Gravitational Constraint Combinations Generate a Lie Algebra

We find a first--order partial differential equation whose solutions are all ultralocal scalar combinations of gravitational constraints with Abelian Poisson brackets between themselves. This is a generalisation of the Kucha\v{r} idea of finding alternative constraints for canonical gravity. The new scalars may be used in place of the hamiltonian constraint of general relativity and, together with the usual momentum constraints, replace the Dirac algebra for pure gravity with a true Lie algebra: the semidirect product of the Abelian algebra of the new constraint combinations with the algebra of spatial diffeomorphisms.Comment: 10 pages, latex, submitted to Classical and Quantum Gravity. Section 3 is expanded and an additional solution provided, minor errors correcte

Report on the first round of the Mock LISA Data Challenges

The Mock LISA Data Challenges (MLDCs) have the dual purpose of fostering the development of LISA data analysis tools and capabilities, and demonstrating the technical readiness already achieved by the gravitational-wave community in distilling a rich science payoff from the LISA data output. The first round of MLDCs has just been completed: nine challenges consisting of data sets containing simulated gravitational-wave signals produced either by galactic binaries or massive black hole binaries embedded in simulated LISA instrumental noise were released in June 2006 with deadline for submission of results at the beginning of December 2006. Ten groups have participated in this first round of challenges. All of the challenges had at least one entry which successfully characterized the signal to better than 95% when assessed via a correlation with phasing ambiguities accounted for. Here, we describe the challenges, summarize the results and provide a first critical assessment of the entries

Shades of Grey: Ethical Dilemmas

No abstract available

Fluctuations and massive separation in three-dimensional shock-wave/boundary-layer interactions

Shock-wave unsteadiness was observed in rapidly compressed supersonic turbulent boundary layer flows with significant separation. A Mach 2.85 shock-wave/turbulent boundary layer flow was set up over a series of cylinder-flare bodies in the High Reynolds Number Channel 1. The transition from fully attached to fully separated flow was studied using axisymmetric flares with increasing compression angles. In the second phase, the 30 deg flare was inclined relative to the cylinder axis, so that the effect on a separated flow of increasing 3 dimensionality could be observed. Two 3-D separated cases are examined. A simple conditional sampling technique is applied to the data to group them according to an associated shock position. Mean velocities and turbulent kinetic energies, computed from the conditionally samples data, are compared to those from the unsorted data and to computed values. Three basic questions were addressed: can conditional sampling be used to provide snapshots of the flow; are averaged turbulence quantities dominated by the bimodal nature of the interaction; and is the shock unsteadiness really important to computational accuracy

The Energy of the Gamma Metric in the M{\o}ller Prescription

We obtain the energy distribution of the gamma metric using the energy-momentum complex of M{\o}ller. The result is the same as obtained by Virbhadra in the Weinberg prescription

The average X-ray/gamma-ray spectrum of radio-quiet Seyfert 1s

We have obtained the average 1--500 keV spectrum of radio-quiet Seyfert 1s using data from EXOSAT, Ginga, HEAO, and GRO/OSSE. The spectral fit to the combined average EXOSAT and OSSE data is fully consistent with that for Ginga and OSSE, confirming results from an earlier Ginga/OSSE sample. The average spectrum is well-fitted by a power-law X-ray continuum with an energy spectral index of $\alpha \simeq 0.9$ moderately absorbed by an ionized medium and with a Compton reflection component. A high-energy cutoff (or a break) in the the power-law component at a few hundred keV or more is required by the data. We also show that the corresponding average spectrum from HEAO A1 and A4 is fully compatible with that obtained from EXOSAT, Ginga and OSSE. These results confirm that the apparent discrepancy between the results of Ginga (with $\alpha \simeq 0.9$) and the previous results of EXOSAT and HEAO (with $\alpha \simeq 0.7$) is indeed due to ionized absorption and Compton reflection first taken into account for Ginga but not for the previous missions. Also, our results confirm that the Seyfert-1 spectra are on average cut off in gamma-rays at energies of at least a few hundred keV, not at $\sim 40$ keV (as suggested earlier by OSSE data alone). The average spectrum is compatible with emission from either an optically-thin relativistic thermal plasma in a disk corona, or with a nonthermal plasma with a power-law injection of relativistic electrons.Comment: 7 pages, 3 Postscript figures, MNRAS accepte

Fermionic Symmetries: Extension of the two to one Relationship Between the Spectra of Even-Even and Neighbouring Odd mass Nuclei

In the single j shell there is a two to one relationship between the spectra of certain even-even and neighbouring odd mass nuclei e.g. the calculated energy levels of J=0^+ states in ^{44}Ti are at twice the energies of corresponding levels in ^{43}Ti(^{43}Sc) with J=j=7/2. Here an approximate extension of the relationship is made by adopting a truncated seniority scheme i.e. for ^{46}Ti and ^{45}Sc we get the relationship if we do not allow the seniority v=4 states to mix with the v=0 and v=2 states. Better than that, we get very close to the two to one relationship if seniority v=4 states are admixed perturbatively. In addition, it is shown that the higher isospin states do not contain seniority 4 admixtures.Comment: 11 pages, RevTex file and no figures, typos added, references changed and changed content

On the stability of solutions of semilinear elliptic equations with Robin boundary conditions on Riemannian manifolds

We investigate existence and nonexistence of stationary stable nonconstant solutions, i.e. patterns, of semilinear parabolic problems in bounded domains of Riemannian manifolds satisfying Robin boundary conditions. These problems arise in several models in applications, in particular in Mathematical Biology. We point out the role both of the nonlinearity and of geometric objects such as the Ricci curvature of the manifold, the second fundamental form of the boundary of the domain and its mean curvature. Special attention is devoted to surfaces of revolution and to spherically symmetric manifolds, where we prove refined results

Towards the electron EDM search. Theoretical study of PbF

We report ab initio relativistic correlation calculations of potential curves and spectroscopic constants for four lowest-lying electronic states of the lead monofluoride. We also calculated parameters of the spin-rotational Hamiltonian for the ground and the first excited states including P,T-odd and P-odd terms. In particular, we have obtained hyperfine constants of the $^{207}$Pb nucleus. For the $^2\Pi_{1/2}$ state $A_\perp=-6859.6$ MHz, $A_\|=9726.9$ MHz and for the A$^2\Sigma^+_{1/2}$ $A_\perp=1720.8$ MHz, $A_\|=3073.3$ MHz. Our values of the ground state hyperfine constants are in good agreement with the previous theoretical studies. We discuss and explain seeming disagreement in the sign of the constant $A_\perp$ with the recent experimental data. The effective electric field on the electron $E_{eff}$, which is important for the planned experiment to search for the electric dipole moment of the electron, is found to be 3.3 * 10^{10} V/cm