Complete description of polarization effects in emission of a photon by an electron in the field of a strong laser wave

We consider emission of a photon by an electron in the field of a strong laser wave. Polarization effects in this process are important for a number of physical problems. A probability of this process for circularly or linearly polarized laser photons and for arbitrary polarization of all other particles is calculated. We obtain the complete set of functions which describe such a probability in a compact invariant form. Besides, we discuss in some detail the polarization effects in the kinematics relevant to the problem of electron to photon conversion at photon-photon and photon-electron colliders.Comment: 18 pages, minor changes, published versio

Natural age dispersion arising from the analysis of broken crystals, part I. Theoretical basis and implications for the apatite (U-Th)/He thermochronometer

Over the last decade major progress has been made in developing both the theoretical and practical aspects of apatite (U-Th)/He thermochronometry and it is now standard practice, and generally seen as best practice, to analyse single grain aliquots. These individual prismatic crystals are often broken and are fragments of larger crystals that have broken during mineral separation along the weak basal cleavage in apatite. This is clearly indicated by the common occurrence of only 1 or no clear crystal terminations present on separated apatite grains, and evidence of freshly broken ends when grains are viewed using a scanning electron microscope. This matters because if the 4He distribution within the whole grain is not homogeneous, because of partial loss due to thermal diffusion for example, then the fragments will all yield ages different from each other and from the whole grain age. Here we use a numerical model with a finite cylinder geometry to approximate 4He ingrowth and thermal diffusion within hexagonal prismatic apatite crystals. This is used to quantify the amount and patterns of inherent, natural age dispersion that arises from analysing broken crystals. A series of systematic numerical experiments were conducted to explore and quantify the pattern and behaviour of this source of dispersion using a set of 5 simple thermal histories that represent a range of plausible geological scenarios. In addition some more complex numerical experiments were run to investigate the pattern and behaviour of grain dispersion seen in several real data sets. The results indicate that natural dispersion of a set of single fragment ages (defined as the range divided by the mean) arising from fragmentation alone varies from c. 7% even for rapid (c. 10 ∘C/Ma), monotonic cooling to over 50% for protracted, complex histories that cause significant diffusional loss of 4He. The magnitude of dispersion arising from fragmentation scales with the grain cylindrical radius, and is of a similar magnitude to dispersion expected from differences in absolute grain size alone (spherical equivalent radii of 40 to 150 μm). This source of dispersion is significant compared with typical analytical uncertainties on individual grain analyses (c. 6%) and standard deviations on multiple grain analyses from a single sample (c. 10-20%). Where there is a significant difference in the U and Th concentration of individual grains (eU), the effect of radiation damage accumulation on 4He diffusivity (assessed using the RDAAM model of Flowers et al. (2009)) is the primary cause of dispersion for samples that have experienced a protracted thermal history, and can cause dispersion in excess of 100% for realistic ranges of eU conentration (i.e. 5-100 ppm). Expected natural dispersion arising from the combined effects of reasonable variations in grain size (radii 40-125 μm), eU concentration (5-150 ppm) and fragmentation would typically exceed 100% for complex thermal histories. In addition to adding a significant component of natural dispersion to analyses, the effect of fragmentation also acts to decouple and corrupt expected correlations between grain ages and absolute grain size and to a lesser extent between grain age and effective uranium concentration (eU). Considering fragmentation explicitly as a source of dispersion and analysing how the different sources of natural dispersion all interact with each other provides a quantitative framework for understanding patterns of dispersion that otherwise appear chaotic. An important outcome of these numerical experiments is that they demonstrate that the pattern of age dispersion arising from fragmentation mimics the pattern of 4He distribution within the whole grains, thus providing an important source of information about the thermal history of the sample. We suggest that if the primary focus of a study is to extract the thermal history information from (U-Th)/He analyses then sampling and analytical strategies should aim to maximise the natural dispersion of grain ages, not minimise it, and should aim to analyse circa 20-30 grains from each sample. The key observations and conclusions drawn here are directly applicable to other thermochronometers, such as the apatite, rutile and titanite U-Pb systems, where the diffusion domain is approximated by the physical grain size

Exploiting Synergy Between Ontologies and Recommender Systems

Recommender systems learn about user preferences over time, automatically finding things of similar interest. This reduces the burden of creating explicit queries. Recommender systems do, however, suffer from cold-start problems where no initial information is available early on upon which to base recommendations. Semantic knowledge structures, such as ontologies, can provide valuable domain knowledge and user information. However, acquiring such knowledge and keeping it up to date is not a trivial task and user interests are particularly difficult to acquire and maintain. This paper investigates the synergy between a web-based research paper recommender system and an ontology containing information automatically extracted from departmental databases available on the web. The ontology is used to address the recommender systems cold-start problem. The recommender system addresses the ontology's interest-acquisition problem. An empirical evaluation of this approach is conducted and the performance of the integrated systems measured

Exploiting synergy between ontologies and recommender systems

Recommender systems learn about user preferences over time, automatically finding things of similar interest. This reduces the burden of creating explicit queries. Recommender systems do, however, suffer from cold-start problems where no initial information is available early on upon which to base recommendations.Semantic knowledge structures, such as ontologies, can provide valuable domain knowledge and user information. However, acquiring such knowledge and keeping it up to date is not a trivial task and user interests are particularly difficult to acquire and maintain. This paper investigates the synergy between a web-based research paper recommender system and an ontology containing information automatically extracted from departmental databases available on the web. The ontology is used to address the recommender systems cold-start problem. The recommender system addresses the ontology's interest-acquisition problem. An empirical evaluation of this approach is conducted and the performance of the integrated systems measured

A determination of the molar gas constant R by acoustic thermometry in helium

We have determined the acoustic and microwave frequencies of a misaligned spherical resonator maintained near the temperature of the triple point of water and filled with helium with carefully characterized molar mass M = (4.002 6032 ± 0.000 0015) g mol-1, with a relative standard uncertainty ur(M) = 0.37×10-6. From these data and traceable thermometry we estimate the speed of sound in our sample of helium at TTPW = 273.16 K and zero pressure to be u0 2 = (945 710.45 ± 0.85) m2 s-2 and correspondingly deduce the value R = (8.314 4743 ± 0.000 0088) J mol-1 K-1 for the molar gas constant. We estimate the value k = R/NA = (1.380 6508 ± 0.000 0015) × 10-23 J K-1 for the Boltzmann constant using the currently accepted value of the Avogadro constant NA. These estimates of R and k, with a relative standard uncertainty of 1.06 × 10-6, are 1.47 parts in 106 above the values recommended by CODATA in 2010

Self-Regulated Growth of Supermassive Black Holes in Galaxies as the Origin of the Optical and X-ray Luminosity Functions of Quasars

We postulate that supermassive black-holes grow in the centers of galaxies until they unbind the galactic gas that feeds them. We show that the corresponding self-regulation condition yields a correlation between black-hole mass (Mbh) and galaxy velocity dispersion (sigma) as inferred in the local universe, and recovers the observed optical and X-ray luminosity functions of quasars at redshifts up to z~6 based on the hierarchical evolution of galaxy halos in a Lambda-CDM cosmology. With only one free parameter and a simple algorithm, our model yields the observed evolution in the number density of optically bright or X-ray faint quasars between 2<z<6 across 3 orders of magnitude in bolometric luminosity and 3 orders of magnitude in comoving density per logarithm of luminosity. The self-regulation condition identifies the dynamical time of galactic disks during the epoch of peak quasar activity (z~2.5) as the origin of the inferred characteristic quasar lifetime of ~10 million years. Since the lifetime becomes comparable to the Salpeter e-folding time at this epoch, the model also implies that the Mbh-sigma relation is a product of feedback regulated accretion during the peak of quasar activity. The mass-density in black-holes accreted by that time is consistent with the local black-hole mass density of ~(0.8-6.3) times 10^5 solar masses per cubic Mpc, which we have computed by combining the Mbh-sigma relation with the measured velocity dispersion function of SDSS galaxies (Sheth et al.~2003). Applying a similar self-regulation principle to supernova-driven winds from starbursts, we find that the ratio between the black hole mass and the stellar mass of galactic spheroids increases with redshift as (1+z)^1.5 although the Mbh-sigma relation is redshift-independent.Comment: 10 pages, 5 figures, submitted to Ap

Creditor Control in Financially Distressed Firms: Empirical Evidence

In this Article we present the results of empirical research that examines how creditor control is manifested in financially troubled firms that have to renegotiate their debt contracts

Capital Offense: The SEC\u27s Continuing Failure to Address Small Business Financing Concerns

Despite years of criticism from small business advocates, the Securities and Exchange Commission has made little effort to ameliorate the severe burdens on small companies seeking to raise capital in compliance with the Securities Act of 1933 and SEC regulations. Substantial SEC attention has been given in recent years to improving the capacity of large, publicly-held companies to market securities, but smaller companies have suffered from less-than-benign neglect. Responding to this concern, the SEC recently adopted several proposals, and has others pending, aimed at small business financing. These proposals and adoptions, while modestly helpful, fall far short of addressing the capital formation problems caused principally by SEC regulation and interpretations. In this article, the authors examine the principal hurdles facing small businesses seeking to raise capital under the securities laws, analyze the background and potential bases for the current regulatory regime, offer a critique based upon the twin goals of protecting investors and providing meaningful financing opportunities for smaller businesses and set forth reform recommendations