Kernels of vector-valued Toeplitz operators

Let $S$ be the shift operator on the Hardy space $H^2$ and let $S^*$ be its adjoint. A closed subspace \FF of $H^2$ is said to be nearly $S^*$-invariant if every element f\in\FF with $f(0)=0$ satisfies S^*f\in\FF. In particular, the kernels of Toeplitz operators are nearly $S^*$-invariant subspaces. Hitt gave the description of these subspaces. They are of the form \FF=g (H^2\ominus u H^2) with $g\in H^2$ and $u$ inner, $u(0)=0$. A very particular fact is that the operator of multiplication by $g$ acts as an isometry on $H^2\ominus uH^2$. Sarason obtained a characterization of the functions $g$ which act isometrically on $H^2\ominus uH^2$. Hayashi obtained the link between the symbol \phii of a Toeplitz operator and the functions $g$ and $u$ to ensure that a given subspace \FF=gK_u is the kernel of T_\phii. Chalendar, Chevrot and Partington studied the nearly $S^*$-invariant subspaces for vector-valued functions. In this paper, we investigate the generalization of Sarason's and Hayashi's results in the vector-valued context.Comment: 20 pages, accepted by Integral Equations and Operator Theor

La creación del lugar Donostia - San Sebastian anterior a 1813: los casos de la colina sobre el puerto y del Campanario

En este trabajo se presenta una investigación cuyo objetivo es conocer, con mayor rigor científico, la formación de la ciudad de Donostia-San Sebastián en el pasado, como instrumento de valor y utilidad para entender la ciudad hoy existente y, así, intervenir mejor en ella. La investigación tiene tres fases: primera, una indagación cuidadosa con un examen minucioso de la documentación existente, tanto escrita como iconográfica, resaltando particularmente la cartografía antigua; segunda, un proceso de reconstitución a escala real de la ciudad hacia 1800, con la realización de un modelo 3D vectorial; y tercera, una lectura interpretativa de la constitución de la ciudad y sus permanencias actuales, acompañada de una transcripción gráfica y visual de las enseñanzas adquiridas. Se muestran dos casos de estudio dentro de esta ciudad del XVIII, el de la colina sobre el puerto y el del campanario, a modo de ejemplo de la investigación que se realiza.L’objet de ce travail est la presentation d’une recherche ayant pour but une connaissance plus rigoureuse et scientifique de la formation physique de la ville de Donostia-San Sebastian dans le passé, d’une grande importance et utilité pour comprendre et mieux intervenir dans la ville d’aujourd’hui. C’est une recherche qui se divise en trois phases: d’abord une recollection et un examen minutieux de la documentation existante aussi bien iconographique qu’écrite, dont la cartographie ancienne joue un rôle majeur, deuxièmement un processus de reconstitution, a son exacte echelle, de la ville vers 1800 grâce à l’élaboration d’un modèle 3D vectoriel et finalement une interpretation de la constitution de la ville et de ses permanences actuelles avec une transcription graphique et visuelle des enseignements acquis. L’étude de la colline surplombant le port et l’étude du clocher, elements importants de la ville du XVIII, servent içi d’exemple de la recherche en cours.This work is about a research whose aim is to know with more scientific rigor the physic formation of the town of Donostia-San Sebastián in the past, as a valuable and useful tool for the understanding of the present day city and a better intervention on it. This research is divided in three phases: first, a collecting and a meticulous examination of the existing both iconographic and written documentation, based mainly on the ancient cartography; secondly, a process of reconstitution of the town in 1800, at full scale, by means of a 3D vectorial model; and last, an interpretation of the town formation and its permanences, with a graphic and visual transcription of acquired information. The study of the hill above the harbour and the Campanile, important features of the XVIIIth century city, is showed here as an example of the current research.Peer Reviewe

Acquisition of French Liaison and Related Child Errors

Although French liaison is a major topic in the fields of adult French phonology and sociolinguistics, its acquisition remains a terra incognita. Moreover, very frequent liaison consonant substitutions ("les- n-ours" instead of the adult form "les ours" with a /z/ liaison) or insertions ("papa-n-ours" instead of "papa ours") are well-known stereotypes of the French "babytalk", but their relationship with the acquisition of liaison has never been considered. Three kinds of data addressing these issues are presented. First, 300 such errors in the speech of a girl (from 2;0 to 3;6) during daily interactions will be analyzed. They suggest that /n/ is the most intrusive liaison consonant (compared with /z/ and /t/). Second, an experimentation has been carried out with 4-year old children (N=24) with the purpose of eliciting errors in words with obligatory liaisons. The results provide confirmation that /n/ is the most intrusive liaison consonant and suggest that some children are prone to use the liaison consonant they have just heard : they say more ofen "un-z-ours" (with a /z/ liaison instead of the adult /n/) after they have heard "des ours" with an adult-like /z/ liaison. Third, an experiment with three age groups [age means: 3;5 (N=15), 4;6 (N=24), 5;8 (N=15)] investigates whether implicit knowledge about probabilistic phonotactic constraints is used in segmenting ambiguous "determiner-noun" sequences. For example, subjects are hearing "determiner + non-word" sequences including a /n/ or a /z/ consonant, whose lexical and syllabic status is ambiguous : in such a sequence as "un (n)apil", one cannot hear whether /n/ is the coda liaison consonant of "un" (un apil), or whether it is the consonantal onset of the non word (un napil). Subjects are then asked to replace the singular determiner "un" with the plural determiner "des" (and vice versa when "des" + non-word sequences are presented). Responses like [dezapil] suggest that they consider /n/ to be a liaison consonant. Responses like [denapil] suggest that they view /n/ as the initial onset of the non-word "napil". Results show that responses of the youngest group do not fit phonotactic constraints (in French, /n/ is more frequent than /z/ as a word initial consonant and /z/ more frequent than /n/ as a liaison consonant) . The discussion addresses two issues : (1) What is the lexical status of liaison in the phonological representation of young children ? (2) If knowlegdge about phonotactic constraints is not available before the age of 4, how could we explain that /n/ is the most intrusive liaison consonant as early as the age of 2

Que reste-t-il de la distinction compétence-performance dans les théories fondées sur l'usage ?

The usage-based approach to language brings together approaches that share the same working hypothesis i.e. that the genesis of language and the way language works both emerge from its usage. Although proponents of this approach criticise or reject the competence-performance distinction, they nonetheless continue to use it. A historical overview of the main reformulations of the Chomskian distinction in three scientific fields (cognitive psycholinguistics, the ethnography of communication and variationist sociolinguistics) establishes that the usage-based approach implements an integrative conception of competence. This conception includes, and sometimes generalises, elements drawn from these reformulations (cognitive processes, socio-cultural aspects to interaction, variation and the probabilistic aspect). As for performance, it seems to be understood as a series of data whereas the notion of usage event describes an interactional episode with its own dynamics. What remains of Chomsky's initial formulation is the idea of a system, with linguistic knowledge being understood not only as a set of processes and decisions called upon during the brief moment of the interaction, but also as a permanent structure of knowledge about language. Due to this desire for integration, the usage-based approach encounters the same difficulty that hampered some of its predecessors: how to model the link between linguistic and social knowledge (indexicality). However, recent elements drawn from cognitive neuroscience and exemplar theory can offer possible ways of meeting this interdisciplinary challenge.L'approche du langage fondée sur l'usage fédère des courants partageant l'hypothèse de travail selon laquelle le fonctionnement et la genèse du langage émergent de son usage. Bien qu'ils critiquent ou rejettent la distinction compétence-performance, les tenants de ce courant continuent à l'utiliser. L'examen des principales reformulations de la distinction chomskyenne dans trois champs scientifiques (psycholinguistique cognitive, ethnographie de la communication, sociolinguistique variationniste) fait apparaître que l'approche fondée sur l'usage met en œuvre une conception intégratrice de la compétence qui inclut et parfois généralise des éléments issus de ces reformulations : processus cognitifs, aspects socioculturel de l'interaction, variation et dimension probabiliste. La performance quant à elle renvoie essentiellement aux données recueillies alors que la notion d'événement d'usage décrit un épisode interactionnel doté d'une dynamique propre. De la formulation chomskyenne initiale, il subsiste la notion de système, la connaissance linguistique n'étant pas seulement perçue comme un ensemble de processus et de décisions mobilisés dans le temps bref de l'interaction, mais aussi comme une structure permanente de connaissances sur la langue. Du fait de cette volonté intégrative, l'approche fondée sur l'usage rencontre, comme ses prédécesseurs, des difficultés pour conceptualiser le lien entre connaissances linguistiques et connaissances sociales (indexicalité). Des éléments récents issus des neurosciences cognitives et de la théorie des exemplaires offrent des pistes pour relever ce défi interdisciplinaire

Electron transport through rectifying self-assembled monolayer diodes on silicon: Fermi level pinning at the molecule-metal interface

We report the synthesis and characterization of molecular rectifying diodes on silicon using sequential grafting of self-assembled monolayers of alkyl chains bearing a pi group at their outer end (Si/sigma-pi/metal junctions). We investigate the structure-performance relationships of these molecular devices and we examine to what extent the nature of the pi end-group (change in the energy position of their molecular orbitals) drives the properties of these molecular diodes. For all the pi-groups investigated here, we observe rectification behavior. These results extend our preliminary work using phenyl and thiophene groups (S. Lenfant et al., Nano Letters 3, 741 (2003)).The experimental current-voltage curves are analyzed with a simple analytical model, from which we extract the energy position of the molecular orbital of the pi-group in resonance with the Fermi energy of the electrodes. We report the experimental studies of the band lineup in these silicon/alkyl-pi conjugated molecule/metal junctions. We conclude that Fermi level pinning at the pi-group/metal interface is mainly responsible for the observed absence of dependence of the rectification effect on the nature of the pi-groups, even though they were chosen to have significant variations in their electronic molecular orbitalsComment: To be published in J. Phys. Chem.

Seismic evidence for olivine phase changes at the 410- and 660-kilometer discontinuities

The view that the seismic discontinuities bounding the mantle transition zone at 410- and 660-kilometer depths are caused by isochemical phase transformations of the olivine structure is debated. Combining converted-wave measurements in East Asia and Australia with seismic velocities from regional tomography studies, we observe a correlation of the thickness of, and wavespeed variations within, the transition zone that is consistent with olivine structural transformations. Moreover, the seismologically inferred Clapeyron slopes are in agreement with the mineralogical Clapeyron slopes of the (Mg,Fe)2SiO4spinel and postspinel transformations

The maintenance of regional dialects: a matter of gender? Boys, but not girls, use local varieties in relation to their friends' nativeness and local identity

The linguistic diversity enduring beyond institutional pressures and social prejudices against nonstandard dialects questions the social forces influencing language maintenance across generations and how children contribute to this process. Children encounter multi-dialectal interactions in their early environment, and increasing evidence shows that the acquisition of sociolinguistic variation is not a side issue but an inherent part of the general acquisition process. Despite these recent advances in sociolinguistic acquisition, children’s sociolinguistic uses remain under-studied in relation to peer social networks and the ability to use dialect for identity purposes. Our study focused on a grammatical sociolinguistic variable consisting of the alternation between a regional and a standard variant of the third person object pronoun in French. The regional variant is a remnant of the Francoprovençal language and its usage by adults is strongly associated with local identity in the French Alps. We described, using questionnaires, the social networks of 117 10-11 year-old girls and boys living in the same restricted rural area. Thirteen native target children (7 girls and 6 boys) were selected from the sample, as well as 39 same-sex friends chosen according to their place of birth (native vs non-native) and the duration of their friendship with the targets (number of years they have known each other). The target children were recorded during spontaneous dyadic conversations during free play at school with each category of friends. Target boys, but not girls, used the regional variant significantly more frequently with their long-term native friends than with their non-native friends. This adjustment mirrored their partners’ uses. Moreover, with long-term native friends, boys used the regional variant twice as frequently as girls. Boys appeared thus as key actors in the maintenance and the diffusion of regional cues in local social networks

The Poisson’s ratio of the Australian crust : geological and geophysical implications

The Poisson ratio, which depends on the VP/VS ratio, provides much tighter constraints on the crustal composition than either the compressional or the shear velocity alone. The crustal Poisson ratio can be determined from the joint analysis of the travel times of waves converted at the Moho and of crustal multiples reflected at the top of the Moho. We have analyzed the records of the permanent stations installed on the Australian continent, complemented by the data of the SKIPPY experiment. The results reveal substantial variations in the Poisson ratio in the different tectonic units. For the Proterozoic crust, an increase of the Poisson ratio with increasing crustal thickness is systematically observed while for the Phanerozoic crust, the Poisson ratio tends to decrease for increasing crustal thicknesses. These observations are in remarkable agreement with the results of the deep seismic soundings that were performed in the former Soviet Union. The variations observed in the Proterozoic provinces can perhaps be explained by underplating of mafic materials at the base of the crust