GASB Statement No. 31: Why No Controversy?

Fair value reporting of investments in the financial statements of commercial enterprises is required under FASB Statement No. 115. The standard created much controversy when issued due to provisions that changes in fair values of certain investments were recognized in the operating statement. A major concern to many organizations was the volatility these recognized, but unrealized, changes in fair value would create in reported earnings. When the GASB issued Statement No. 31 requiring fair value reporting of investments there was little controversy concerning volatility to reported earnings of governmental entities, even though the standard required much broader application of fair value reporting. This study examined a possible explanation for the lack of controversy surrounding fair value reporting in the public sector. An analysis of the financial reports of the major U.S. municipalities provided empirical evidence of the significance of investments earnings to municipal revenues, investment assets to total assets, and the significance of changes in fair values of investments to investment earnings and total revenues. Financial reports and accompanying notes for fiscal years 1994 to 1998 were examined. Results indicate that overall, investments earnings were not a significant component of governmental fund revenues. However, investment earnings were significant for certain governmental fund types. The difference between costs and fair market values of investments also did not appear to be material to most governmental funds. The minimal impact of the fair value reporting on earnings offers a partial explanation for the lack of debate surrounding adoption of fair value reporting of investment by governmental entities

Aerodynamic heating in large cavities in an array of RSI tiles

A large panel of reusable surface insulation (RSI) tiles including lost tile cavities was aerothermally tested in the Langley 8 foot high temperature structures tunnel to determine both the heat load within the cavities and the structural performance of the RSI surrounding the cavities. Tests were conducted with a turbulent boundary layer at a nominal free stream Mach number of 6.6, a total temperature of 1800 K, a Reynolds number per meter of 5 million, and a dynamic pressure of 62 kPa. The maximum aerodynamic heating to the floor of the cavity was two to three times the normal surface heating. The cavity heating rates agreed with data from other facilities and were successfully correlated with an empirical equation. A zippering failure occurred to a tile downstream of a double tile cavity when the separated flow attached to the floor of the cavity and forced the tile from its position

The role of dust in "active" and "passive" low-metallicity star formation

We investigate the role of dust in star formation activity of extremely metal-poor blue compact dwarf galaxies (BCDs). Observations suggest that star formation in BCDs occurs in two different regimes: "active" and "passive". The "active" BCDs host super star clusters (SSCs), and are characterised by compact size, rich H2 content, large dust optical depth, and high dust temperature; the "passive" BCDs are more diffuse with cooler dust, and lack SSCs and large amounts of H2. By treating physical processes concerning formation of stars and dust, we are able to simultaneously reproduce all the above properties of both modes of star formation (active and passive). We find that the difference between the two regimes can be understood through the variation of the "compactness" of the star-forming region: an "active" mode emerges if the region is compact (with radius \la 50 pc) and dense (with gas number density \ga 500 cm$^{-3}$). The dust, supplied from Type II supernovae in a compact star-forming region, effectively reprocesses the heating photons into the infrared and induces a rapid H2 formation over a period of several Myr. This explains the high infrared luminosity, high dust temperature, and large H2 content of active BCDs. Moreover, the gas in "active" galaxies cools (\la 300 K) on a few dynamical timescales, producing a "run-away" star formation episode because of the favourable (cool) conditions. The mild extinction and relatively low molecular content of passive BCDs can also be explained by the same model if we assume a diffuse region (with radius \ga 100 pc and gas number density \la 100 cm$^{-3}$). We finally discuss primordial star formation in high-redshift galaxies in the context of the "active" and "passive" star formation scenario.Comment: Astronomy and Astrophysics, in press, 16 pages, 8 figure

The size--density relation of extragalactic HII regions

We investigate the size--density relation in extragalactic HII regions, with the aim of understanding the role of dust and different physical conditions in the ionized medium. First, we compiled several observational data sets for Galactic and extragalactic HII regions and confirm that extragalactic HII regions follow the same size (D)--density (n) relation as Galactic ones. Motivated by the inability of static models to explain this, we then modelled the evolution of the size--density relation of HII regions by considering their star formation history, the effects of dust, and pressure-driven expansion. The results are compared with our sample data whose size and density span roughly six orders of magnitude. We find that the extragalactic size--density relation does not result from an evolutionary sequence of HII regions but rather reflects a sequence with different initial gas densities (``density hierarchy''). Moreover, the size of many HII regions is limited by dust absorption of ionizing photons, rather than consumption by ionizing neutral hydrogen. Dust extinction of ionizing photons is particularly severe over the entire lifetime of compact HII regions with typical gas densities of greater than 10^3 cm^{-3}. Hence, as long as the number of ionizing photons is used to trace massive star formation, much star-formation activity could be missed. Such compact dense environments, the ones most profoundly obscured by dust, have properties similar to ``maximum--intensity starbursts''. This implies that submillimeter and infrared wavelengths may be necessary to accurately assess star formation in these extreme conditions both locally and at high redshift.Comment: 18 pages, 11 figures, accepted for publication in Astronomy and Astrophysic

Parallels between control PDE's (Partial Differential Equations) and systems of ODE's (Ordinary Differential Equations)

System theorists understand that the same mathematical objects which determine controllability for nonlinear control systems of ordinary differential equations (ODEs) also determine hypoellipticity for linear partial differentail equations (PDEs). Moreover, almost any study of ODE systems begins with linear systems. It is remarkable that Hormander's paper on hypoellipticity of second order linear p.d.e.'s starts with equations due to Kolmogorov, which are shown to be analogous to the linear PDEs. Eigenvalue placement by state feedback for a controllable linear system can be paralleled for a Kolmogorov equation if an appropriate type of feedback is introduced. Results concerning transformations of nonlinear systems to linear systems are similar to results for transforming a linear PDE to a Kolmogorov equation

Canonical coordinates for partial differential equations

Necessary and sufficient conditions are found under which operators of the form Sigma(m, j=1) X(2)sub j + X sub 0 can be made constant coefficient. In addition, necessary and sufficient conditions are derived which classify those linear partial differential operators that can be moved to the Kolmogorov type

Observability for two dimensional systems

Sufficient conditions that a two-dimensional system with output is locally observable are presented. Known results depend on time derivatives of the output and the inverse function theorem. In some cases, no informaton is provided by these theories, and one must study observability by other methods. The observability problem is dualized to the controllability problem, and the deep results of Hermes on local controllability are applied to prove a theorem concerning local observability

A canonical form for nonlinear systems

The conceptions of transformation and canonical form have been much used to analyze the structure of linear systems. A coordinate system and a corresponding canonical form are developed for general nonlinear control systems. Their usefulness is demonstrated by showing that every feedback linearizable system becomes a system with only feedback paths in the canonical form

Materials constitutive models for nonlinear analysis of thermally cycled structures

Effects of inelastic materials models on computed stress-strain solutions for thermally loaded structures were studied by performing nonlinear (elastoplastic creep) and elastic structural analyses on a prismatic, double edge wedge specimen of IN 100 alloy that was subjected to thermal cycling in fluidized beds. Four incremental plasticity creep models (isotropic, kinematic, combined isotropic kinematic, and combined plus transient creep) were exercised for the problem by using the MARC nonlinear, finite element computer program. Maximum total strain ranges computed from the elastic and nonlinear analyses agreed within 5 percent. Mean cyclic stresses, inelastic strain ranges, and inelastic work were significantly affected by the choice of inelastic constitutive model. The computing time per cycle for the nonlinear analyses was more than five times that required for the elastic analysis