Stability of stationary solutions of the forced Navier-Stokes equations on the two-torus

We study the linear and nonlinear stability of stationary solutions of the forced two-dimensional Navier-Stokes equations on the domain [0,2π]x[0,2π/α], where α ϵ(0,1], with doubly periodic boundary conditions. For the linear problem we employ the classical energy{enstrophy argument to derive some fundamental properties of unstable eigenmodes. From this it is shown that forces of pure χ2-modes having wavelengths greater than 2π do not give rise to linear instability of the corresponding primary stationary solutions. For the nonlinear problem, we prove the equivalence of nonlinear stability with respect to the energy and enstrophy norms. This equivalence is then applied to derive optimal conditions for nonlinear stability, including both the high-and low-Reynolds-number limits.

Searching for happiness across cultures

Three experiments examined the cultural relativity of emotion recognition using the visual search task. Caucasian-English and Japanese participants were required to search for an angry or happy discrepant face target against an array of competing distractor faces. Both cultural groups performed the task with displays that consisted of Caucasian and Japanese faces in order to investigate the effects of racial congruence on emotion detection performance. Under high perceptual load conditions, both cultural groups detected the happy face more efficiently than the angry face. When perceptual load was reduced such that target detection could be achieved by feature-matching, the English group continued to show a happiness advantage in search performance that was more strongly pronounced for other race faces. Japanese participants showed search time equivalence for happy and angry targets. Experiment 3 encouraged participants to adopt a perceptual based strategy for target detection by removing the term 'emotion' from the instructions. Whilst this manipulation did not alter the happiness advantage displayed by our English group, it reinstated it for our Japanese group, who showed a detection advantage for happiness only for other race faces. The results demonstrate cultural and linguistic modifiers on the perceptual saliency of the emotional signal and provide new converging evidence from cognitive psychology for the interactionist perspective on emotional expression recognition.

Measuring students' emotions in the early years: the Achievement Emotions Questionnaire-Elementary School (AEQ-ES)

This article reports about the development and validation of a measurement instrument assessing elementary school students' achievement emotions (Achievement Emotions Questionnaire-Elementary School, AEQ-ES). Specifically, the instrument assesses students' enjoyment, anxiety, and boredom pertaining to three types of academic settings (i.e., attending class, doing homework, and taking tests and exams). Scale construction was based on Pekrun's (2006) control-value theory of achievement emotions. The instrument was tested using samples from German and American elementary school classrooms. The results of Study 1 (German sample) corroborate the reliability and structural validity of the new emotion measure. Moreover, they show that students' achievement emotions were linked with their control and value appraisals as well as their academic performance, thus supporting the external validity of the measure as well as propositions of Pekrun's (2006) control-value theory of achievement emotions. Study 2 (American sample) corroborated the cross-cultural equivalence of the measure and the generalizability of findings across the German and American samples. Implications for research on achievement emotions and educational practice are discussed. (PsycINFO Database Record (c) 2013 APA, all rights reserved)(journal abstract)

Conceptual representation in bilinguals: the role of language specificity and conceptual change

Most prominent models of bilingual representation assume a degree of interconnection or shared representation at the conceptual level. However, in the context of linguistic and cultural specificity of human concepts, and given recent findings that reveal a considerable amount of bidirectional conceptual transfer and conceptual change in bilinguals, a particular challenge that bilingual models face is to account for non-equivalence or partial equivalence of L1 and L2 specific concepts in bilingual conceptual store. The aim of the current paper is to provide a state-of-the-art review of the available empirical evidence from the fields of psycholinguistics, cognitive, experimental, and cross-cultural psychology, and discuss how these may inform and develop further traditional and more recent accounts of bilingual conceptual representation. Based on a synthesis of the available evidence against theoretical postulates of existing models, I argue that the most coherent account of bilingual conceptual representation combines three fundamental assumptions. The first one is the distributed, multi-modal nature of representation. The second one concerns cross-linguistic and cross-cultural variation of concepts. The third one makes assumptions about the development of concepts, and the emergent links between those concepts and their linguistic instantiations.

Infrared absorption spectra, radiative efficiencies, and global warming potentials of newly-detected halogenated compounds: CFC-113a, CFC-112 and HCFC-133a

CFC-113a (CF3CCl3), CFC-112 (CFCl2CFCl2) and HCFC-133a (CF3CH2Cl) are three newly detected molecules in the atmosphere that are almost certainly emitted as a result of human activity. It is important to characterise the possible contribution of these gases to radiative forcing of climate change and also to provide information on the CO2-equivalence of their emissions. We report new laboratory measurements of absorption cross-sections of these three compounds at a resolution of 0.01 cm−1 for two temperatures 250 K and 295 K in the spectral range of 600–1730 cm−1. These spectra are then used to calculate the radiative efficiencies and global warming potentials (GWP). The radiative efficiencies are found to be between 0.15 and 0.3 W∙m−2∙ppbv−1. The GWP for a 100 year time horizon, relative to carbon dioxide, ranges from 340 for the relatively short-lived HCFC-133a to 3840 for the longer-lived CFC-112. At current (2012) concentrations, these gases make a trivial contribution to total radiative forcing; however, the concentrations of CFC-113a and HCFC-133a are continuing to increase. The 2012 CO2-equivalent emissions, using the GWP (100), are estimated to be about 4% of the current global CO2-equivalent emissions of HFC-134a

Interpolation of Hilbert and Sobolev spaces: quantitative estimates and counterexamples

This paper provides an overview of interpolation of Banach and Hilbert spaces, with a focus on establishing when equivalence of norms is in fact equality of norms in the key results of the theory. (In brief, our conclusion for the Hilbert space case is that, with the right normalisations, all the key results hold with equality of norms.) In the final section we apply the Hilbert space results to the Sobolev spaces Hs(Ω) and tildeHs(Ω), for s in R and an open Ω in R^n. We exhibit examples in one and two dimensions of sets Ω for which these scales of Sobolev spaces are not interpolation scales. In the cases when they are interpolation scales (in particular, if Ω is Lipschitz) we exhibit examples that show that, in general, the interpolation norm does not coincide with the intrinsic Sobolev norm and, in fact, the ratio of these two norms can be arbitrarily large.

The STEP scale: a measure of short-term export performance improvement

This article is a direct response to a recent observation in the literature that managers appear to be short-term oriented in their assessment of the performance of an export venture (Madsen 1998). On the basis of a cross-national survey of exporting firms, the authors present a three-dimensional scale for assessing managerial judgment of short-term export performance (i.e., the STEP scale). The three dimensions are (1) satisfaction with short-term performance improvement, (2) short-term exporting intensity improvement, and (3) expected short-term performance improvement. The scale presents evidence of reliability as well as convergent, discriminant, and nomological validity, and it reveals factorial similarity and factorial equivalence across both samples. The authors outline managerial and public policy implications that stem from the scale and identify avenues for further export marketing research.

Representation errors and retrievals in linear and nonlinear data assimilation

This article shows how one can formulate the representation problem starting from Bayes’ theorem. The purpose of this article is to raise awareness of the formal solutions,so that approximations can be placed in a proper context. The representation errors appear in the likelihood, and the different possibilities for the representation of reality in model and observations are discussed, including nonlinear representation probability density functions. Specifically, the assumptions needed in the usual procedure to add a representation error covariance to the error covariance of the observations are discussed,and it is shown that, when several sub-grid observations are present, their mean still has a representation error ; socalled ‘superobbing’ does not resolve the issue. Connection is made to the off-line or on-line retrieval problem, providing a new simple proof of the equivalence of assimilating linear retrievals and original observations. Furthermore, it is shown how nonlinear retrievals can be assimilated without loss of information. Finally we discuss how errors in the observation operator model can be treated consistently in the Bayesian framework, connecting to previous work in this area.

Observational and energetics constraints on the non-conservation of potential/Conservative Temperature and implications for ocean modelling

This paper seeks to elucidate the fundamental differences between the nonconservation of potential temperature and that of Conservative Temperature, in order to better understand the relative merits of each quantity for use as the heat variable in numerical ocean models. The main result is that potential temperature is found to behave similarly to entropy, in the sense that its nonconservation primarily reflects production/destruction by surface heat and freshwater fluxes; in contrast, the nonconservation of Conservative Temperature is found to reflect primarily the overall compressible work of expansion/contraction. This paper then shows how this can be exploited to constrain the nonconservation of potential temperature and entropy from observed surface heat fluxes, and the nonconservation of Conservative Temperature from published estimates of the mechanical energy budgets of ocean numerical models. Finally, the paper shows how to modify the evolution equation for potential temperature so that it is exactly equivalent to using an exactly conservative evolution equation for Conservative Temperature, as was recently recommended by IOC et al. (2010). This result should in principle allow ocean modellers to test the equivalence between the two formulations, and to indirectly investigate to what extent the budget of derived nonconservative quantities such as buoyancy and entropy can be expected to be accurately represented in ocean models.

Metacognition and proofreading: the roles of aging, motivation, and interest

Objectives: The current study examined younger and older adults’ error detection accuracy, prediction calibration, and postdiction calibration on a proofreading task, to determine if age-related difference would be present in this type of common error detection task. Method: Participants were given text passages, and were first asked to predict the percentage of errors they would detect in the passage. They then read the passage and circled errors (which varied in complexity and locality), and made postdictions regarding their performance, before repeating this with another passage and answering a comprehension test of both passages. Results: There were no age-related differences in error detection accuracy, text comprehension, or metacognitive calibration, though participants in both age groups were overconfident overall in their metacognitive judgments. Both groups gave similar ratings of motivation to complete the task. The older adults rated the passages as more interesting than younger adults did, although this level of interest did not appear to influence error-detection performance. Discussion: The age equivalence in both proofreading ability and calibration suggests that the ability to proofread text passages and the associated metacognitive monitoring used in judging one’s own performance are maintained in aging. These age-related similarities persisted when younger adults completed the proofreading tasks on a computer screen, rather than with paper and pencil. The findings provide novel insights regarding the influence that cognitive aging may have on metacognitive accuracy and text processing in an everyday task.

Emission of polycyclic aromatic hydrocarbons from gasohol and ethanol vehicles

The exhaust emission of the polycyclic aromatic hydrocarbons (PAHs) considered toxic to human health were investigated on two spark ignition light duty vehicles, one being gasohol (Gasohol, in Brazil, is the generic denomination for mixtures of pure gasoline plus 20-25% of anhydrous ethyl alcohol fuel (AEAF).)-fuelled and the other a flexible-fuel vehicle fuelled with hydrated ethanol. The influence of fuel type and quality, aged lubricant oil type and use of fuel additives on the formation of these compounds was tested using standardized tests identical to US FTP-75 cycle. PAH sampling and chemical analysis followed the basic recommendations of method TO-13 (United States. Environmental Protection Agency, 1999. Compendium Method TO-13A - Determination of polycyclic Aromatic hydrocarbons (PAH) in Ambient Air Using Gas Chromatography/Mass Spectrometry (CG/MS). Center for environmental research information, Cincinnati, p. 78), with the necessary modification for this particular application. Results showed that the total PAH emission factor varied from 41.9 mu g km(-1) to 612 mu g km(-1) in the gasohol vehicle, and from 11.7 mu g km(-1) to 27.4 mu g km(-1) in the ethanol-fuelled vehicle, a significant difference in favor of the ethanol vehicle. Generally, emission of light molecular weight PAHs was predominant, while high molecular weights PAHs were not detected. In terms of benzo(a)pyrene toxicity equivalence, emission factors varied from 0.00984 mu g TEQ km(-1) to 4.61 mu g TEQ km(-1) for the gasohol vehicle and from 0.0117 mu g TEQ km(-1) to 0.0218 mu g TEQ km(-1) in the ethanol vehicle. For the gasohol vehicle, results showed that the use of fuel additive causes a significant increase in the emission of naphthalene and phenanthrene at a confidence level of 90% or higher; the use of rubber solvent on gasohol showed a reduction in the emission of naphthalene and phenanthrene at the same confidence level; the use of synthetic oil instead of mineral oil also contributed significantly to a decrease in the emission of naphthalene and fluorene. In relation to the ethanol vehicle, the same factors were tested and showed no statistically significant influence on PAH emission. (c) 2008 Elsevier Ltd. All rights reserved.

Use of Bayesian Methods for Multivariate Bioequivalence Measures

In this paper, we introduce a Bayesian analysis for bioequivalence data assuming multivariate pharmacokinetic measures. With the introduction of correlation parameters between the pharmacokinetic measures or between the random effects in the bioequivalence models, we observe a good improvement in the bioequivalence results. These results are of great practical interest since they can yield higher accuracy and reliability for the bioequivalence tests, usually assumed by regulatory offices. An example is introduced to illustrate the proposed methodology by comparing the usual univariate bioequivalence methods with multivariate bioequivalence. We also consider some usual existing discrimination Bayesian methods to choose the best model to be used in bioequivalence studies.

SINGULARITY THEORY AND FORCED SYMMETRY BREAKING IN EQUATIONS

A theory of bifurcation equivalence for forced symmetry breaking bifurcation problems is developed. We classify (O(2), 1) problems of corank 2 of low codimension and discuss examples of bifurcation problems leading to such symmetry breaking.

On the continuity of pullback attractors for evolution processes

In this paper we give general results on the continuity of pullback attractors for nonlinear evolution processes. We then revisit results of [D. Li, P.E. Kloeden, Equi-attraction and the continuous dependence of pullback attractors on parameters, Stoch. Dyn. 4 (3) (2004) 373-384] which show that, under certain conditions, continuity is equivalent to uniformity of attraction over a range of parameters (""equi-attraction""): we are able to simplify their proofs and weaken the conditions required for this equivalence to hold. Generalizing a classical autonomous result [A.V. Babin, M.I. Vishik, Attractors of Evolution Equations, North Holland, Amsterdam, 1992] we give bounds on the rate of convergence of attractors when the family is uniformly exponentially attracting. To apply these results in a more concrete situation we show that a non-autonomous regular perturbation of a gradient-like system produces a family of pullback attractors that are uniformly exponentially attracting: these attractors are therefore continuous, and we can give an explicit bound on the distance between members of this family. (C) 2009 Elsevier Ltd. All rights reserved.

STABILITY FOR RETARDED FUNCTIONAL DIFFERENTIAL EQUATIONS

It is known that retarded functional differential equations can be regarded as Banach-space-valued generalized ordinary differential equations (GODEs). In this paper, some stability concepts for retarded functional differential equations are introduced and they are discussed using known stability results for GODEs. Then the equivalence of the different concepts of stabilities considered here are proved and converse Lyapunov theorems for a very wide class of retarded functional differential equations are obtained by means of the correspondence of this class of equations with GODEs.