Charity Oversight: An Alternative Approach

In this paper, a former director of the Internal Revenue Services Exempt Organization Division argues that the IRS is structurally ill suited for the task of providing vigorous oversight of the nations growing number of nonprofit organizations. The author proposes a new, national institution, modeled loosely on the corporate sectors National Association of Securities Dealers that would, among other features, derive sufficient funding for vigorous oversight through contributions from nonprofit organizations. The author envisions an amendment to the Internal Revenue Code that would enable the nonprofit organizations to take a credit against excise taxes, particularly the excise tax on the net investment income of private foundations, they would otherwise pay to the federal government. This publication is Hauser Center Working Paper No. 33.4. Hauser Working Paper Series Nos. 33.1-33.9 were prepared as background papers for the Nonprofit Governance and Accountability Symposium October 3-4, 2006.The author, Marcus S. Owens is with Caplin & Drysdale; Chartered

Derivatives of Entropy Rate in Special Families of Hidden Markov Chains

Consider a hidden Markov chain obtained as the observation process of an ordinary Markov chain corrupted by noise. Zuk, et. al. [13], [14] showed how, in principle, one can explicitly compute the derivatives of the entropy rate of at extreme values of the noise. Namely, they showed that the derivatives of standard upper approximations to the entropy rate actually stabilize at an explicit finite time. We generalize this result to a natural class of hidden Markov chains called ``Black Holes.'' We also discuss in depth special cases of binary Markov chains observed in binary symmetric noise, and give an abstract formula for the first derivative in terms of a measure on the simplex due to Blackwell.Comment: The relaxed condtions for entropy rate and examples are taken out (to be part of another paper). The section about general principle and an example to determine the domain of analyticity is taken out (to be part of another paper). A section about binary Markov chains corrupted by binary symmetric noise is adde

Hopf-Galois extensions and an exact sequence for HH-Picard groups

Let $H$ be a Hopf algebra, and $A$ an $H$-Galois extension. We investigate $H$-Morita autoequivalences of $A$, introduce the concept of $H$-Picard group, and we establish an exact sequence linking the $H$-Picard group of $A$ and the Picard group of $A^{{\rm co}H}$.Comment: 35 pages; to appear in J. Algebr

Approaching Carnot efficiency at maximum power in linear response regime

We construct an example of heat engine whose efficiency at maximum power breaks down the previously derived bounds in the linear response regime. Such example takes a classical harmonic oscillator as the working substance undergoing a finite-time Otto cycle. Using a specific kind of shortcut to adiabaticity, valid only in the linear response regime, quasistatic work is performed at arbitrarily short times. The cycle duration is then reduced to the sum of relaxation times during the thermalization strokes exclusively. Thus, power is maximum since the work is maximum (quasistatic work) and the cycle duration is minimum. Efficiency at maximum power can be made arbitrarily close to Carnot efficiency with an appropriate choice of the ratio between the temperatures of the two heat baths.Comment: 6 pages, 2 figure

Effects of truncation in modal representations of thermal convection

The Galerkin (including single-mode and Lorenz) equations were examined for convection in a sphere to determine which physical processes are neglected when the equations of motion are truncated too severely. The conclusions were tested by calculating solutions to the equations of motion for different values of the Rayleigh number and for different values of the limit of the horizontal spatial resolution. It was shown that the transitions from steady state to periodic, then to aperiodic convection depend not only on the Rayleigh number but also very strongly on the horizontal resolution. One of the effects of truncation is to enhance the high wavenumber end of the kinetic energy and thermal variance spectra. The numerical examples indicate that as long as the kinetic energy spectrum decreases with wavenumber, a truncation gives a qualitatively correct solution