Bergman spaces of natural G-manifolds

Let G be a unimodular Lie group, X a compact manifold with boundary, and M the total space of a principal bundle G--> M-->X so that M is also a strongly pseudoconvex complex manifold. In this work, we show that if there exists a point p in bM such that T_p(G) is contained in the complex tangent space of bM at p, then the Bergman space of M is large. Natural examples include the gauged G-complexifications of Heinzner, Huckleberry, and Kutzschebauch.Comment: 24 pages, no figure

Classical novae and type I X-ray bursts: challenges for the 21st century

Classical nova explosions and type I X-ray bursts are the most frequent types of thermonuclear stellar explosions in the Galaxy. Both phenomena arise from thermonuclear ignition in the envelopes of accreting compact objects in close binary star systems. Detailed observations of these events have stimulated numerous studies in theoretical astrophysics and experimental nuclear physics. We discuss observational features of these phenomena and theoretical efforts to better understand the energy production and nucleosynthesis in these explosions. We also examine and summarize studies directed at identifying nuclear physics quantities with uncertainties that significantly affect model predictions.Comment: 40 pages, accepted for AIP Advances: Stardust - Progress and Problems in Nuclear Astrophysic

AGT relations for abelian quiver gauge theories on ALE spaces

We construct level one dominant representations of the affine Kac-Moody algebra $\widehat{\mathfrak{gl}}_k$ on the equivariant cohomology groups of moduli spaces of rank one framed sheaves on the orbifold compactification of the minimal resolution $X_k$ of the $A_{k-1}$ toric singularity $\mathbb{C}^2/\mathbb{Z}_k$. We show that the direct sum of the fundamental classes of these moduli spaces is a Whittaker vector for $\widehat{\mathfrak{gl}}_k$, which proves the AGT correspondence for pure $\mathcal{N}=2$ $U(1)$ gauge theory on $X_k$. We consider Carlsson-Okounkov type Ext-bundles over products of the moduli spaces and use their Euler classes to define vertex operators. Under the decomposition $\widehat{\mathfrak{gl}}_k\simeq \mathfrak{h}\oplus \widehat{\mathfrak{sl}}_k$, these vertex operators decompose as products of bosonic exponentials associated to the Heisenberg algebra $\mathfrak{h}$ and primary fields of $\widehat{\mathfrak{sl}}_k$. We use these operators to prove the AGT correspondence for $\mathcal{N}=2$ superconformal abelian quiver gauge theories on $X_k$.Comment: 58 pages; v2: typos corrected, reference added; v3: Introduction expanded, minor corrections and clarifying remarks added throughout, references added and updated; Final version published in Journal of Geometry and Physic

Nucleosynthesis in Type I X-ray Bursts

Type I X-ray bursts are thermonuclear explosions that occur in the envelopes of accreting neutron stars. Detailed observations of these phenomena have prompted numerous studies in theoretical astrophysics and experimental nuclear physics since their discovery over 35 years ago. In this review, we begin by discussing key observational features of these phenomena that may be sensitive to the particular patterns of nucleosynthesis from the associated thermonuclear burning. We then summarize efforts to model type I X-ray bursts, with emphasis on determining the nuclear physics processes involved throughout these bursts. We discuss and evaluate limitations in the models, particularly with regard to key uncertainties in the nuclear physics input. Finally, we examine recent, relevant experimental measurements and outline future prospects to improve our understanding of these unique environments from observational, theoretical and experimental perspectives.Comment: Accepted by Prog. Part. Nucl. Phys., 45 pages, 14 figure

Accurate measurement of absolute experimental inelastic mean free paths and EELS differential cross-sections

Methods are described for measuring accurate absolute experimental inelastic mean free paths and differential cross-sections using DualEELS. The methods remove the effects of surface layers and give the results for the bulk materials. The materials used are VC0.83,TiC0.98,VN0.97and TiN0.88but the method should be applicable to a wide range of materials. The data were taken at 200 keVusing a probe half angle of 29mradand a collection angle of 36mrad. The background can be subtracted from under the ionisation edges, which can then be separated from each other. This is achieved by scaling Hartree-Slater calculated cross-sections to the edges in the atomic regions well above the threshold. The average scaling factors required are 1.00 for the non-metal K-edges and 1.01 for the metal L-edges (with uncertainties of a few per cent). If preliminary measurements of the chromatic effects in the post-specimen lenses are correct, both drop to 0.99. The inelastic mean free path for TiC0.98 was measured as 103.6±0.5 nm compared to the prediction of 126.9 nm based on the widely used Iakoubovskii parameterisation

World Real Interest Rates

We think of the expected real interest rate for ten OECD countries (our counterpart of the world economy) as determined by the equation of aggregate investment demand to aggregate desired saving. Stock-market returns isolate shifts to investment demand, and changes in oil prices, monetary growth, and fiscal variables isolate shifts to desired saving. We estimated the reduced form for CDP-weighted world averages of the expected short-term real interest rate and the investment ratio over the period 1959-88. The estimates reveal significant effects in the predicted direction for world stock returns, oil prices, and world monetary growth, but fiscal variables turned out to be unimportant. Structural estimation implies that an increase by one percentage point in the expected real interest rate raises the desired saving rate by onethird of a percentage point. Simulations of the model indicated that fluctuations in world stock returns and oil prices explain a good deal of the time series for the world average of expected real interest rates; specifically, why the rates were low in 1974-79 and high in 1981-86. The model also explains the fall in real rates in 1987-88 and the subsequent upturn in 1989. The fitted relation forecasts an increase in the world average of real interest rates in 1990 to a value, 5.6 %, that is nearly a full percentage point above the highest value attained in the entire prior sample, 1958-89. We estimated systems of equations for individual countries' expected real interest rates and investment ratios. One finding is that each country's expected real interest rate depends primarily on world factors, rather than own-country factors, thereby suggesting a good deal of integration of world capital and goods markets.

Phillips Curves and Unemployment Dynamics: A Critique and a Holistic Perspective

The conventional wisdom that inflation and unemployment are unrelated in the long-run implies the compartmentalisation of macroeconomics. While one branch of the literature models inflation dynamics and estimates the unemployment rate compatible with inflation stability, another one determines the real economic factors that drive the natural rate of unemployment. In the context of the new Phillips curve (NPC), we show that frictional growth, i.e. the interplay between lags and growth, generates an inflation-unemployment tradeoff in the long-run. We thus argue that a holistic framework, like the chain reaction theory (CRT), should be used to jointly explain the evolution of inflation and unemployment. A further attraction of the CRT approach is that it provides a synthesis of the traditional structural macroeconometric models and the (structural) vector autoregressions (VARs)Natural rate of unemployment; new Phillips Curve; frictional growth; inflation-unemployment tradeoff; inflation dynamics; unemployment dynamics; impulse response function