Bifurcations in the Space of Exponential Maps

This article investigates the parameter space of the exponential family $z\mapsto \exp(z)+\kappa$. We prove that the boundary (in \C) of every hyperbolic component is a Jordan arc, as conjectured by Eremenko and Lyubich as well as Baker and Rippon. In fact, we prove the stronger statement that the exponential bifurcation locus is connected in \C, which is an analog of Douady and Hubbard's celebrated theorem that the Mandelbrot set is connected. We show furthermore that $\infty$ is not accessible through any nonhyperbolic ("queer") stable component. The main part of the argument consists of demonstrating a general "Squeezing Lemma", which controls the structure of parameter space near infinity. We also prove a second conjecture of Eremenko and Lyubich concerning bifurcation trees of hyperbolic components.Comment: 29 pages, 3 figures. The main change in the new version is the introduction of Theorem 1.1 on the connectivity of the bifurcation locus, which follows from the results of the original version but was not explicitly stated. Also, some small revisions have been made and references update

Model Averaging in Risk Management with an Application to Futures Markets

This paper considers the problem of model uncertainty in the case of multi-asset volatility models and discusses the use of model averaging techniques as a way of dealing with the risk of inadvertently using false models in portfolio management. Evaluation of volatility models is then considered and a simple Value-at-Risk (VaR) diagnostic test is proposed for individual as well as ‘average ’ models. The asymptotic as well as the exact finite-sample distribution of the test statistic, dealing with the possibility of parameter uncertainty, are established. The model averaging idea and the VaR diagnostic tests are illustrated by an application to portfolios of daily returns on six currencies, four equity indices, four ten year government bonds and four commodities over the period 1991-2007. The empirical evidence supports the use of ‘thick’ model averaging strategies over single models or Bayesian type model averaging procedures

Kinetics and Solvent Effects in the Synthesis of Ionic Liquids

Ionic liquids (ILs) are being recognized as environmentally friendly ("green") solvents. However, their synthesis is often conducted in the very solvents that they will reportedly replace. This research has investigated the kinetics and solvent effects involved in synthesizing ILs in organic solvents and using compressed carbon dioxide. The kinetics for producing ILs have been found to be highly dependent on solvent polarities, and varied by over an order of magnitude. These dramatic effects were correlated to various polarity parameters to predict the kinetic rates. A detailed study of solvent toxicity and environmental impact was conducted to explore greener synthesis methods. Compressed CO2 was investigated as a potential benign alternative as the phase behavior and kinetics can be tuned for combined reaction and separation. Through understanding the kinetics, human/environmental impact, and phase equilibrium, ILs may be produced in a manner which may achieve their environmentally-benign potential

A separable strong-anisotropy approximation for pure qP-wave propagation in transversely isotropic media

CAPES - COORDENAÇÃO DE APERFEIÇOAMENTO DE PESSOAL DE NÍVEL SUPERIORCNPQ - CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICOThe wave equation can be tailored to describe wave propagation in vertical-symmetry axis transversely isotropic (VTI) media. The qP- and qS-wave eikonal equations derived from the VTI wave equation indicate that in the pseudoacoustic approximation, their dispersion relations degenerate into a single one. Therefore, when using this dispersion relation for wave simulation, for instance, by means of finite-difference approximations, both events are generated. To avoid the occurrence of the pseudo-S-wave, the qP-wave dispersion relation alone needs to be approximated. This can be done with or without the pseudoacoustic approximation. A Pade expansion of the exact qP-wave dispersion relation leads to a very good approximation. Our implementation of a separable version of this equation in the mixed space-wavenumber domain permits it to be compared with a low-rank solution of the exact qP-wave dispersion relation. Our numerical experiments showed that this approximation can provide highly accurate wave-fields, even in strongly anisotropic inhomogeneous media.The wave equation can be tailored to describe wave propagation in vertical-symmetry axis transversely isotropic (VTI) media. The qP- and qS-wave eikonal equations derived from the VTI wave equation indicate that in the pseudoacoustic approximation, their dispersion relations degenerate into a single one. Therefore, when using this dispersion relation for wave simulation, for instance, by means of finite-difference approximations, both events are generated. To avoid the occurrence of the pseudo-S-wave, the qP-wave dispersion relation alone needs to be approximated. This can be done with or without the pseudoacoustic approximation. A Pade expansion of the exact qP-wave dispersion relation leads to a very good approximation. Our implementation of a separable version of this equation in the mixed space-wavenumber domain permits it to be compared with a low-rank solution of the exact qP-wave dispersion relation. Our numerical experiments showed that this approximation can provide highly accurate wave-fields, even in strongly anisotropic inhomogeneous media.816C337C354CAPES - COORDENAÇÃO DE APERFEIÇOAMENTO DE PESSOAL DE NÍVEL SUPERIORCNPQ - CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICOCAPES - COORDENAÇÃO DE APERFEIÇOAMENTO DE PESSOAL DE NÍVEL SUPERIORCNPQ - CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICOsem informaçãosem informaçã

The effects of a background potential in star cluster evolution: a delay in the relaxation time-scale and runaway collision processes

Runaway stellar collisions in dense star clusters are invoked to explain the presence of very massive stars or blue stragglers in the center of those systems. This process has also been explored for the first star clusters in the Universe and shown to yield stars that may collapse at some points into an intermediate mass black hole. Although the early evolution of star clusters requires the explicit modeling of the gas out of which the stars form, these calculations would be extremely time-consuming and often the effects of the gas can be accurately treated by including a background potential to account for the extra gravitational force. We apply this approximation to model the early evolution of the first dense star clusters formed in the Universe by performing $N$-body simulations, our goal is to understand how the additional gravitational force affects the growth of a very massive star through stellar mergers in the central parts of the star cluster. Our results show that the background potential increases the velocities of the stars, causing an overall delay in the evolution of the clusters and in the runaway growth of a massive star at the center. The population of binary stars is lower due to the increased kinetic energy of the stars, initially reducing the number of stellar collisions, and we show that relaxation processes are also affected. Despite these effects, the external potential enhances the mass of the merger product by a factor $\sim$2 if the collisions are maintained for long times.Comment: 16 pages. Accepted for publication in Astronomy and Astrophysic

Efficacy Evaluation of Foliar Fungicide Application Timing in Field Corn in Central Nebraska, 2011

A foliar fungicide efficacy timing trial was conducted at the University of Nebraska-Lincoln South Central Agricultural Laboratory near Clay Center, NE. DeKalb corn hybrid DKC 62-54, rating of “good” (6 out of 9) for gray leaf spot (GLS) and “excellent” (2 out of 9) for common rust (CR), was planted on 3 May in 30 in. rows with a target population of 32,000 plants/A. The trial area was disked with a crop history of seven years of continuous corn. On 9 May before plant emergence, a herbicide program of Roundup (1 pt/A), Verdict (16 fl oz/A) and Atrazine (1 lb/A) was applied to the trial site. Eight treatments and a non-treated control were replicated six times in a randomized complete block design. Each plot was four rows (10 ft) wide by 40 ft in length. . . . There were significant differences among treatments for 500-count kernel weights as weights ranged from 6.11 oz to 6.39 oz. There were no statistical differences in grain moisture at harvest as percentages ranged from 14.9% to 15.3%. There were no statistical differences between treatments for dry yield. Priaxor, 4 fl oz/A at V6 was the lowest yielding treatment at 231.5 bu/A. Priaxor, 2 fl oz/A at V6 followed by Headline AMP, 10 fl oz/A at R1 was the highest yielding treatment with 244.0 bu/A

Kinetics and solvent effects in the synthesis of ionic liquids: imidazolium

This is the published version. Copyright 2009 Royal Society of ChemistryIonic liquids (ILs) are being considered as a promising class of potentially environmentally-friendly (“green”) solvents and materials for use in a variety of applications. However, ionic liquids are conventionally synthesized by batch, without known kinetics, in non-sustainable solvents. For ILs to be a truly “green” technology for widespread use, they must themselves be made in a correspondingly benign manner for low cost, as enabled by process development. This investigation will illustrate the kinetics and large solvent effects in the synthesis of 1-hexyl-3-methyl-imidazolium bromide in 10 different solvents: acetone, acetonitrile, 2-butanone, chlorobenzene, dichloromethane, dimethyl sulfoxide (DMSO), ethyl formate, ethyl lactate, methanol, and cyclopentanone. The kinetic rate constant for the synthesis in DMSO is over an order-of-magnitude larger than that in methanol. While the kinetic rate of these type of SN2 reactions is generally known to increase with solvent “polarity”, multi-parameter solvent descriptors, e.g. of Kamlet and Taft, are required to quantify these effects in a Linear Solvation Energy Relationship. These relationships are used with environmental and toxicity databases, such as the Rowan Solvent Selection Table, to rapidly optimize the solvent for favorable kinetics and minimal human and environmental impact

Dealing with Drought Stress in Home Lawns

Although cool-season turfgrasses in South Dakota typically suffer from summer stress during July and August, many lawns in the state experience stress earlier than normal during drought. You can make cultural modifications in lawn management to reduce injury or loss of turf and to conserve water resources. The majority of South Dakota lawns are a composite of one or more cool-season turfgrasses plus a number of assorted plant species considered weeds. Although Kentucky bluegrass is generally the major component in turfgrass seed mixtures purchased by homeowners, perennial ryegrass and fineleaf fescues are often included. Fineleaf fescues, such as hard fescue, chewings fescue, creeping red fescue, and sheep fescue, typically tolerate moderate drought conditions fairly well. Perennial ryegrass drought tolerance tends to be relatively poorer. Several options are available that will reduce watering costs and conserve water resources

Efficacy Evaluation of Foliar Fungicide Application Timing in Field Corn in Central Nebraska, 2011

A foliar fungicide efficacy timing trial was conducted at the University of Nebraska-Lincoln South Central Agricultural Laboratory near Clay Center, NE. DeKalb corn hybrid DKC 62-54, rating of “good” (6 out of 9) for gray leaf spot (GLS) and “excellent” (2 out of 9) for common rust (CR), was planted on 3 May in 30 in. rows with a target population of 32,000 plants/A. The trial area was disked with a crop history of seven years of continuous corn. On 9 May before plant emergence, a herbicide program of Roundup (1 pt/A), Verdict (16 fl oz/A) and Atrazine (1 lb/A) was applied to the trial site. Eight treatments and a non-treated control were replicated six times in a randomized complete block design. Each plot was four rows (10 ft) wide by 40 ft in length. . . . There were significant differences among treatments for 500-count kernel weights as weights ranged from 6.11 oz to 6.39 oz. There were no statistical differences in grain moisture at harvest as percentages ranged from 14.9% to 15.3%. There were no statistical differences between treatments for dry yield. Priaxor, 4 fl oz/A at V6 was the lowest yielding treatment at 231.5 bu/A. Priaxor, 2 fl oz/A at V6 followed by Headline AMP, 10 fl oz/A at R1 was the highest yielding treatment with 244.0 bu/A