0 \sim 2$ is likely in LCDM, but more likely in QCDM. Inverse application of Bayes' Theorem makes the Anthropic Principle a predictive scientific principle: the data implies that the prior probability for $\mathcal R_0$ must be essentially flat over the anthropically allowed range. Interpreting this prior as a distribution over {\em theories} lets us predict that any future theory of initial conditions must be indifferent to $\mathcal R_0$. This application of the Anthropic Principle does not demand the existence of other universes.Comment: 17 pages AAS LATEX, including 2 tables, 3 figures (Postscript

Weighted Bergman kernels and virtual Bergman kernels

We introduce the notion of "virtual Bergman kernel" and apply it to the computation of the Bergman kernel of "domains inflated by Hermitian balls", in particular when the base domain is a bounded symmetric domain.Comment: 12 pages. One-hour lecture for graduate students, SCV 2004, August 2004, Beijing, P.R. China. V2: typo correcte

Measurement of the hyperfine structure of the S1/2-D5/2 transition in 43Ca+

The hyperfine structure of the S1/2-D5/2 quadrupole transition at 729 nm in 43Ca+ has been investigated by laser spectroscopy using a single trapped 43Ca+ ion. We determine the hyperfine structure constants of the metastable level as A=-3.8931(2) MHz and B=-4.241(4) MHz. The isotope shift of the transition with respect to 40Ca+ was measured to be 4134.713(5) MHz. We demonstrate the existence of transitions that become independent of the first-order Zeeman shift at non-zero low magnetic fields. These transitions might be better suited for building a frequency standard than the well-known 'clock transitions' between m=0 levels at zero magnetic field.Comment: corrected for sign errors in the hyperfine constants. No corrections to were made to the data analysi

A 2-year prospective study of patient-relevant outcomes in patients operated on for knee osteoarthritis with tibial osteotomy

BACKGROUND: Tibial osteotomy is a treatment for younger and/or physically active patients suffering from uni-compartmental knee osteoarthritis. The open wedge osteotomy by the hemicallotasis technique includes the use of external fixation. The use of external fixation has several advantages, as early mobilization and the opportunity for optimal correction. However, the hemicallotasis technique has also been described as a cumbersome procedure for the patient. The aim of this study was to prospectively evaluate patient-relevant outcomes during the first 2 post-operative years. Especially the treatment period, during which external fixation was used, was closely monitored. METHODS: In an uncontrolled study, fifty-eight consecutive patients, 30 men and 28 women (mean age 54 years) were operated on by the hemicallotasis technique were evaluated with the patient-relevant outcome measure Knee injury and Osteoarthritis Outcome Score (KOOS) preoperatively, during the treatment with external fixation, one week after removal of the external fixation, at 6 months, and at one and two years postoperatively. RESULTS: At the 2-year postoperative follow-up, all subscales of the KOOS were improved (p < 0.001), mostly in pain (41–80 on a 0–100 worst to best scale) and knee-related quality of life (21–61 on a 0–100 worst to best scale), compared to the preoperative status. Significant improvements in pain and other symptoms, function of daily life and quality of life were seen already during the treatment period (mean 98 ± 18 days) with the external fixation. More demanding functions such as kneeling, squatting, jumping and running, were improved first after extraction of the external fixation device and the pins. CONCLUSION: Tibial osteotomy by the hemicallotasis technique yields large improvement in self-rated pain, function and quality of life, which persists over two years. Surprisingly, large improvements occurred already during the immediate post-operative period when the external fixation was still used

Influence of adatom interactions on second layer nucleation

We develop a theory for the inclusion of adatom interactions in second layer nucleation occurring in epitaxial growth. The interactions considered are due to ring barriers between pairs of adatoms and binding energies of unstable clusters. The theory is based on a master equation, which describes the time development of microscopic states that are specified by cluster configurations on top of an island. The transition rates are derived by scaling arguments and tested against kinetic Monte-Carlo simulations. As an application we reanalyze experiments to determine the step edge barrier for Ag/Pt(111).Comment: 4 pages, 4 figure

A High Merger Fraction in the Rich Cluster MS1054-03 at z=0.83: Direct Evidence for Hierarchical Formation of Massive Galaxies

We present a morphological study of the galaxy population of the luminous X-ray cluster MS1054-03 at z=0.83. The sample consists of 81 spectroscopically confirmed cluster members in a 3 x 2 Mpc area imaged in F606W and F814W with WFPC2. We find thirteen ongoing mergers in MS1054-03, comprising 17% of the L > L* cluster population. Most of these mergers will likely evolve into luminous (\sim 2 L*) elliptical galaxies, and some may evolve into S0 galaxies. Assuming the galaxy population in MS1054-03 is typical for its redshift it is estimated that \sim 50% of present-day cluster ellipticals experienced a major merger at z < 1. The mergers are preferentially found in the outskirts of the cluster, and probably occur in small infalling clumps. Morphologies, spectra, and colors of the mergers show that their progenitors were typically E/S0s or early-type spirals with mean stellar formation redshifts z* \gtrsim 1.7. The red colors of the merger remnants are consistent with the low scatter in the color-magnitude relation in rich clusters at lower redshift. The discovery of a high fraction of mergers in this young cluster is direct evidence against formation of ellipticals in a single ``monolithic'' collapse at high redshift, and in qualitative agreement with predictions of hierarchical models for structure formation.Comment: Added GIF version of Figure 1. At http://www.astro.rug.nl/~dokkum/preprints/merger_fig1.eps.gz the PS file is available. Accepted for publication in ApJ Letter