On determinism and well-posedness in multiple time dimensions

We study the initial value problem for the wave equation and the ultrahyperbolic equation for data posed on initial surface of mixed signature (both spacelike and timelike). Under a nonlocal constraint, we show that the Cauchy problem on codimension-one hypersurfaces has global unique solutions in the Sobolev spaces $H^{m}$, thus it is well-posed. In contrast, we show that the initial value problem on higher codimension hypersurfaces is ill-posed, at least when specifying a finite number of derivatives of the data, due to the failure of uniqueness. This is in contrast to a uniqueness result which Courant and Hilbert deduce from Asgeirsson's mean value theorem, for which we give an independent derivation. The proofs use Fourier synthesis and the Holmgren-John uniqueness theorem

Employment Trends in the Public Sector

A detailed assessment of employment trends in the public sector from 1979 to 2001 is provided. Particular attention is paid to the relative level of public sector employment is Wisconsin . The analysis also examines the relationship between the size of state and local government and overall employment growth from 1979-2001. Results suggest that growth in total employment and employment in the public sector are highly correlated; higher shares of total employment in the public sector in the beginning of the period are not correlated with subsequent growth rates; but a state that sees the public sector grow faster then overall employment growth tends to be associated with slower overall growth. In addition, when measuring the size of the public sector in terms of employment, Wisconsin does not appear to be out of balance when compared to other states. Employment growth in state government over the period 1979-2001 is one of the lowest in the country and employment growth at the local government level is slightly above the national average. Detailed changes in employment by category are also examined for the US and Wisconsin from 1993 to 2002. These data suggest that there has been significant disinvestment in several areas that contribute to the overall quality of life in Wisconsin which may in turn hinder the future potential for economic growth and development.

The Fiscal Health of Wisconsin Municipalities: An Update for 2007

A web-based survey of fiscal health was administered to Wisconsin cities and villages during the spring of 2007. A total of 200 communities responded to the survey. Of those responding, 49 percent reported that their current revenue base is inadequate and more than 64 percent responded that their fiscal condition in five years will be inadequate. Some of the strategies most actively pursued in response to fiscal stress include delaying capital expenditures, targeted budget cuts and delaying routine maintenance expenditures. Strategies least likely to be pursued include reducing hours of public facilities, eliminating services and pursuing regional cooperation agreements. The same survey was administered in 2004 and while statistical comparisons are not permissible due to differences in responding communities, a few points are noteworthy. Compared to 2004, communities are slightly more optimistic today about their current financial condition (46 percent had adequate revenues in 2007 compared to 51 percent in 2004). Conversely, communities have dimmer prospects looking out the next five years today compared to 2004 (64 percent foresee having inadequate revenues in 2007 compared to 54 percent in 2004).

The shape of hyperbolic Dehn surgery space

In this paper we develop a new theory of infinitesimal harmonic deformations for compact hyperbolic 3-manifolds with ``tubular boundary''. In particular, this applies to complements of tubes of radius at least R_0 = \arctanh(1/\sqrt{3}) \approx 0.65848 around the singular set of hyperbolic cone manifolds, removing the previous restrictions on cone angles. We then apply this to obtain a new quantitative version of Thurston's hyperbolic Dehn surgery theorem, showing that all generalized Dehn surgery coefficients outside a disc of ``uniform'' size yield hyperbolic structures. Here the size of a surgery coefficient is measured using the Euclidean metric on a horospherical cross section to a cusp in the complete hyperbolic metric, rescaled to have area 1. We also obtain good estimates on the change in geometry (e.g. volumes and core geodesic lengths) during hyperbolic Dehn filling. This new harmonic deformation theory has also been used by Bromberg and his coworkers in their proofs of the Bers Density Conjecture for Kleinian groups.Comment: 46 pages, 3 figure

A regional model of endogenous growth with creative destruction

We consider a two region growth model with vertical innovations where technical externalities in R&D lead to a technology leading region being the most attractive location for innovative firms. Innovations are produced in the form of quality improvements building on available knowledge and firms choose a technologically advanced location to maximise the productivity of R&D and maintain their niche monopoly. The partial nature of spillovers causes an additional force for agglomeration: the clustering effect. Agglomerated locations have the benefit of local inter-varietal knowledge spillovers for growth while peripheral locations depend on trade and regional knowledge spillovers

How Stressed Are Wisconsin Cities and Villages?

For the fourth time since 1997, a web-based survey of fiscal health was administered to administrative officials of Wisconsin cities and villages during the summer of 2010. A total of 195 municipalities responded to the survey. Of those administrative officials responding, 53 percent reported that their current revenue base was inadequate and more than 62 percent responded that their fiscal condition in five years will be inadequate. Some of the strategies most actively pursued in response to fiscal stress include the adoption or increase in user fees and charges, improved productivity through better management and pursuit of grants from federal/state governments. Strategies least likely to be pursued include laying off workers, increasing short-term debt and reducing hours of operation.