City versus Countryside: Environmental Equity in Context

This Article takes an approach to the problem of environmental equity that is different from the remedies advocated by the leaders of the environmental equity movement. The plea that the benefits of environmental protection be extended to all groups in society is, of course, a legitimate one, but the movement is too narrowly focused and its aims are too modest. I dissent from the two central premises held by environmental equity advocates. First, the movement assumes that judicially recognized and enforced rights will lead to improved public health. Second, the movement asserts that disadvantaged communities should adopt a “Not in My Backyard” (NIMBY) strategy. In contrast, I argue that the current focus of the environmental equity movement, important as it is, is too narrow because the legal strategy of the civil rights movement is largely inapplicable to environmental issues. Environmental protection is not a rights-based movement. Thus, the judiciary’s role in promoting environmental quality is limited compared to its role in promoting racial justice through the recognition and enforcement of constitutionally-based civil rights. In addition, I argue that the NIMBY strategy is equally shortsighted. Environmental equity takes current environmental protection strategies as a given at a time when the science and ethics of environmental protection are undergoing a profound re-evaluation

City versus Countryside: Environmental Equity in Context

This Article takes an approach to the problem of environmental equity that is different from the remedies advocated by the leaders of the environmental equity movement. The plea that the benefits of environmental protection be extended to all groups in society is, of course, a legitimate one, but the movement is too narrowly focused and its aims are too modest. I dissent from the two central premises held by environmental equity advocates. First, the movement assumes that judicially recognized and enforced rights will lead to improved public health. Second, the movement asserts that disadvantaged communities should adopt a “Not in My Backyard” (NIMBY) strategy. In contrast, I argue that the current focus of the environmental equity movement, important as it is, is too narrow because the legal strategy of the civil rights movement is largely inapplicable to environmental issues. Environmental protection is not a rights-based movement. Thus, the judiciary’s role in promoting environmental quality is limited compared to its role in promoting racial justice through the recognition and enforcement of constitutionally-based civil rights. In addition, I argue that the NIMBY strategy is equally shortsighted. Environmental equity takes current environmental protection strategies as a given at a time when the science and ethics of environmental protection are undergoing a profound re-evaluation

Transcendence measures and algebraic growth of entire functions

In this paper we obtain estimates for certain transcendence measures of an entire function $f$. Using these estimates, we prove Bernstein, doubling and Markov inequalities for a polynomial $P(z,w)$ in ${\Bbb C}^2$ along the graph of $f$. These inequalities provide, in turn, estimates for the number of zeros of the function $P(z,f(z))$ in the disk of radius $r$, in terms of the degree of $P$ and of $r$. Our estimates hold for arbitrary entire functions $f$ of finite order, and for a subsequence $\{n_j\}$ of degrees of polynomials. But for special classes of functions, including the Riemann $\zeta$-function, they hold for all degrees and are asymptotically best possible. From this theory we derive lower estimates for a certain algebraic measure of a set of values $f(E)$, in terms of the size of the set $E$.Comment: 40 page

A Detailed Kinematic Map of Cassiopeia A's Optical Main Shell and Outer High-Velocity Ejecta

We present three-dimensional kinematic reconstructions of optically emitting material in the young Galactic supernova remnant Cassiopeia A (Cas A). These Doppler maps have the highest spectral and spatial resolutions of any previous survey of Cas A and represent the most complete catalog of its optically emitting material to date. We confirm that the bulk of Cas A's optically bright ejecta populate a torus-like geometry tilted approximately 30 degrees with respect to the plane of the sky with a -4000 to +6000 km/s radial velocity asymmetry. Near-tangent viewing angle effects and an inhomogeneous surrounding CSM/ISM environment suggest that this geometry and velocity asymmetry may not be faithfully representative of the remnant's true 3D structure or the kinematic properties of the original explosion. The majority of the optical ejecta are arranged in several well-defined and nearly circular ring-like structures with diameters between approximately 30 arcsec (0.5 pc) and 2 arcmin (2 pc). These ejecta rings appear to be a common phenomenon of young core-collapse remnants and may be associated with post-explosion input of energy from plumes of radioactive 56Ni-rich ejecta that rise, expand, and compress non-radioactive material. Our optical survey also encompassed Cas A's faint outlying ejecta knots and exceptionally high-velocity NE and SW streams of S-rich debris often referred to as `jets'. These outer knots, which exhibit a chemical make-up suggestive of an origin deep within the progenitor star, appear to be arranged in opposing and wide-angle outflows with opening half-angles of approximately 40 degrees.Comment: 15 pages, 11 figures, accepted by ApJ, associated movie files can be found at https://www.cfa.harvard.edu/~dmilisav

Multi-battle contests

We study equilibrium in a multistage race in which players compete in a sequence of simultaneous move component contests. Players may win a prize for winning each component contest, as well as a prize for winning the overall race. Each component contest is an all-pay auction with complete information. We characterize the unique equilibrium analytically and demonstrate that it exhibits endogenous uncertainty. Even a large lead by one player does not fully discourage the other player, and each feasible state is reached with positive probability in equilibrium (pervasiveness). Total effort may exceed the value of the prize by a factor that is proportional to the maximum number of stages. Important applications are to war, sports, and R&D contests and the results have empirical counterparts there

Pade interpolation by F-polynomials and transfinite diameter

We define $F$-polynomials as linear combinations of dilations by some frequencies of an entire function $F$. In this paper we use Pade interpolation of holomorphic functions in the unit disk by $F$-polynomials to obtain explicitly approximating $F$-polynomials with sharp estimates on their coefficients. We show that when frequencies lie in a compact set $K\subset\mathbb C$ then optimal choices for the frequencies of interpolating polynomials are similar to Fekete points. Moreover, the minimal norms of the interpolating operators form a sequence whose rate of growth is determined by the transfinite diameter of $K$. In case of the Laplace transforms of measures on $K$, we show that the coefficients of interpolating polynomials stay bounded provided that the frequencies are Fekete points. Finally, we give a sufficient condition for measures on the unit circle which ensures that the sums of the absolute values of the coefficients of interpolating polynomials stay bounded.Comment: 16 page