On the classical WN(l)W_N^{(l)} algebras

We analyze the W_N^l algebras according to their conjectured realization as the second Hamiltonian structure of the integrable hierarchy resulting from the interchange of x and t in the l^{th} flow of the sl(N) KdV hierarchy. The W_4^3 algebra is derived explicitly along these lines, thus providing further support for the conjecture. This algebra is found to be equivalent to that obtained by the method of Hamiltonian reduction. Furthermore, its twisted version reproduces the algebra associated to a certain non-principal embedding of sl(2) into sl(4), or equivalently, the u(2) quasi-superconformal algebra. The general aspects of the W_N^l algebras are also presented.Comment: 28 page

Discrete Geometric Structures in Homogenization and Inverse Homogenization with application to EIT

We introduce a new geometric approach for the homogenization and inverse homogenization of the divergence form elliptic operator with rough conductivity coefficients $\sigma(x)$ in dimension two. We show that conductivity coefficients are in one-to-one correspondence with divergence-free matrices and convex functions $s(x)$ over the domain $\Omega$. Although homogenization is a non-linear and non-injective operator when applied directly to conductivity coefficients, homogenization becomes a linear interpolation operator over triangulations of $\Omega$ when re-expressed using convex functions, and is a volume averaging operator when re-expressed with divergence-free matrices. Using optimal weighted Delaunay triangulations for linearly interpolating convex functions, we obtain an optimally robust homogenization algorithm for arbitrary rough coefficients. Next, we consider inverse homogenization and show how to decompose it into a linear ill-posed problem and a well-posed non-linear problem. We apply this new geometric approach to Electrical Impedance Tomography (EIT). It is known that the EIT problem admits at most one isotropic solution. If an isotropic solution exists, we show how to compute it from any conductivity having the same boundary Dirichlet-to-Neumann map. It is known that the EIT problem admits a unique (stable with respect to $G$-convergence) solution in the space of divergence-free matrices. As such we suggest that the space of convex functions is the natural space in which to parameterize solutions of the EIT problem

X rays from old open clusters: M 67 and NGC 188

We have observed the old open clusters M 67 and NGC 188 with the ROSAT PSPC. In M 67 we detect a variety of X-ray sources. The X-ray emission by a cataclysmic variable, a single hot white dwarf, two contact binaries, and some RS CVn systems is as expected. The X-ray emission by two binaries located below the subgiant branch in the Hertzsprung Russell diagram of the cluster, by a circular binary with a cool white dwarf, and by two eccentric binaries with orbital period > 700 d is puzzling. Two members of NGC 188 are detected, including the FK Com type star D719. Another possible FK Com type star, probably not a member of NGC 188, is also detected.Comment: 10 pages, 5 figures. Accepted for publication on Astronomy & Astrophysic

The Boltzmann Equation in Classical Yang-Mills Theory

We give a detailed derivation of the Boltzmann equation, and in particular its collision integral, in classical field theory. We first carry this out in a scalar theory with both cubic and quartic interactions and subsequently in a Yang-Mills theory. Our method is not relied on a doubling of the fields, rather it is based on a diagrammatic approach representing the classical solution to the problem.Comment: 24 pages, 7 figures; v2: typos corrected, reference added, published in Eur. Phys. J.

Integrability of the quantum KdV equation at c = -2

We present a simple a direct proof of the complete integrability of the quantum KdV equation at $c=-2$, with an explicit description of all the conservation laws.Comment: 9 page

Stellar Radial Velocities in the Old Open Cluster M67 (NGC 2682) I. Memberships, Binaries, and Kinematics

(Abridged) We present results from 13776 radial-velocity (RV) measurements of 1278 candidate members of the old (4 Gyr) open cluster M67 (NGC 2682). The measurements are the results of a long-term survey that includes data from seven telescopes with observations for some stars spanning over 40 years. For narrow-lined stars, RVs are measured with precisions ranging from about 0.1 to 0.8 km/s. The combined stellar sample reaches from the brightest giants in the cluster down to about 4 magnitudes below the main-sequence turnoff (V = 16.5), covering a mass range of about 1.34 MSun to 0.76 MSun. Spatially, the sample extends to a radius of 30 arcmin (7.4 pc in projection at a distant of 850 pc or 6-7 core radii). We find M67 to have a mean RV of +33.64 km/s (with an internal precision of +/- 0.03 km/s). For stars with >=3 measurements, we derive RV membership probabilities and identify RV variables, finding 562 cluster members, 142 of which show significant RV variability. We use these cluster members to construct a color-magnitude diagram and identify a rich sample of stars that lie far from the standard single star isochrone, including the well-known blue stragglers, sub-subgiants and yellow giants. These exotic stars have a binary frequency of (at least) 80%, more than three times that detected for stars in the remainder of the sample. We confirm that the cluster is mass segregated, finding the binaries to be more centrally concentrated than the single stars in our sample at the 99.8% confidence level. The blue stragglers are centrally concentrated as compared to the solar-type main-sequence single stars in the cluster at the 99.7% confidence level. Accounting for both measurement precision and undetected binaries, we derive a RV dispersion in M67 of 0.59 +0.07 -0.06 km/s, which yields a virial mass for the cluster of 2100 +610 -550 MSun. WIYN Open Cluster Study. LXVII.Comment: 19 pages, 10 figures, 4 tables, accepted for publication in The Astronomical Journa