Affine descents and the Steinberg torus

Let $W\ltimes L$ be an irreducible affine Weyl group with Coxeter complex $\Sigma$, where $W$ denotes the associated finite Weyl group and $L$ the translation subgroup. The Steinberg torus is the Boolean cell complex obtained by taking the quotient of $\Sigma$ by the lattice $L$. We show that the ordinary and flag $h$-polynomials of the Steinberg torus (with the empty face deleted) are generating functions over $W$ for a descent-like statistic first studied by Cellini. We also show that the ordinary $h$-polynomial has a nonnegative $\gamma$-vector, and hence, symmetric and unimodal coefficients. In the classical cases, we also provide expansions, identities, and generating functions for the $h$-polynomials of Steinberg tori.Comment: 24 pages, 2 figure

Smart Money, Noise Trading and Stock Price Behavior

This paper derives and estimates an equilibrium model of stock price behavior in which exogenous "noise traders" interact with risk-averse "smart money" investors. The model assumes that changes in exponentially detrended dividends and prices are normally distributed, and that smart money investors have constant absolute risk aversion. In equilibrium, the stock price is the present value of expected dividends, discounted at the riskless interest rate, less a constant risk premium, plus a term which is due to noise trading. The model expresses both stock prices and dividends as sums of unobserved components in continuous time. The model is able to explain the volatility and predictability of U.S. stock returns in the period 1871-1986 in either of two ways. Either the discount rate is 4% or below, and the constant risk premium is large; or the discount rate is 5% or above, and noise trading, correlated with fundamentals, increases the volatility of stock prices. The data are not well able to distinguish between these explanations.

Accurate solutions, parameter studies and comparisons for the Euler and potential flow equations

Parameter studies are conducted using the Euler and potential flow equation models for unsteady and steady flows in both two and three dimensions. The Euler code is an implicit, upwind, finite volume code which uses the Van Leer method of flux-vector-splitting which has been recently extended for use on dynamic meshes and maintain all the properties of the original splitting. The potential flow code is an implicit, finite difference method for solving the transonic small disturbance equations and incorporates both entropy and vorticity corrections into the solution procedures thereby extending its applicability into regimes where shock strength normally precludes its use. Parameter studies resulting in benchmark type calculations include the effects of spatial and temporal refinement, spatial order of accuracy, far field boundary conditions for steady flow, frequency of oscillation, and the use of subiterations at each time step to reduce linearization and factorization errors. Comparisons between Euler and potential flows results are made as well as with experimental data where available

Interannual variability in North American grassland biomass/productivity detected by SeaWinds scatterometer backscatter

We analyzed 2000–2004 growing-season SeaWinds Ku-band microwave backscatter and MODIS leaf area index (LAI) data over North America. Large anomalies in mid-growing-season mean backscatter and LAI, relative to 5-year mean values, occurred primarily in the western Great Plains; backscatter and LAI anomalies had similar spatial patterns across this region. Backscatter and LAI time series data for three ∼103 km2 regions in the western Great Plains were strongly correlated (r2 ∼ 0.6–0.8), and variability in mid-growing season values was well-correlated with annual precipitation (October through September). The results indicate that SeaWinds backscatter is sensitive to interannual variability in grassland biomass/productivity, and can provide an assessment that is completely independent of optical/near-infrared remote sensing instruments