Representations of integers by certain positive definite binary quadratic forms

We prove part of a conjecture of Borwein and Choi concerning an estimate on the square of the number of solutions to n=x^2+Ny^2 for a squarefree integer N.Comment: 8 pages, submitte

Optical Imaging and Spectroscopic Observation of the Galactic Supernova Remnant G85.9-0.6

Optical CCD imaging with H$\alpha$ and [SII] filters and spectroscopic observations of the galactic supernova remnant G85.9-0.6 have been performed for the first time. The CCD image data are taken with the 1.5m Russian-Turkish Telescope (RTT150) at TUBITAK National Observatory (TUG) and spectral data are taken with the Bok 2.3 m telescope on Kitt Peak, AZ. The images are taken with narrow-band interference filters H$\alpha$, [SII] and their continuum. [SII]/H$\alpha$ ratio image is performed. The ratio obtained from [SII]/H$\alpha$ is found to be $\sim$0.42, indicating that the remnant interacts with HII regions. G85.9-0.6 shows diffuse-shell morphology. [SII]$\lambda\lambda 6716/6731$ average flux ratio is calculated from the spectra, and the electron density $N_{e}$ is obtained to be 395 $cm^{-3}$. From [OIII]/H$\beta$ ratio, shock velocity has been estimated, pre-shock density of $n_{c}=14$ $cm^{-3}$, explosion energy of $E=9.2\times10^{50}$ ergs, interstellar extinction of $E(B-V)=0.28$, and neutral hydrogen column density of $N(HI)=1.53\times10^{21}$ $cm^{-2}$ are reported.Comment: 20 pages, 4 tables, 4 figures. Accepted for publication in Astrophysics & Space Scienc

The propagation of a cultural or biological trait by neutral genetic drift in a subdivided population

We study fixation probabilities and times as a consequence of neutral genetic drift in subdivided populations, motivated by a model of the cultural evolutionary process of language change that is described by the same mathematics as the biological process. We focus on the growth of fixation times with the number of subpopulations, and variation of fixation probabilities and times with initial distributions of mutants. A general formula for the fixation probability for arbitrary initial condition is derived by extending a duality relation between forwards- and backwards-time properties of the model from a panmictic to a subdivided population. From this we obtain new formulae, formally exact in the limit of extremely weak migration, for the mean fixation time from an arbitrary initial condition for Wright's island model, presenting two cases as examples. For more general models of population subdivision, formulae are introduced for an arbitrary number of mutants that are randomly located, and a single mutant whose position is known. These formulae contain parameters that typically have to be obtained numerically, a procedure we follow for two contrasting clustered models. These data suggest that variation of fixation time with the initial condition is slight, but depends strongly on the nature of subdivision. In particular, we demonstrate conditions under which the fixation time remains finite even in the limit of an infinite number of demes. In many cases - except this last where fixation in a finite time is seen - the time to fixation is shown to be in precise agreement with predictions from formulae for the asymptotic effective population size.Comment: 17 pages, 8 figures, requires elsart5p.cls; substantially revised and improved version; accepted for publication in Theoretical Population Biolog

P-Wave Charmonium Production in B-Meson Decays

We calculate the decay rates of $B$ mesons into P-wave charmonium states using new factorization formulas that are valid to leading order in the relative velocity of the charmed quark and antiquark and to all orders in the running coupling constant of QCD. We express the production rates for all four P states in terms of two nonperturbative parameters, the derivative of the wavefunction at the origin and another parameter related to the probability for a charmed-quark-antiquark pair in a color-octet S-wave state to radiate a soft gluon and form a P-wave bound state. Using existing data on $B$ meson decays into $\chi_{c1}$ to estimate the color-octet parameter, we find that the color-octet mechanism may account for a significant fraction of the $\chi_{c1}$ production rate and that $B$ mesons should decay into $\chi_{c2}$ at a similar rate.Comment: 14 page

Very Low Temperature Tunnelling Spectroscopy in the heavy fermion superconductor PrOs4_4Sb12_{12}

We present scanning tunnelling spectroscopy measurements on the heavy fermion superconductor PrOs$_4$Sb$_{12}$. Our results show that the superconducting gap opens over a large part of the Fermi surface. The deviations from isotropic BCS s-wave behavior are discussed in terms of a finite distribution of values of the superconducting gap.Comment: 4 pages, 4 figure

2D and 3D Polar Plume Analysis from the Three Vantage Positions of STEREO/EUVI A, B, and SOHO/EIT

Polar plumes are seen as elongated objects starting at the solar polar regions. Here, we analyze these objects from a sequence of images taken simultaneously by the three spacecraft telescopes STEREO/EUVI A and B, and SOHO/EIT. We establish a method capable of automatically identifying plumes in solar EUV images close to the limb at 1.01 - 1.39 R in order to study their temporal evolution. This plume-identification method is based on a multiscale Hough-wavelet analysis. Then two methods to determined their 3D localization and structure are discussed: First, tomography using the filtered back-projection and including the differential rotation of the Sun and, secondly, conventional stereoscopic triangulation. We show that tomography and stereoscopy are complementary to study polar plumes. We also show that this systematic 2D identification and the proposed methods of 3D reconstruction are well suited, on one hand, to identify plumes individually and on the other hand, to analyze the distribution of plumes and inter-plume regions. Finally, the results are discussed focusing on the plume position with their cross-section area.Comment: 22 pages, 10 figures, Solar Physics articl

The 2-Channel Kondo Model I: Review of Experimental Evidence for its Realization in Metal Nanoconstrictions

Certain zero-bias anomalies (ZBAs) in the voltage, temperature and magnetic field dependence of the conductance $G(V,T,H)$ of quenched Cu point contacts have previously been interpreted to be due to non-magnetic 2-channel Kondo (2CK) scattering from near-degenerate atomic two-level tunneling systems (Ralph and Buhrman, 1992; Ralph et al. 1994), and hence to represent an experimental realization of the non-Fermi-liquid physics of the T=0 fixed point of the 2-channel Kondo model. In this, the first in a series of three papers (I,II,III) devoted to 2-channel Kondo physics, we present a comprehensive review of the quenched Cu ZBA experiments and their 2CK interpretation, including new results on ZBAs in constrictions made from Ti or from metallic glasses. We first review the evidence that the ZBAs are due to electron scattering from stuctural defects that are not static, but possess internal dynamics. In order to distinguish between several mechanisms proposed to explain the experiments, we then analyze the scaling properties of the conductance at low temperature and voltage and extract from the data a universal scaling function $\Gamma(v)$. The theoretical calculation of the corresponding scaling function within the 2CK model is the subject of papers II and III. The main conclusion of our work is that the properties of the ZBAs, and most notably their scaling behavior, are in good agreement with the 2CK model and clearly different from several other proposed mechanisms.Comment: 35 pages RevTeX, 19 encapsulated postscript figures; this final published version features two additional authors, an additional section reviewing recent experiments on Ti nanoconstrictions that agree very well with the 2-channel Kondo model, 6 new figures (and is much shorter the previous 53 page version, due to reformatting

Search for the Rare Decay KL --> pi0 ee

The KTeV/E799 experiment at Fermilab has searched for the rare kaon decay KL--> pi0ee. This mode is expected to have a significant CP violating component. The measurement of its branching ratio could support the Standard Model or could indicate the existence of new physics. This letter reports new results from the 1999-2000 data set. One event is observed with an expected background at 0.99 +/- 0.35 events. We set a limit on the branching ratio of 3.5 x 10^(-10) at the 90% confidence level. Combining the results with the dataset taken in 1997 yields the final KTeV result: BR(KL --> pi0 ee) < 2.8 x 10^(-10) at 90% CL.Comment: 4 pages, three figure

Gravitational Lensing at Millimeter Wavelengths

With today's millimeter and submillimeter instruments observers use gravitational lensing mostly as a tool to boost the sensitivity when observing distant objects. This is evident through the dominance of gravitationally lensed objects among those detected in CO rotational lines at z>1. It is also evident in the use of lensing magnification by galaxy clusters in order to reach faint submm/mm continuum sources. There are, however, a few cases where millimeter lines have been directly involved in understanding lensing configurations. Future mm/submm instruments, such as the ALMA interferometer, will have both the sensitivity and the angular resolution to allow detailed observations of gravitational lenses. The almost constant sensitivity to dust emission over the redshift range z=1-10 means that the likelihood for strong lensing of dust continuum sources is much higher than for optically selected sources. A large number of new strong lenses are therefore likely to be discovered with ALMA, allowing a direct assessment of cosmological parameters through lens statistics. Combined with an angular resolution <0.1", ALMA will also be efficient for probing the gravitational potential of galaxy clusters, where we will be able to study both the sources and the lenses themselves, free of obscuration and extinction corrections, derive rotation curves for the lenses, their orientation and, thus, greatly constrain lens models.Comment: 69 pages, Review on quasar lensing. Part of a LNP Topical Volume on "Dark matter and gravitational lensing", eds. F. Courbin, D. Minniti. To be published by Springer-Verlag 2002. Paper with full resolution figures can be found at ftp://oden.oso.chalmers.se/pub/tommy/mmviews.ps.g

Antithrombin attenuates myocardial dysfunction and reverses systemic fluid accumulation following burn and smoke inhalation injury: a randomized, controlled, experimental study

Introduction: We hypothesized that maintaining physiological plasma levels of antithrombin attenuates myocardial dysfunction and inflammation as well as vascular leakage associated with burn and smoke inhalation injury. Therefore, the present prospective, randomized experiment was conducted using an established ovine model. Methods: Following 40% of total body surface area, third degree flame burn and 4 × 12 breaths of cold cotton smoke, chronically instrumented sheep were randomly assigned to receive an intravenous infusion of 6 IU/kg/h recombinant human antithrombin (rhAT) or normal saline (control group; n = 6 each). In addition, six sheep were designated as sham animals (not injured, continuous infusion of vehicle). During the 48 h study period the animals were awake, mechanically ventilated and fluid resuscitated according to standard formulas. Results: Compared to the sham group, myocardial contractility was severely impaired in control animals, as suggested by lower stroke volume and left ventricular stroke work indexes. As a compensatory mechanism, heart rate increased, thereby increasing myocardial oxygen consumption. In parallel, myocardial inflammation was induced via nitric oxide production, neutrophil accumulation (myeloperoxidase activity) and activation of the p38-mitogen-activated protein kinase pathway resulting in cytokine release (tumor necrosis factor-alpha, interleukin-6) in control vs. sham animals. rhAT-treatment significantly attenuated these inflammatory changes leading to a myocardial contractility and myocardial oxygen consumption comparable to sham animals. In control animals, systemic fluid accumulation progressively increased over time resulting in a cumulative positive fluid balance of about 4,000 ml at the end of the study period. Contrarily, in rhAT-treated animals there was only an initial fluid accumulation until 24 h that was reversed back to the level of sham animals during the second day. Conclusions: Based on these findings, the supplementation of rhAT may represent a valuable therapeutic approach for cardiovascular dysfunction and inflammation after burn and smoke inhalation injury.<br