Public Law by Private Bargain: Title VII Consent Decrees and the Fairness of Negotiated Institutional Reform

Large-scale Title VII remedies are typical of public law litigation, which differs in kind from the conventional compensatory lawsuit. Title VII remedies are commonly adopted by way of consent decrees. By approving these consent decrees, federal courts take responsibility for extensive institutional reforms while acting independently of the adversary process. Courts have frequently approved consent decrees without fair hearings for those whose interests are at stake. Professor Schwarzschild suggests a systematic procedure for approving Title VII consent decrees. This procedure would not discourage settlements, but would ensure that courts act on the basis of fair hearings, consistently with the quasi-legislative character of public law remedies

Large area CCD image sensors for space astronomy

The Defense Advanced Research Projects Agency (DARPA) has a substantial program to develop a 2200 x 2200 pixel CCD (Charge Coupled Device) mosaic array made up of 400 individual CCD's, 110 x 110 pixels square. This type of image sensor appeared to have application in space and ground-based astronomy. Under this grant a CCD television camera system was built which was capable of operating an array of 4 CCD's to explore the suitability of the CCD's to explore the suitability of the CCD for astronomical applications. Two individual packaged CCD's were received and evaluated. Evaluation of the basic characteristics of the best individual chips was encouraging, but the manufacturer found that their yield in manufacturing this design is two low to supply sufficient CDD's for the DARPA mosaic array. The potential utility of large mosaic arrays in astronomy is still substantial and continued monitoring of the manufacturers progress in the coming year is recommended

Distributional Energy-Momentum Densities of Schwarzschild Space-Time

For Schwarzschild space-time, distributional expressions of energy-momentum densities and of scalar concomitants of the curvature tensors are examined for a class of coordinate systems which includes those of the Schwarzschild and of Kerr-Schild types as special cases. The energy-momentum density $\tilde T_\mu^{\nu}(x)$ of the gravitational source and the gravitational energy-momentum pseudo-tensor density $\tilde t_\mu^{\nu}$ have the expressions $\tilde T_\mu^{\nu}(x) =-Mc^2\delta_\mu^0\delta_0^{\nu} \delta^{(3)}x)$ and $\tilde t_\mu^{\nu}=0$, respectively. In expressions of the curvature squares for this class of coordinate systems, there are terms like $\delta^{(3)}(x)/r^3$ and [\delta^{(3)}(x)}]^2, as well as other terms, which are singular at $x=0$. It is pointed out that the well-known expression $R^{\rho\sigma\mu\nu}({}) R_{\rho\sigma\mu\nu}({})$ $=48G^{2}M^{2}/c^{4}r^{6}$ is not correct, if we define $1/r^6 = \lim_{\epsilon\to 0}1/(r^2+\epsilon^2)^3$.}Comment: 21 pages, LaTeX, uses amssymb.sty. To appear in Prog. Theor. Phys. 98 (1997

Absolute spectrophotometry in M31 and M32

For a number of places in the bulge of M31 and for two places in M32 photometric scans from 3300 A to 10,600 A have been obtained with the multichannel spectrometer on the 5-meter Hale telescope. The scans show that in both objects the color temperature (particularly shortwards of 5000 A) decreases towards the center and that the strength of the CN bands increases towards the center in both objects in agreement with earlier observations. The new data can all be interpreted in terms of an increase of heavy element abundance towards the center in both objects by a factor probably less than 2 and by an excess of heavy elements in M31 compared to M32 by a factor probably greater than 2, in qualitative agreement with earlier conclusions

Static spherically symmetric perfect fluid solutions in f(R)f(R) theories of gravity

Static spherically symmetric perfect fluid solutions are studied in metric $f(R)$ theories of gravity. We show that pressure and density do not uniquely determine $f(R)$ ie. given a matter distribution and an equation state, one cannot determine the functional form of $f(R)$. However, we also show that matching the outside Schwarzschild-de Sitter-metric to the metric inside the mass distribution leads to additional constraints that severely limit the allowed fluid configurations.Comment: 5 page

NGC 1300 Dynamics: II. The response models

We study the stellar response in a spectrum of potentials describing the barred spiral galaxy NGC 1300. These potentials have been presented in a previous paper and correspond to three different assumptions as regards the geometry of the galaxy. For each potential we consider a wide range of $\Omega_p$ pattern speed values. Our goal is to discover the geometries and the $\Omega_p$ supporting specific morphological features of NGC 1300. For this purpose we use the method of response models. In order to compare the images of NGC 1300 with the density maps of our models, we define a new index which is a generalization of the Hausdorff distance. This index helps us to find out quantitatively which cases reproduce specific features of NGC 1300 in an objective way. Furthermore, we construct alternative models following a Schwarzschild type technique. By this method we vary the weights of the various energy levels, and thus the orbital contribution of each energy, in order to minimize the differences between the response density and that deduced from the surface density of the galaxy, under certain assumptions. We find that the models corresponding to $\Omega_p\approx16$\ksk and $\Omega_p\approx22$\ksk are able to reproduce efficiently certain morphological features of NGC 1300, with each one having its advantages and drawbacks.Comment: 13 pages, 10 figures, accepted for publication in MNRA

An Expanding Locally Anisotropic (ELA) Metric Describing Matter in an Expanding Universe

It is suggested an expanding locally anisotropic metric (ELA) ansatz describing matter in a flat expanding universe which interpolates between the Schwarzschild (SC) metric near point-like central bodies of mass 'M' and the Robertson-Walker (RW) metric for large radial coordinate: 'ds^2=Z(cdt)2 - 1/Z (dr1-(Hr1/c) Z^(alpha/2+1/2)(cdt))^2-r1^2 dOmega', where 'Z=1-U' with 'U=2GM/(c^2r1)', 'G' is the Newton constant, 'c' is the speed of light, 'H=H(t)=\dot(a)/a' is the time-dependent Hubble rate, 'dOmega=dtheta^2+sin^2(theta) dvarphi^2' is the solid angle element, 'a' is the universe scale factor and we are employing the coordinates 'r1=ar', being 'r' the radial coordinate for which the RW metric is diagonal. For constant exponent 'alpha=alpha0=0' it is retrieved the isotropic McVittie (McV) metric and for 'alpha=alpha0=1' it is retrieved the locally anisotropic Cosmological-Schwarzschild (SCS) metric, both already discussed in the literature. However it is shown that only for constant exponent 'alpha=alpha0> 1' exists an event horizon at the SC radius 'r1=2GM/c^2' and only for 'alpha=alpha0>= 3' space-time is singularity free for this value of the radius. These bounds exclude the previous existing metrics, for which the SC radius is a naked extended singularity. In addition it is shown that for 'alpha=alpha0>5' space-time is approximately Ricci flat in a neighborhood of the event horizon such that the SC metric is a good approximation in this neighborhood. It is further shown that to strictly maintain the SC mass pole at the origin 'r1=0' without the presence of more severe singularities it is required a radial coordinate dependent correction to the exponent 'alpha(r1)=alpha0+alpha1 '2GM/(c^2 r1)' with a negative coefficient 'alpha1<0'. The energy-momentum density, pressures and equation of state are discussed.Comment: 6 pages; 2 figures; covers some of the derivations in arXiv:0907.0847 with corrected terminology and a new discussion of the event horizon