"Fiscal Equalization in Japan: Assessment and Recommendations"

Intergovernmental fiscal relations in Japan have been strained in recent years. This paper seeks to assess the Japanese equalization transfer in the light of the theory of fiscal federalism. This paper argues that the case for equalization lies in offsetting net fiscal benefit (NFB) differentials across jurisdictions. It has been shown that the case for equalization and its design depend on the type of public good being provided as well as the mode of finance. Moreover, where equalization is called for, its form and level can be very different depending on whether the relevant policy goal is that of fiscal equity or fiscal efficiency. Studying the institutional context, we arrive at the conclusion that the system of equalization transfers in Japan is consistent with the application of those principles.

Representation of a complex Green function on a real basis: I. General Theory

When the Hamiltonian of a system is represented by a finite matrix, constructed from a discrete basis, the matrix representation of the resolvent covers only one branch. We show how all branches can be specified by the phase of a complex unit of time. This permits the Hamiltonian matrix to be constructed on a real basis; the only duty of the basis is to span the dynamical region of space, without regard for the particular asymptotic boundary conditions that pertain to the problem of interest.Comment: about 40 pages with 5 eps-figure

Exponential speed-up with a single bit of quantum information: Testing the quantum butterfly effect

We present an efficient quantum algorithm to measure the average fidelity decay of a quantum map under perturbation using a single bit of quantum information. Our algorithm scales only as the complexity of the map under investigation, so for those maps admitting an efficient gate decomposition, it provides an exponential speed up over known classical procedures. Fidelity decay is important in the study of complex dynamical systems, where it is conjectured to be a signature of quantum chaos. Our result also illustrates the role of chaos in the process of decoherence.Comment: 4 pages, 2 eps figure

The Extinction and Distance of Maffei 1

We have obtained low- and high-resolution spectra of the core of the highly-reddened elliptical galaxy Maffei 1. From these data, we have obtained the first measurement of the Mg2 index, and have measured the velocity dispersion and radial velocity with improved accuracy. To evaluate the extinction, a correlation between the Mg2 index and effective V-I colour has been established for elliptical galaxies. Using a new method for correcting for effective wavelength shifts, we find A_V = 4.67 +/- 0.19 mag, which is lower by 0.4 mag than previously thought. To establish the distance, the Fundamental Plane for elliptical galaxies has been constructed in I. The velocity dispersion of Maffei 1, measured to be 186.8 +/- 7.4 km/s, in combination with modern wide-field photometry in I, leads to a distance of 2.92 +/- 0.37 Mpc. The Dn-sigma relation, which is independently calibrated, gives 3.08 +/- 0.85 Mpc and 3.23 +/- 0.67 Mpc from photometry in B and K`, respectively. The weighted mean of the three estimates is 3.01 +/- 0.30 Mpc. The distance and luminosity make Maffei 1 the nearest giant elliptical galaxy. The radial velocity of Maffei 1 is +66.4 +/- 5.0 km/s, significantly higher than the accepted value of -10 km/s. The Hubble distance corresponding to the mean velocity of Maffei 1, Maffei 2 and IC342 is 3.5 Mpc. Thus, it is unlikely that Maffei 1 has had any influence on Local Group dynamics

Non-Riemannian Gravity and the Einstein-Proca System

We argue that all Einstein-Maxwell or Einstein-Proca solutions to general relativity may be used to construct a large class of solutions (involving torsion and non-metricity) to theories of non-Riemannian gravitation that have been recently discussed in the literature.Comment: 9 pages Plain Tex (No Figures), Letter to Editor Classical and Quantum Gravit

On the derivative of the associated Legendre function of the first kind of integer order with respect to its degree

In our recent works [R. Szmytkowski, J. Phys. A 39 (2006) 15147; corrigendum: 40 (2007) 7819; addendum: 40 (2007) 14887], we have investigated the derivative of the Legendre function of the first kind, $P_{\nu}(z)$, with respect to its degree $\nu$. In the present work, we extend these studies and construct several representations of the derivative of the associated Legendre function of the first kind, $P_{\nu}^{\pm m}(z)$, with respect to the degree $\nu$, for $m\in\mathbb{N}$. At first, we establish several contour-integral representations of $\partial P_{\nu}^{\pm m}(z)/\partial\nu$. They are then used to derive Rodrigues-type formulas for $[\partial P_{\nu}^{\pm m}(z)/\partial\nu]_{\nu=n}$ with $n\in\mathbb{N}$. Next, some closed-form expressions for $[\partial P_{\nu}^{\pm m}(z)/\partial\nu]_{\nu=n}$ are obtained. These results are applied to find several representations, both explicit and of the Rodrigues type, for the associated Legendre function of the second kind of integer degree and order, $Q_{n}^{\pm m}(z)$; the explicit representations are suitable for use for numerical purposes in various regions of the complex $z$-plane. Finally, the derivatives $[\partial^{2}P_{\nu}^{m}(z)/\partial\nu^{2}]_{\nu=n}$, $[\partial Q_{\nu}^{m}(z)/\partial\nu]_{\nu=n}$ and $[\partial Q_{\nu}^{m}(z)/\partial\nu]_{\nu=-n-1}$, all with $m>n$, are evaluated in terms of $[\partial P_{\nu}^{-m}(\pm z)/\partial\nu]_{\nu=n}$.Comment: LateX, 40 pages, 1 figure, extensive referencin

Studies of the nonlinear dynamics effects of APPLE-II type EPUs at the ALS

Elliptically Polarizing Undulators (EPUs) have become more and more popular at synchrotron radiation sources, providing full polarization control of the photon beam. The fields of the most commonly used APPLE-II type EPUs have a very fast, intrinsic field roll-off, creating significant non-linearities of the beam motion with in some cases large impact on the dynamic (momentum) aperture. In general, the nonlinear effects get stronger with longer periods and higher undulator magnetic fields. One of the planned future beamlines at the ALS (MERLIN) will use a quasiperiodic EPU with 9 cm period and maximum B fields of about 1.3 T. We will present simulation studies for the proposed shimming schemes for this future device to reduce the nonlinear effects to acceptable values, as well as experimental studies for the existing 5 cm period EPUs already installed in the ALS