Affine insertion and Pieri rules for the affine Grassmannian

We study combinatorial aspects of the Schubert calculus of the affine Grassmannian Gr associated with SL(n,C). Our main results are: 1) Pieri rules for the Schubert bases of H^*(Gr) and H_*(Gr), which expresses the product of a special Schubert class and an arbitrary Schubert class in terms of Schubert classes. 2) A new combinatorial definition for k-Schur functions, which represent the Schubert basis of H_*(Gr). 3) A combinatorial interpretation of the pairing between homology and cohomology of the affine Grassmannian. These results are obtained by interpreting the Schubert bases of Gr combinatorially as generating functions of objects we call strong and weak tableaux, which are respectively defined using the strong and weak orders on the affine symmetric group. We define a bijection called affine insertion, generalizing the Robinson-Schensted Knuth correspondence, which sends certain biwords to pairs of tableaux of the same shape, one strong and one weak. Affine insertion offers a duality between the weak and strong orders which does not seem to have been noticed previously. Our cohomology Pieri rule conjecturally extends to the affine flag manifold, and we give a series of related combinatorial conjectures.Comment: 98 page

Le Luxe en fleurs dans la Naissance du jour

Cette étude s'efforce de retracer l'ascendance et les développements d'une vision du luxe dans la Naissance dujour . Tandis qu'il est possible de montrer que Colette, dans des articles sur la mode et à travers son oeuvre, souscrit pleinement au luxe industriel, il n'est pas sans intérêt de constater qu'une autre vision du luxe est mise en place dans ce récit poétique publié en 1928. En des pages très denses qui évoquent le bonheur de la retraite, se tranforme l'espace intime marqué par le calme et la douceur de vivre en un lieu où s'exalte et se raffine le désir.This study will attempt to trace the ascendancy and the developments of a particular vision of luxury in la Naissance du jour. If on the one hand it is possible to show, that Colette, in her articles on fashion and throughout her works, subscribes fully to luxury in its industrial meaning, on the other it is possible to notice that in this 1928 poetical narrative, another vision of luxury is put into place. In a compact style by which Colette evokes the joys of a retreat from Paris, she celebrates the transformation of intimate space marked by serenity into a place of exaltation and refinement of desire

kk-Schur functions and affine Schubert calculus

This book is an exposition of the current state of research of affine Schubert calculus and $k$-Schur functions. This text is based on a series of lectures given at a workshop titled "Affine Schubert Calculus" that took place in July 2010 at the Fields Institute in Toronto, Ontario. The story of this research is told in three parts: 1. Primer on $k$-Schur Functions 2. Stanley symmetric functions and Peterson algebras 3. Affine Schubert calculusComment: 213 pages; conference website: http://www.fields.utoronto.ca/programs/scientific/10-11/schubert/, updates and corrections since v1. This material is based upon work supported by the National Science Foundation under Grant No. DMS-065264

L'expérience affective des psychothérapeutes en séance : adaptation française et validation du Feeling Word Checklist 58

L'étude consiste en la traduction française et la validation du Feeling Word Checklist 58 (FWC-58; Røssberg, Hoffart, & Friis, 2003), un court questionnaire permettant à un thérapeute d'évaluer les réactions affectives vécues au cours d'une séance de psychothérapie. Le FWC-58 a été traduit en français à l'aide de la méthode de traduction inversée, puis les données ont été amassées auprès d'un échantillon de 236 psychologues et doctorants en psychologie clinique pratiquant la psychothérapie. À des fins de validation, le Countertransference Questionnaire (CTQ; Betan, Heim, Conklin, & Westen, 2005) et un questionnaire sociodémographique inspiré du Clinical Data Form (Westen & Shedler, 1999) évaluant différentes variables cliniques ont été utilisés. Une analyse factorielle exploratoire a permis de faire émerger une structure à six facteurs qui est satisfaisante au plan statistique et intéressante au plan clinique. La validité interne de cette version française, de même que la validité convergente et clinique de l'instrument sont discutées

Star colloids in nematic liquid crystals

We present a study of the elastic alignment, accompanying director field distortions, and elastic pair interactions of star-shaped colloids suspended in aligned nematic liquid crystals. We design and fabricate lithographic colloids, “N-stars”, containing N rod-like protrusions (i.e. “rays” or “arms”) each having a constant angle between adjacent rays. N-star geometries contain concave regions while retaining the rotational and mirror symmetries of regular polygonal platelets having N sides. Planar anchoring of the nematic director at N-star surfaces induces elastic deformations of the uniform background director, resulting in distinct orientational states and pair interactions that depend upon N. Director fields around isolated N-stars are characterized using polarized optical microscopy. For each N-star, we observe long-lived metastable orientational states with accompanying metastable director configurations, which are topologically distinct from the ground state director field. We develop a model, based on a superposition of the elastic energy of rod-like inclusions at appropriate angles to the far-field director, to estimate the energies in both cases. Numerical calculations of the director field around an individual ray elucidate the effect of azimuthal degeneracy in the anchoring and cross-sectional shape of the ray. The analytical results agree with the simulations, however, we find that the total elastic energy must be rescaled to account for weaker anchoring. The long-range elastic pair interactions between N-stars are probed using optical tweezers and video microscopy. We observe a distinct multipole depending on whether N is even or odd, which dominates the distance-dependence for attractive elastic forces between pairs of N-stars. Finally, we discuss assemblies made up of mixtures of different types of N-stars that display a variety of aggregated states

A Blueprint for Short-Term Petroleum Supply Crises Management

For most North Carolinians, and for that matter, most Americans, thoughts of the Organization of Petroleum Exporting Countries' (OPEC) oil embargo during the winter and spring of 1973 do not provide pleasant memories. It was a time of personal hardship, dramatically changing daily routines, considerable inconvenience, and a deepened national recession. However, the embargo's end saw most of the population return to normal routines, changed somewhat to accomodate higher petroleum prices, but unhampered by fuel shortages. A sluggish economy began the long slow road to recovery. But suspicion still lingers that the problem of future petroleum embargoes, and subsequent economic and daily chaos, remained unaddressed. Would the national and state governments be able to respond quickly and boldly should another sudden supply interruption occur in the near future? Are we better prepared for this contingency in the near future, and if we are, at what levels of preparedness are we? This paper is written to dispel some of the apprehension which now surrounds any discussion of petroleum embargoes. Its focus is short term supply crisis management caused by an embargo or natural catastrophe such as a break in the Alaskan pipeline. It describes the legislated national goals which will be operating during the next supply denial and briefly details the national programs which have been developed around them. It closes with a summary of actions which have been taken in North Carolina, and some comments on the basic orientation of the management framework and its implications to state and local policy making

Schubert Polynomials for the affine Grassmannian of the symplectic group

We study the Schubert calculus of the affine Grassmannian Gr of the symplectic group. The integral homology and cohomology rings of Gr are identified with dual Hopf algebras of symmetric functions, defined in terms of Schur's P and Q-functions. An explicit combinatorial description is obtained for the Schubert basis of the cohomology of Gr, and this is extended to a definition of the affine type C Stanley symmetric functions. A homology Pieri rule is also given for the product of a special Schubert class with an arbitrary one.Comment: 45 page

Brownian dynamics of colloidal microspheres with tunable elastic properties from soft to hard

We study the Brownian thermal motion of a colloidal model system made by emulsifying hot liquid α-eicosene wax into an aqueous surfactant solution of sodium dodecyl sulfate (SDS). When this waxy oil-in-water emulsion is cooled below α- eicosene's melting point of Tc ≃ 25 °C, the microscale emulsion droplets solidify, effectively yielding a dispersed particulate system. So, the interiors of these wax droplets can be tuned from a viscous liquid to an elastic solid through very modest changes in absolute temperature. Using the multiple light scattering technique of diffusing wave spectroscopy (DWS), which is very sensitive to small-scale motion and shape fluctuations of dispersed colloidal objects, we show that the thermal fluctuations of the interfaces of these liquid droplets at higher temperature, seen in the DWS intensity–intensity correlation function at early times, effectively disappear when these droplets solidify at lower temperature. Thus, we show that the early-time behavior of this DWS correlation function can be used to probe mechanical properties of viscoelastic soft materials dispersed as droplets