On asymptotic behavior at infinity and the finite section method for integral equations on the half-line

e consider integral equations on the half-line of the form and the finite section approximation to x obtained by replacing the infinite limit of integration by the finite limit β. We establish conditions under which, if the finite section method is stable for the original integral equation (i.e. exists and is uniformly bounded in the space of bounded continuous functions for all sufficiently large β), then it is stable also for a perturbed equation in which the kernel k is replaced by k + h. The class of perturbations allowed includes all compact and some non-compact perturbations of the integral operator. Using this result we study the stability and convergence of the finite section method in the space of continuous functions x for which ()()()=−∫∞dttxt,sk)s(x0()syβxβx()sxsp+1 is bounded. With the additional assumption that ()(tskt,sk−≤ where ()()(),qsomefor,sassOskandRLkq11>+∞→=∈− we show that the finite-section method is stable in the weighted space for ,qp≤≤0 provided it is stable on the space of bounded continuous functions. With these results we establish error bounds in weighted spaces for x - xβ and precise information on the asymptotic behaviour at infinity of x. We consider in particular the case when the integral operator is a perturbation of a Wiener-Hopf operator and illustrate this case with a Wiener-Hopf integral equation arising in acoustics.

Poverty-of-the-stimulus and SLA epistemology: considering L2 knowledge of aspectual phrasal semantics

Coupling a review of previous studies on the acquisition of grammatical aspects undertaken from contrasting paradigmatic views of second language acquisition (SLA) with new experimental data from L2 Portuguese, the present study contributes to this specific literature as well as general debates in L2 epistemology. We tested 31 adult English learners of L2 Portuguese across three experiments, examining the extent to which they had acquired the syntax and (subtle) semantics of grammatical aspect. Demonstrating that many individuals acquired target knowledge of what we contend is a poverty-of-the-stimulus semantic entailment related to the checking of aspectual features encoded in Portuguese preterit and imperfect morphology, namely, a [±accidental] distinction that obtains in a restricted subset of contexts, we conclude that UG-based approaches to SLA are in a better position to tap and gauge underlying morphosyntactic competence, since based on independent theoretical linguistic descriptions, they make falsifiable predictions that are amenable to empirical scrutiny, seek to describe and explain beyond performance, and can account for L2 convergence on poverty-of-the-stimulus knowledge as well as L2 variability/optionality.

The ocean’s role in setting the mean position of the Inter-Tropical Convergence Zone

Through study of observations and coupled climate simulations, it is argued that the mean position of the Inter-Tropical Convergence Zone (ITCZ) north of the equator is a consequence of a northwards heat transport across the equator by ocean circulation. Observations suggest that the hemispheric net radiative forcing of climate at the top of the atmosphere is almost perfectly symmetric about the equator, and so the total (atmosphere plus ocean) heat transport across the equator is small (order 0.2 PW northwards). Due to the Atlantic ocean’s meridional overturning circulation, however, the ocean carries significantly more heat northwards across the equator (order 0.4 PW) than does the coupled system. There are two primary consequences. First, atmospheric heat transport is southwards across the equator to compensate (0.2 PW southwards), resulting in the ITCZ being displaced north of the equator. Second, the atmosphere, and indeed the ocean, is slightly warmer (by perhaps 2 °C) in the northern hemisphere than in the southern hemisphere. This leads to the northern hemisphere emitting slightly more outgoing longwave radiation than the southern hemisphere by virtue of its relative warmth, supporting the small northward heat transport by the coupled system across the equator. To conclude, the coupled nature of the problem is illustrated through study of atmosphere–ocean–ice simulations in the idealized setting of an aquaplanet, resolving the key processes at work.

Optimal convergence estimates for the trace of the polynomial L2-projection operator on a simplex

In this paper we study convergence of the L2-projection onto the space of polynomials up to degree p on a simplex in Rd, d >= 2. Optimal error estimates are established in the case of Sobolev regularity and illustrated on several numerical examples. The proof is based on the collapsed coordinate transform and the expansion into various polynomial bases involving Jacobi polynomials and their antiderivatives. The results of the present paper generalize corresponding estimates for cubes in Rd from [P. Houston, C. Schwab, E. Süli, Discontinuous hp-finite element methods for advection-diffusion-reaction problems. SIAM J. Numer. Anal. 39 (2002), no. 6, 2133-2163].

Developmental changes in the balance of disparity, blur and looming/proximity cues to drive ocular alignment and focus

Accurate co-ordination of accommodation and convergence is necessary to view near objects and develop fine motor co-ordination. We used a remote haploscopic videorefraction paradigm to measure longitudinal changes in simultaneous ocular accommodation and vergence to targets at different depths, and to all combinations of blur, binocular disparity, and change-in-size (“proximity”) cues. Infants were followed longitudinally and compared to older children and young adults, with the prediction that sensitivity to different cues would change during development. Mean infant responses to the most naturalistic condition were similar to those of adults from 6-7 weeks (accommodation) and 8-9 weeks (vergence). Proximity cues influenced responses most in infants less than 14 weeks of age, but sensitivity declined thereafter. Between 12-28 weeks of age infants were equally responsive to all three cues, while in older children and adults manipulation of disparity resulted in the greatest changes in response. Despite rapid development of visual acuity (thus increasing availability of blur cues), responses to blur were stable throughout development. Our results suggest that during much of infancy, vergence and accommodation responses are not dependent on the development of specific depth cues, but make use of any cues available to drive appropriate changes in response.

Sparse polynomial approximation in positive order Sobolev spaces with bounded mixed derivatives and applications to elliptic problems with random loading

In the present paper we study the approximation of functions with bounded mixed derivatives by sparse tensor product polynomials in positive order tensor product Sobolev spaces. We introduce a new sparse polynomial approximation operator which exhibits optimal convergence properties in L2 and tensorized View the MathML source simultaneously on a standard k-dimensional cube. In the special case k=2 the suggested approximation operator is also optimal in L2 and tensorized H1 (without essential boundary conditions). This allows to construct an optimal sparse p-version FEM with sparse piecewise continuous polynomial splines, reducing the number of unknowns from O(p2), needed for the full tensor product computation, to View the MathML source, required for the suggested sparse technique, preserving the same optimal convergence rate in terms of p. We apply this result to an elliptic differential equation and an elliptic integral equation with random loading and compute the covariances of the solutions with View the MathML source unknowns. Several numerical examples support the theoretical estimates.

Sea-surface temperature records of Termination 1 in the Gulf of California: Challenges for seasonal and interannual analogues of tropical Pacific climate change

Centennial-scale records of sea-surface temperature and opal composition spanning the Last Glacial Maximum and Termination 1 (circa 25–6 ka) are presented here from Guaymas Basin in the Gulf of California. Through the application of two organic geochemistry proxies, the U37K′ index and the TEX86H index, we present evidence for rapid, stepped changes in temperatures during deglaciation. These occur in both temperature proxies at 13 ka (∼3°C increase in 270 years), 10.0 ka (∼2°C decrease over ∼250 years) and at 8.2 ka (3°C increase in <200 years). An additional rapid warming step is also observed in TEX86H at 11.5 ka. In comparing the two temperature proxies and opal content, we consider the potential for upwelling intensity to be recorded and link this millennial-scale variability to shifting Intertropical Convergence Zone position and variations in the strength of the Subtropical High. The onset of the deglacial warming from 17 to 18 ka is comparable to a “southern hemisphere” signal, although the opal record mimics the ice-rafting events of the north Atlantic (Heinrich events). Neither the modern seasonal cycle nor El Niño/Southern Oscillation patterns provide valid analogues for the trends we observe in comparison with other regional records. Fully coupled climate model simulations confirm this result, and in combination we question whether the seasonal or interannual climate variations of the modern climate are valid analogues for the glacial and deglacial tropical Pacific.

‘Getting known’: Beckett, Ireland and the creative industries

In the context of national and global trends of producing Beckett’s work, this essay will investigate recent productions of Beckett’s drama which originate in Ireland and tour internationally, examining how these relate to the concept of national identity and its marketability, as well the conceptual and material spaces provided by large-scale festival events. In the last few months, Pan Pan has toured its production of All that Fall from Dublin to the Beckett festival in Enniskillen to New York’s BAM. The Gate Theatre, always a powerhouse of Beckett productions, continues its revival of Barry McGovern’s adaptation of Watt; after the Edinburgh festival, the show will play London’s Barbican in March 2013. While originating in Ireland, these productions – those of the Gate in particular – have an international, as well as domestic, appeal. Examining these and forthcoming Gate productions, I query to what extent a theatre company’s cultural origins and international profile may create a perceived sense of authenticity or definitiveness among critical discourses at ‘home’ and abroad, and how such markers of identity are utilized by the marketing strategies which surround these productions. This article will interrogate the potential convergence of the globalized branding of both Beckett’s work and Irish identity, drawing on the writings of Bourdieu to elucidate how identity may be converted into economic and cultural capital, as well as examining the role that the festival event plays in this process.

A GCSS model intercomparison for a tropical squall line observed during toga-coare. II: Intercomparison of single-column models and a cloud-resolving model

This paper presents single-column model (SCM) simulations of a tropical squall-line case observed during the Coupled Ocean-Atmosphere Response Experiment of the Tropical Ocean/Global Atmosphere Programme. This case-study was part of an international model intercomparison project organized by Working Group 4 ‘Precipitating Convective Cloud Systems’ of the GEWEX (Global Energy and Water-cycle Experiment) Cloud System Study. Eight SCM groups using different deep-convection parametrizations participated in this project. The SCMs were forced by temperature and moisture tendencies that had been computed from a reference cloud-resolving model (CRM) simulation using open boundary conditions. The comparison of the SCM results with the reference CRM simulation provided insight into the ability of current convection and cloud schemes to represent organized convection. The CRM results enabled a detailed evaluation of the SCMs in terms of the thermodynamic structure and the convective mass flux of the system, the latter being closely related to the surface convective precipitation. It is shown that the SCMs could reproduce reasonably well the time evolution of the surface convective and stratiform precipitation, the convective mass flux, and the thermodynamic structure of the squall-line system. The thermodynamic structure simulated by the SCMs depended on how the models partitioned the precipitation between convective and stratiform. However, structural differences persisted in the thermodynamic profiles simulated by the SCMs and the CRM. These differences could be attributed to the fact that the total mass flux used to compute the SCM forcing differed from the convective mass flux. The SCMs could not adequately represent these organized mesoscale circulations and the microphysicallradiative forcing associated with the stratiform region. This issue is generally known as the ‘scale-interaction’ problem that can only be properly addressed in fully three-dimensional simulations. Sensitivity simulations run by several groups showed that the time evolution of the surface convective precipitation was considerably smoothed when the convective closure was based on convective available potential energy instead of moisture convergence. Finally, additional SCM simulations without using a convection parametrization indicated that the impact of a convection parametrization in forced SCM runs was more visible in the moisture profiles than in the temperature profiles because convective transport was particularly important in the moisture budget.

Forecast convergence score: a forecaster's approach to analysing hydro-meteorological forecast systems.

In this paper the properties of a hydro-meteorological forecasting system for forecasting river flows have been analysed using a probabilistic forecast convergence score (FCS). The focus on fixed event forecasts provides a forecaster's approach to system behaviour and adds an important perspective to the suite of forecast verification tools commonly used in this field. A low FCS indicates a more consistent forecast. It can be demonstrated that the FCS annual maximum decreases over the last 10 years. With lead time, the FCS of the ensemble forecast decreases whereas the control and high resolution forecast increase. The FCS is influenced by the lead time, threshold and catchment size and location. It indicates that one should use seasonality based decision rules to issue flood warnings.

Results of PMIP2 coupled simulations of the mid-Holocene and Last Glacial Maximum, Part 2: feedbacks with emphasis on the location of the ITCZ and mid- and high latitudes heat budget

A set of coupled ocean-atmosphere(-vegetation) simulations using state of the art climate models is now available for the Last Glacial Maximum (LGM) and the Mid-Holocene (MH) through the second phase of the Paleoclimate Modeling Intercomparison Project (PMIP2). Here we quantify the latitudinal shift of the location of the Intertropical Convergence Zone (ITCZ) in the tropical regions during boreal summer and the change in precipitation in the northern part of the ITCZ. For both periods the shift is more pronounced over the continents and East Asia. The maritime continent is the region where the largest spread is found between models. We also clearly establish that the larger the increase in the meridional temperature gradient in the tropical Atlantic during summer at the MH, the larger the change in precipitation over West Africa. The vegetation feedback is however not as large as found in previous studies, probably due to model differences in the control simulation. Finally, we show that the feedback from snow and sea-ice at mid and high latitudes contributes for half of the cooling in the Northern Hemisphere for the LGM, with the remaining being achieved by the reduced CO2 and water vapour in the atmosphere. For the MH the snow and albedo feedbacks strengthen the spring cooling and enhance the boreal summer warming, whereas water vapour reinforces the late summer warming. These feedbacks are modest in the Southern Hemisphere. For the LGM most of the surface cooling is due to CO2 and water vapour.

Screening for convergence insufficiency using the CISS is not indicated in young adults

Aim This paper presents Convergence Insufficiency Symptom Survey (CISS) and orthoptic findings in a sample of typical young adults who considered themselves to have normal eyesight apart from weak spectacles. Methods The CISS questionnaire was administered,followed by a full orthoptic evaluation, to 167 university undergraduate and postgraduate students during the recruitment phase of another study. The primary criterion for recruitment to this study was that participants‘feltthey had normal eyesight'. A CISS score of ≥21 was used to define‘significant’symptoms, and convergence insufficiency (CI) was defined as convergence≥8cm from the nose with a fusion range <15Δ base-out with small or no exophoria. Results The group mean CISS score was 15.4. In all, 17(10%) of the participants were diagnosed with CI, but 11(65%) of these did not have significant symptoms. 41(25%) participants returned a‘high’CISS score of ≥21 but only 6 (15%) of these had genuine CI. Sensitivity of the CISS to detect CI in this asymptomatic sample was 38%; specificity 77%; positive predictive value 15%; and negative predictive value 92%. The area under a receiver operating characteristic curve was 0.596 (95% CI 0.46 to 0.73). Conclusions‘Visual symptoms’are common in young adults, but often not related to any clinical defect, while true CI may be asymptomatic. This study suggests that screening for CI is not indicated

LTE and LTE-A interworking and interoperability with 3GPP and non-3GPP wireless networks

This paper provides a high-level overview of E-UTRAN interworking and interoperability with existing Third Generation Partnership Project (3GPP) and non-3GPP wireless networks. E-UTRAN access networks (LTE and LTE-A) are currently the latest technologies for 3GPP evolution specified in Release 8, 9 and beyond. These technologies promise higher throughputs and lower latency while also reducing the cost of delivering the services to fit with subscriber demands. 3GPP offers a direct transition path from the current 3GPP UTRAN/GERAN networks to LTE including seamless handover. E-UTRAN and other wireless networks interworking is an option that allows operators to maximize the life of their existing network components before a complete transition to truly 4G networks. Network convergence, backward compatibility and interpretability are regarded as the next major challenge in the evolution and the integration of mobile wireless communications. In this paper, interworking and interoperability between the E-UTRAN Evolved Packet Core (EPC) architecture and 3GPP, 3GPP2 and IEEE based networks are clearly explained. How the EPC is designed to deliver multimedia and facilitate interworking is also explained. Moreover, the seamless handover needed to perform this interworking efficiently is described briefly. This study showed that interoperability and interworking between existing networks and E-UTRAN are highly recommended as an interim solution before the transition to full 4G. Furthermore, wireless operators have to consider a clear interoperability and interworking plan for their existing networks before making a decision to migrate completely to LTE. Interworking provides not only communication between different wireless networks; in many scenarios it contributes to add technical enhancements to one or both environments.

When rules and principles are not enough: insiders’ views and narratives on the global financial crisis

Much has been written about Wall Street and the global financial crisis (GFC). From a fraudulent derivatives market to a contestable culture of banking bonuses, culpability has been examined within the frames of American praxis, namely that of American exceptionalism. This study begins with an exploratory analysis of non-US voices concerning the nature of the causes of the GFC. The analysis provides glimpses of the globalized extent of assumptions shared, but not debated within the globalization convergence of financial markets as the neo-liberal project. Practical and paradigmatic tensions are revealed in the capture of a London-based set of views articulated by senior financial executives of financial service organizations, the outcomes of which are not overly optimistic for any significant change in praxis within the immediate future.