Splitting Behavior of SnS_n-Polynomials

We analyze the probability that, for a fixed finite set of primes S, a random, monic, degree n polynomial f(x) with integer coefficients in a box of side B around 0 satisfies: (i) f(x) is irreducible over the rationals, with splitting field over the rationals having Galois group $S_n$; (ii) the polynomial discriminant Disc(f) is relatively prime to all primes in S; (iii) f(x) has a prescribed splitting type at each prime p in S. The limit probabilities as $B \to \infty$ are described in terms of values of a one-parameter family of measures on $S_n$, called splitting measures, with parameter $z$ evaluated at the primes p in S. We study properties of these measures. We deduce that there exist degree n extensions of the rationals with Galois closure having Galois group $S_n$ with a given finite set of primes S having given Artin symbols, with some restrictions on allowed Artin symbols for p<n. We compare the distributions of these measures with distributions formulated by Bhargava for splitting probabilities for a fixed prime $p$ in such degree $n$ extensions ordered by size of discriminant, conditioned to be relatively prime to $p$.Comment: 33 pages, v2 34 pages, introduction revise

Rapidity gap survival in the black-disk regime

We summarize how the approach to the black-disk regime (BDR) of strong interactions at TeV energies influences rapidity gap survival in exclusive hard diffraction pp -> p + H + p (H = dijet, Qbar-Q, Higgs). Employing a recently developed partonic description of such processes, we discuss (a) the suppression of diffraction at small impact parameters by soft spectator interactions in the BDR; (b) further suppression by inelastic interactions of hard spectator partons in the BDR; (c) correlations between hard and soft interactions. Hard spectator interactions substantially reduce the rapidity gap survival probability at LHC energies compared to previously reported estimates.Comment: 4 pages, 3 figures. Proceedings of XV International Workshop on Deep-Inelastic Scattering and Related Subjects (DIS 2007), Munich, Germany, Apr. 16-20, 200

Detailed AGB evolutionary models and near infrared colours of intermediate-age stellar populations: Tests on star clusters

We investigate the influence of Asymptotic Giant Branch stars on integrated colours of star clusters of ages between ~100 Myr and a few gigayears, and composition typical for the Magellanic Clouds. We use state-of-the-art stellar evolution models that cover the full thermal pulse phase, and take into account the influence of dusty envelopes on the emerging spectra. We present an alternative approach to the usual isochrone method, and compute integrated fluxes and colours using a Monte Carlo technique that enables us to take into account statistical fluctuations due to the typical small number of cluster stars. We demonstrate how the statistical variations in the number of Asymptotic Giant Branch stars and the temperature and luminosity variations during thermal pulses fundamentally limit the accuracy of the comparison (and calibration, for population synthesis models that require a calibration of the Asymptotic Giant Branch contribution to the total luminosity) with star cluster integrated photometries. When compared to observed integrated colours of individual and stacked clusters in the Magellanic Clouds, our predictions match well most of the observations, when statistical fluctuations are taken into account, although there are discrepancies in narrow age ranges with some (but not all) set of observations.Comment: 12 pages, 14 figures, accepted for publication in A&

Transverse imaging of the proton in exclusive diffractive pp scattering

In a recent paper (hep-ph/0608271) we describe a new approach to rapidity gap survival (RGS) in the production of high-mass systems (H = dijet, Higgs, etc.) in exclusive double-gap diffractive pp scattering, pp -> p + H + p. It is based on the idea that hard and soft interactions are approximately independent (QCD factorization), and allows us to calculate the RGS probability in a model-independent way in terms of the gluon generalized parton distributions (GPDs) in the colliding protons and the pp elastic scattering amplitude. Here we focus on the transverse momentum dependence of the cross section. By measuring the "diffraction pattern," one can perform detailed tests of the interplay of hard and soft interactions, and even extract information about the gluon GPD in the proton from the data.Comment: 4 pages, 2 figures, uses ws-procs9x6.cls. Proceedings of XIV International Workshop on Deep Inelastic Scattering (DIS2006), Tsukuba City, Japan, Apr 20 - 24, 200

The Role of Dust in Models of Population Synthesis

We have employed state-of-the-art evolutionary models of low and intermediate-mass AGB stars, and included the effect of circumstellar dust shells on the spectral energy distribution (SED) of AGB stars, to revise the Padua library of isochrones (Bertelli et al. 1994). The major revision involves the thermally pulsing AGB phase, that is now taken from fully evolutionary calculations by Weiss & Ferguson (2009). Two libraries of about 600 AGB dust-enshrouded SEDs each have also been calculated, one for oxygen-rich M-stars and one for carbon-rich C-stars. Each library accounts for different values of input parameters like the optical depth {\tau}, dust composition, and temperature of the inner boundary of the dust shell. These libraries of dusty AGB spectra have been implemented into a large composite library of theoretical stellar spectra, to cover all regions of the Hertzsprung-Russell Diagram (HRD) crossed by the isochrones. With the aid of the above isochrones and libraries of stellar SEDs, we have calculated the spectro-photometric properties (SEDs, magnitudes, and colours) of single-generation stellar populations (SSPs) for six metallicities, more than fifty ages (from 3 Myr to 15 Gyr), and nine choices of the Initial Mass Function. The new isochrones and SSPs have been compared to the colour-magnitude diagrams (CMDs) of field populations in the LMC and SMC, with particular emphasis on AGB stars, and the integrated colours of star clusters in the same galaxies, using data from the SAGE (Surveying the Agents of Galaxy Evolution) catalogues. We have also examined the integrated colours of a small sample of star clusters located in the outskirts of M31. The agreement between theory and observations is generally good. In particular, the new SSPs reproduce the red tails of the AGB star distribution in the CMDs of field stars in the Magellanic Clouds.Comment: Accepted for publication in MNRA

Optical Properties of Quantum-Dot-Doped Liquid Scintillators

Semiconductor nanoparticles (quantum dots) were studied in the context of liquid scintillator development for upcoming neutrino experiments. The unique optical and chemical properties of quantum dots are particularly promising for the use in neutrinoless double beta decay experiments. Liquid scintillators for large scale neutrino detectors have to meet specific requirements which are reviewed, highlighting the peculiarities of quantum-dot-doping. In this paper, we report results on laboratory-scale measurements of the attenuation length and the fluorescence properties of three commercial quantum dot samples. The results include absorbance and emission stability measurements, improvement in transparency due to filtering of the quantum dot samples, precipitation tests to isolate the quantum dots from solution and energy transfer studies with quantum dots and the fluorophore PPO.Comment: version 2, minor text update

Ground state energy of a homogeneous Bose-Einstein condensate beyond Bogoliubov

The standard calculations of the ground-state energy of a homogeneous Bose gas rely on approximations which are physically reasonable but difficult to control. Lieb and Yngvason [Phys. Rev. Lett. 80, 2504 (1998)] have proved rigorously that the commonly accepted leading order term of the ground state energy is correct in the zero-density-limit. Here, strong indications are given that also the next to leading term is correct. It is shown that the first terms obtained in a perturbative treatment provide contributions which are lost in the Bogoliubov approach.Comment: 6 pages, accepted for publication in Europhys. Lett. http://www.epletters.ch

South Carolina Slave Prices, 1722-1809

Based on data from several samples of probate inventories we construct and analyze a time series of slave prices for South Carolina from 1722 to 1809. These estimates reveal that prices fluctuated without trend prior to the 1760s and then began to rise rapidly, more than doubling by the early nineteenth century. Estimates of supply and demand functions indicate that while long-run slave supply was highly elastic, the short-run supply function was quite inelastic. Our analysis of the slave price series indicates that the price of rice was the major determinant of the demand for slaves and in turn largely explains the rise in slave prices. These findings have important implications for the interpretation of evidence on rising yields in rice production over the eighteenth century and the sources of wealth accumulation in South Carolina.

Conjectural Estimates of Economic Growth in the Lower South, 1720 to 1800

This paper describes the first step in a larger project to build up regional estimates of economic growth before 1800 in the parts of North America that became the United States. In it we employ the method of conjectural estimation to develop new estimates of the rate of economic growth in the Lower South (modern day North Carolina, South Carolina, Georgia, and Tennessee) from 1720 to 1800 for both colonists and the Native American population of the region. Contrary to the widely held view that GDP per capita grew at a rate of 0.3 to 0.6 percent per year during the eighteenth century our best estimate is that per capita GDP grew at just 0.09 percent per year. Despite the slow growth of GDP per capita, however, the region's economy did achieve appreciable extensive growth, and achieving any advance in per capita production can be viewed as a significant accomplishment in light of the challenges that this growth posed for the economy. The difference between our estimate and those of previous studies appears to be the result of earlier scholars' undue focus on export performance. In contrast, our approach allows us to accurately account for the effect of the slowly growing domestic sector of the economy.