How Much Are You Paying To Teach?

Those of us who have the good fortune to be married to a member of the teaching profession share a common bond; the depressing, from the educator\u27s viewpoint, state of teacher salaries is a frequent topic of conversation in our homes. These discussions usually begin with our mate bemoaning the fact that his or her income lags far behind this or that other occupation. We then respond in order to soothe the ego, and perhaps if the discussion occurs at the dinner table, to move the conversation to a more palatable subject that the hours are short, the vacations long, and the nonpecuniary rewards of the profession are without equal. Often as not, if the students have been manageable that day, this answer will suffice. As an economist, married to an educator employed by the Virginia public school system, the proper response to this familiar dissatisfac­tion with salaries is a more vexing problem

The Influence of Representation in Intrastate Grant Disbursement

A common rationale in allocating government grants and aid is income redistribution. Consider receipts by individuals for example. Under a host of programs, economic hardship is a necessary and often sufficient condition for receiving benefits. A second major beneficiary category for federal and state aid is municipalities and localities. There again equity considerations frequently affect grant receipts, although purely demographic factors such as population can also influence the level of assistance. Considered together, one would expect disbursements across these two broad aid categories to be explained by varying economic and demographic factors consistent with the intended equity rationale. Recently, however, economists have begun to question the primacy of the proffered redistributive motive. They suggest instead that political influence vested in committee assignments, chairmanships, and legislative tenure accounts significantly, if not exclusively, for the allocation of federal grants across states. At present, the empirical support for this hypothesis is growing, but neither overwhelming nor without its critics. Perhaps the fairest assessment of the empirical literature on this issue is that it is in its incipiency

The Information Geometry of the Ising Model on Planar Random Graphs

It has been suggested that an information geometric view of statistical mechanics in which a metric is introduced onto the space of parameters provides an interesting alternative characterisation of the phase structure, particularly in the case where there are two such parameters -- such as the Ising model with inverse temperature $\beta$ and external field $h$. In various two parameter calculable models the scalar curvature ${\cal R}$ of the information metric has been found to diverge at the phase transition point $\beta_c$ and a plausible scaling relation postulated: ${\cal R} \sim |\beta- \beta_c|^{\alpha - 2}$. For spin models the necessity of calculating in non-zero field has limited analytic consideration to 1D, mean-field and Bethe lattice Ising models. In this letter we use the solution in field of the Ising model on an ensemble of planar random graphs (where $\alpha=-1, \beta=1/2, \gamma=2$) to evaluate the scaling behaviour of the scalar curvature, and find ${\cal R} \sim | \beta- \beta_c |^{-2}$. The apparent discrepancy is traced back to the effect of a negative $\alpha$.Comment: Version accepted for publication in PRE, revtex

A projective Dirac operator on CP^2 within fuzzy geometry

We propose an ansatz for the commutative canonical spin_c Dirac operator on CP^2 in a global geometric approach using the right invariant (left action-) induced vector fields from SU(3). This ansatz is suitable for noncommutative generalisation within the framework of fuzzy geometry. Along the way we identify the physical spinors and construct the canonical spin_c bundle in this formulation. The chirality operator is also given in two equivalent forms. Finally, using representation theory we obtain the eigenspinors and calculate the full spectrum. We use an argument from the fuzzy complex projective space CP^2_F based on the fuzzy analogue of the unprojected spin_c bundle to show that our commutative projected spin_c bundle has the correct SU(3)-representation content.Comment: reduced to 27 pages, minor corrections, minor improvements, typos correcte

Fuzzy Scalar Field Theory as a Multitrace Matrix Model

We develop an analytical approach to scalar field theory on the fuzzy sphere based on considering a perturbative expansion of the kinetic term. This expansion allows us to integrate out the angular degrees of freedom in the hermitian matrices encoding the scalar field. The remaining model depends only on the eigenvalues of the matrices and corresponds to a multitrace hermitian matrix model. Such a model can be solved by standard techniques as e.g. the saddle-point approximation. We evaluate the perturbative expansion up to second order and present the one-cut solution of the saddle-point approximation in the large N limit. We apply our approach to a model which has been proposed as an appropriate regularization of scalar field theory on the plane within the framework of fuzzy geometry.Comment: 1+25 pages, replaced with published version, minor improvement

The Quasinormal Mode Spectrum of a Kerr Black Hole in the Eikonal Limit

It is well established that the response of a black hole to a generic perturbation is characterized by a spectrum of damped resonances, called quasinormal modes; and that, in the limit of large angular momentum ($l \gg 1$), the quasinormal mode frequency spectrum is related to the properties of unstable null orbits. In this paper we develop an expansion method to explore the link. We obtain new closed-form approximations for the lightly-damped part of the spectrum in the large-$l$ regime. We confirm that, at leading order in $l$, the resonance frequency is linked to the orbital frequency, and the resonance damping to the Lyapunov exponent, of the relevant null orbit. We go somewhat further than previous studies to establish (i) a spin-dependent correction to the frequency at order $1 / l$ for equatorial ($m = \pm l$) modes, and (ii) a new result for polar modes ($m = 0$). We validate the approach by testing the closed-form approximations against frequencies obtained numerically with Leaver's method.Comment: 18 pages, 3 tables, 3 figure

A Photometric Study of the Young Stellar Population Throughout the lambda Orionis Star-Forming Region

We present VRI photometry of 320,917 stars with 11 < R < 18 throughout the lambda Orionis star-forming region. We statistically remove the field stars and identify a representative PMS population throughout the interior of the molecular ring. The spatial distribution of this population shows a concentration of PMS stars around lambda Ori and in front of the B35 dark cloud. Few PMS stars are found outside these pockets of high stellar density, suggesting that star formation was concentrated in an elongated cloud extending from B35 through lambda Ori to the B30 cloud. We find a lower limit for the global stellar mass of about 500 Mo. We find that the global ratio of low- to high-mass stars is similar to that predicted by the field initial mass function, but this ratio varies strongly as a function of position in the star-forming region. Locally, the star-formation process does not produce a universal initial mass function. We construct a history of the star-forming complex. This history incorporates a recent supernova to explain the distribution of stars and gas today.Comment: 42 pages, 11 figures; to appear in the Astronomical Journa

The Hubble Space Telescope high speed photometer

The Hubble Space Telescope will provide the opportunity to perform precise astronomical photometry above the disturbing effects of the atmosphere. The High Speed Photometer is designed to provide the observatory with a stable, precise photometer with wide dynamic range, broad wavelenth coverage, time resolution in the microsecond region, and polarimetric capability. Here, the scientific requirements for the instrument are examined, the unique design features of the photometer are explored, and the improvements to be expected over the performance of ground-based instruments are projected

Effective Potential on Fuzzy Sphere

The effective potential of quantized scalar field on fuzzy sphere is evaluated to the two-loop level. We see that one-loop potential behaves like that in the commutative sphere and the Coleman-Weinberg mechanism of the radiatively symmetry breaking could be also shown in the fuzzy sphere system. In the two-loop level, we use the heavy-mass approximation and the high-temperature approximation to perform the evaluations. The results show that both of the planar and nonplanar Feynman diagrams have inclinations to restore the symmetry breaking in the tree level. However, the contributions from planar diagrams will dominate over those from nonplanar diagrams by a factor N^2. Thus, at heavy-mass limit or high-temperature system the quantum field on the fuzzy sphere will behave like those on the commutative sphere. We also see that there is a drastic reduction of the degrees of freedom in the nonplanar diagrams when the particle wavelength is smaller than the noncommutativity scale.Comment: Latex 18 pages, some typos correcte

Bioactive nutrients - Time for tolerable upper intake levels to address safety.

There is increasing interest by consumers, researchers, and regulators into the roles that certain bioactive compounds, derived from plants and other natural sources, can play in health maintenance and promotion, and even prolonging a productive quality of life. Research has rapidly emerged suggesting that a wide range of compounds and mixtures in and from plants (such as fruits and vegetables, tea and cocoa) and animals (such as fish and probiotics) may exert substantial health benefits. There is interest in exploring the possibility of establishing recommended intakes or dietary guidance for certain bioactive substances to help educate consumers. A key aspect of establishing dietary guidance is the assessment of safety/toxicity of these substances. Toxicologists need to be involved in both the development of the safety framework and in the evaluation of the science to establish maximum intake/upper limits