The MacLane class and the Eremenko-Lyubich class

In 1970 G. R. MacLane asked if it is possible for a locally univalent function in the class A to have an arc tract. This question remains open, but several results about it have been given. We significantly strengthen these results, in particular replacing the condition of local univalence by the more general condition that the set of critical values is bounded. Also, we adapt a recent powerful technique of C. J. Bishop in order to show that there is a function in the Eremenko-Lyubich class for the disc that is not in the class A

Higgs-Yukawa model on the lattice

We present results from two projects on lattice calculations for the Higgs-Yukawa model. First we report progress on the search of first-order thermal phase transitions in the presence of a dimension-six operator, with the choices of bare couplings that lead to viable phenomenological predictions. In this project the simulations are performed using overlap fermions to implement the required chiral symmetry. Secondly, our study for applying finite-size scaling techniques near the Gaussian fixed point of the Higgs-Yukawa model is presented. We discuss the analytical formulae for the Higgs Yukawa model and show results for a first numerical study in the pure $O(4)$ scalar sector of the theory.Comment: 8 pages, 4 figures; Contribution to the proceedings of the 35th International Symposium on Lattice Field Theory, 18 - 24 June 2017, Granada, Spai

A lattice study of a chirally invariant Higgs-Yukawa model including a higher dimensional Φ6\Phi^6-term

We discuss the non-thermal phase structure of a chirally invariant Higgs-Yukawa model on the lattice in the presence of a higher dimensional $\Phi^6$-term. For the exploration of the phase diagram we use analytical, lattice perturbative calculations of the constraint effectice potential as well as numerical simulations. We also present first results of the effects of the $\Phi^6$-term on the lower Higgs boson mass bounds

Stabilizing the electroweak vacuum by higher dimensional operators in a Higgs-Yukawa model

The Higgs boson discovery at the LHC with a mass of approximately 126 GeV suggests, that the electroweak vacuum of the standard model may be metastable at very high energies. However, any new physics beyond the standard model can change this picture. We want to address this important question within a lattice Higgs-Yukawa model as the limit of the standard model (SM). In this framework we will probe the effect of a higher dimensional operator for which we take a $(\phi^{\dagger}\phi)^3$-term. Such a term could easily originate as a remnant of physics beyond the SM at very large scales. As a first step we investigate the phase diagram of the model including such a $(\phi^{\dagger}\phi)^3$ operator. Exploratory results suggest the existence of regions in parameter space where first order transitions turn to second order ones, indicating the existence of a tri-critical line. We will explore the phase structure and the consequences for the stability of the SM, both analytically by investigating the constraint effective potential in lattice perturbation theory, and by studying the system non-perturbatively using lattice simulations.Comment: 7 pages, 6 figures; Proceedings of the 31st International Symposium on Lattice Field Theory - LATTICE 201

Phase structure and Higgs boson mass in a Higgs-Yukawa model with a dimension-6 operator

We investigate the impact of a $\lambda_6 \varphi^6$ term included in a chirally invariant lattice Higgs-Yukawa model. Such a term could emerge from BSM physics at some larger energy scale. We map out the phase structure of the Higgs-Yukawa model with positive $\lambda_6$ and negative quartic self coupling of the scalar fields. To this end, we evaluate the constraint effective potential in lattice perturbation theory and also determine the magnetization of the model via numerical simulations which allow us to reach also non-perturbative values of the couplings. As a result, we find a complex phase structure with first and second order phase transitions identified through the magnetization. Further we analyze the effect of such a $\varphi^6$ term on the lower Higgs boson mass bound to see, whether the standard model lower mass bound can be altered.Comment: proceedings for The 32nd International Symposium on Lattice Field Theor

Spatial Externalities in Agriculture: Empirical Analysis, Statistical Identification, and Policy Implications

Spatial externalities can affect economic welfare and landscape pattern by linking farm returns on adjoining parcels of land. While policy can be informed by research that documents spatial externalities, statistically quantifying the presence of externalities from landscape pattern is insufficient for policy guidance unless the underlying cause of the externality can be identified as positive or negative. This article provides a springboard for empirical research by examining the underlying structure, social-environmental interactions, and statistical identification strategies for the analysis and quantification of agricultural spatial externalities that are derived from observations of landscape change. The potential for original policy treatments of agricultural spatial externalities in development and environment outcomes are highlighted.

Hydrostatic Gas Constraints On Supermassive Black Hole Masses: Implications For Hydrostatic Equilibrium And Dynamical Modeling In A Sample Of Early-Type Galaxies

We present new mass measurements for the supermassive black holes (SMBHs) in the centers of three early-type galaxies. The gas pressure in the surrounding, hot interstellar medium (ISM) is measured through spatially resolved spectroscopy with the Chandra X-ray Observatory, allowing the SMBH mass (M(BH)) to be inferred directly under the hydrostatic approximation. This technique does not require calibration against other SMBH measurement methods and its accuracy depends only on the ISM being close to hydrostatic, which is supported by the smooth X-ray isophotes of the galaxies. Combined with results from our recent study of the elliptical galaxy NGC4649, this brings the number of galaxies with SMBHs measured in this way to four. Of these, three already have mass determinations from the kinematics of either the stars or a central gas disk, and hence join only a handful of galaxies with MBH measured by more than one technique. We find good agreement between the different methods, providing support for the assumptions implicit in both the hydrostatic and the dynamical models. The stellar mass-to-light ratios for each galaxy inferred by our technique are in agreement with the predictions of stellar population synthesis models assuming a Kroupa initial mass function (IMF). This concurrence implies that no more than similar to 10%-20% of the ISM pressure is nonthermal, unless there is a conspiracy between the shape of the IMF and nonthermal pressure. Finally, we compute Bondi accretion rates (M(bondi)), finding that the two galaxies with the highest M(bondi) exhibit little evidence of X-ray cavities, suggesting that the correlation with the active galactic nuclei jet power takes time to be established.NASA NAS5-26555, NNG04GE76G, G07-8083XAstronom

The effect of spatial and temporal accumulation rate variability in west Antarctica on soluble ion deposition

Annually‐dated snowpit and ice core records from two areas of West Antarctica are used to investigate spatial accumulation patterns and to evaluate temporal accumulation rate/glaciochemical concentration and flux relationships. Mean accumulation rate gradients in Marie Byrd Land (11–23 gcm−2yr−1 over 150 km, decreasing to the south) and Siple Dome (10–18 gcm−2yr−1 over 60 km, decreasing to the south) are consistent for at least the last several decades, and demonstrate the influence of the offshore quasi‐permanent Amundsen Sea low pressure system on moisture flux into the region. Local and regional‐scale topography in both regions appears to affect orographic lifting, air mass trajectories, and accumulation distribution. Linear regression of mean annual soluble ion concentration and flux data vs. accumulation rates in both regions indicates that 1) concentrations are independent of and thus not a rescaling of accumulation rate time‐series, and 2) chemical flux to the ice sheet surface is mainly via wet deposition, and changes in atmospheric concentration play a significant role. We therefore suggest that, in the absence of detailed air/snow transfer models, ice core chemical concentration and not flux time‐series provide a better estimate of past aerosol loading in West Antarctica

New Zealand Guidelines for cyanobacteria in recreational fresh waters: Interim Guidelines

This document is divided into four main sections, plus 14 appendices. Section 1. Introduction provides an overview of the purpose and status of the document as well as advice on who should use it. Section 2. Framework provides a background to the overall guidelines approach, recommendations on agency roles and responsibilities, and information on the condition of use of this document. Section 3. Guidelines describes the recommended three-tier monitoring and action sequence for planktonic and benthic cyanobacteria. Section 4. Sampling provides advice on sampling planktonic and benthic cyanobacteria. The appendices give further background information and include templates for data collection and reporting, including: • background information on known cyanotoxins and their distribution in New Zealand • information on the derivation of guideline values • photographs of typical bloom events • a list of biovolumes for common New Zealand cyanobacteria • templates for field assessments • suggested media releases and warning sign templates. A glossary provides definitions for abbreviations and terms used in these guidelines