A combinatorial Li-Yau inequality and rational points on curves

We present a method to control gonality of nonarchimedean curves based on graph theory. Let k denote a complete nonarchimedean valued field.We first prove a lower bound for the gonality of a curve over the algebraic closure of k in terms of the minimal degree of a class of graph maps, namely: one should minimize over all so-called finite harmonic graph morphisms to trees, that originate from any refinement of the dual graph of the stable model of the curve. Next comes our main result: we prove a lower bound for the degree of such a graph morphism in terms of the first eigenvalue of the Laplacian and some “volume” of the original graph; this can be seen as a substitute for graphs of the Li–Yau inequality from differential geometry, although we also prove that the strict analogue of the original inequality fails for general graphs. Finally,we apply the results to give a lower bound for the gonality of arbitraryDrinfeld modular curves over finite fields and for general congruence subgroups Γ of Γ (1) that is linear in the index [Γ (1) : Γ ], with a constant that only depends on the residue field degree and the degree of the chosen “infinite” place. This is a function field analogue of a theorem of Abramovich for classical modular curves. We present applications to uniform boundedness of torsion of rank two Drinfeld modules that improve upon existing results, and to lower bounds on the modular degree of certain elliptic curves over function fields that solve a problem of Papikian

A note on the expectations hypothesis at the founding of the Fed

One of the most influential tests of the expectations hypothesis is Mankiw and Miron (1986), who found that the spread between the long-term and short-term rates provided predictive power for the short-term rate before the Fed's founding but not after. They suggested that the failure of the expectations hypothesis after the Fed's founding was due to the Fed's practice of smoothing short-term interest rates. We show that their finding that the expectations hypothesis fares better prior to the Fed's founding is due to the fact that the test they employ tends to generate results that are more favorable to the expectations hypothesis during periods when there is extreme volatility in the short-term rate. (Earlier version titled: The expectations theory and the founding of the Fed: another look at the evidence)Interest rates ; Rational expectations (Economic theory) ; Federal Reserve System - History

Dutch corporate liquidity mangement: New evidence on aggregation

In this paper we investigate Dutch corporate liquidity management in general, and target adjustment behaviour in particular. To this purpose, we use a simple error correction model of corporate liquidity holdings applied to firm-level data for the period 1977-1997. We confirm the existence of long-run liquidity targets at the firm level. We also find that changes in liquidity holdings are driven by short-run shocks as well as the urge to converge towards targeted liquidity levels. The rate of target convergence is higher when we include more firm-specific information in the target. This result supports the idea that increased precision in defining liquidity targets associates with a faster observed rate of target convergence. It also suggests that the slow speeds of adjustment obtained in many macro studies on money demand are artefacts of aggregation bias.corporate liquidity demand, precautionary liquidity

Industries and the bank lending effects of bank credit demand and monetary policy in Germany

This paper presents evidence on the industry effects of bank lending in Germany and identifies the industry effects of bank lending associated with changes in monetary policy and industryspecific bank credit demand. To this end, we estimate individual bank lending functions for 13 manufacturing and non-manufacturing industries and five banking groups using quarterly bank balance sheet and bank lending data for the period 1992:1-2002:4. The evidence from dynamic panel data models shows that industry-specific bank lending growth predominantly responds to changes in industry-specific bank credit demand rather than to changes in monetary policy. In fact, conclusions regarding the bank lending effects of monetary policy are very sensitive to the choice of industry. The empirical results lend strong support to the existence of industry effects of bank lending. Because industries are a prominent source of variation in the bank lending effects of bank credit demand and monetary policy, the paper concludes that the industry composition of bank credit portfolios is an important determinant of bank lending growth and monetary policy effectiveness. --Monetary policy transmission,credit channel,industry structure,dynamic panel data

On the Column Density of AGN Outflows: the Case of NGC 5548

We re-analyze the HST high resolution spectroscopic data of the intrinsic absorber in NGC 5548 and find that the C IV absorption column density is at least four times larger than previously determined. This increase arises from accounting for the kinematical nature of the absorber and from our conclusion that the outflow does not cover the narrow emission line region in this object. The improved column density determination begins to bridge the gap between the high column densities measured in the X-ray and the low ones previously inferred from the UV lines. Combined with our findings for outflows in high luminosity quasars these results suggest that traditional techniques for measuring column densities: equivalent width, curve-of-growth and Gaussian modeling, are of limited value when applied to absorption associated with AGN outflows.Comment: Published ApJ version (566, 699), including a new figure with FUSE data and a useful algebraic expression for the optical depth solutio

Rigidity and reconstruction for graphs

The edge reconstruction conjecture of Harary (1964) states that a finite graph G can be reconstructed up to isomorphism from the multiset of its edge-deleted subgraphs G–e (with e running over the edges of G). We put this conjecture in the framework of measure-theoretic rigidity, revealing the importance of the lengths of labeled closed walks for the problem

Accretion disk reversal and the spin-up/spin-down of accreting pulsars

We numerically investigate the hydrodynamics of accretion disk reversal and relate our findings to the observed spin-rate changes in the accreting X-ray pulsar GX~1+4. In this system, which accretes from a slow wind, the accretion disk contains two dynamically distinct regions. In the inner part viscous forces are dominant and disk evolution occurs on a viscous timescale. In the outer part dynamical mixing of material with opposite angular momentum is more important, and the externally imposed angular momentum reversal timescale governs the flow. In this outer region the disk is split into concentric rings of material with opposite senses of rotation that do not mix completely but instead remain distinct, with a clear gap between them. We thus predict that torque reversals resulting from accretion disk reversals will be accompanied by minima in accretion luminosity.Comment: 13 pages, 7 figures, accepted for publication in Ap

VLT + UVES Spectroscopy of the Low-Ionization Intrinsic Absorber in SDSS J001130.56+005550.7

We analyse high-resolution VLT+UVES spectra of the low-ionization intrinsic absorber observed in the BAL QSO SDSS J001130.56+005550.7. Two narrow absorption systems at velocities -600 km/s and -22000 km/s are detected. The low-velocity system is part of the broad absorption line (BAL), while the high-velocity one is well detached. While most narrow absorption components are only detected in the high-ionization species, the lowest velocity component is detected in both high- and low-ionization species, including in the excited SiII* and CII* lines. From the analysis of doublet lines, we find that the narrow absorption lines at the low-velocity end of the BAL trough are completely saturated but do not reach zero flux, their profiles being dominated by a velocity-dependent covering factor. The covering factor is significantly smaller for MgII than for SiIV and NV, which demonstrates the intrinsic nature of absorber. From the analysis of the excited SiII* and CII* lines in the lowest velocity component, we find an electron density ~ 1000 cm^{-3}. Assuming photoionization equilibrium, we derive a distance ~ 20 kpc between the low-ionization region and the quasar core. The correspondence in velocity of the high- and low-ionization features suggests that all these species must be closely associated, hence formed at the same distance of ~ 20 kpc, much higher than the distance usually assumed for BAL absorbers.Comment: Accepted for publication in A&