Monoid of self-equivalences and free loop spaces

Let be a simply-connected closed oriented -dimensional manifold. We prove that for any field of coefficients there exists a natural homomorphism of commutative graded algebras where is the loop algebra defined by Chas and Sullivan. As usual denotes the monoid of self-equivalences homotopic to the identity, and the space of based loops. When is of characteristic zero, yields isomorphisms where denotes the Hodge decomposition on .

     

Entropy-stabilized smectic C phase in a system of zigzag-shaped molecules

We report Monte Carlo simulations of a system of rigid zigzag-shaped molecules that demonstrate that simple excluded-volume interactions are sufficient to produce a fluid tilted lamellar [smectic C (SmC)] liquid crystal phase. The molecules are composed of three rigidly linked hard spherocylinders arranged in a zigzag fashion. By varying the zigzag angle we have mapped out the whole phase diagram as a function of pressure and zigzag angle Psi. For Psi between 35 degrees and 80 degrees our model simulation exhibits the SmC phase. This is the first conclusive evidence where steric interactions arising out of molecular shape alone induce the occurrence of the SmC phase for a wide range of zigzag angles. For smaller Psi, a transition from tilted crystal to crystal is observed.     

Embedding optimisation algorithms with Mosel

Algebraic modelling languages allow models to be implemented in such a way that they can easily be understood and modified. They are therefore a working environment commonly used by practitioners in Operations Research. Having once developed models, they need to be integrated inside the company information system. This step often involves embedding a model into a programming language environment: many existing algebraic modelling languages make possible to run parameterised models and subsequently retrieve their results, but without any facility for interacting with the model during the model generation or solution process.In this paper we show how to use the Mosel environment to implement complex algorithms directly in the modelling language.The Office cleaning problem is solved by a branch-and-cut algorithm, implemented entirely in the modelling language (including the definition of the callback function for the solver). Secondly, a cutting stock problem is solved by column generation, also implemented in the modelling language.AMS classification: 90Cxx, 65K05, 68N15     

Dissipative flow and vortex shedding in the Painlevé boundary layer of a Bose-Einstein condensate

This paper addresses the drag force and formation of vortices in the boundary layer of a Bose-Einstein condensate stirred by a laser beam following the experiments of Phys. Rev. Lett. 83, 2502 (1999)]. We make our analysis in the frame moving at constant speed where the beam is fixed. We find that there is always a drag around the laser beam. We also analyze the mechanism of vortex nucleation. At low velocity, there are no vortices and the drag has its origin in a wakelike phenomenon: This is a particularity of trapped systems since the density gets small in an extended region. The shedding of vortices starts only at a threshold velocity and is responsible for a large increase in drag. This critical velocity for vortex nucleation is lower than the critical velocity computed for the corresponding 2D problem at the center of the cloud.     

Double incoherent Raman scattering induced by molecular interactions in gases

A new Raman band is observed in two gases, CF4 and CH4. It is attributable to a double incoherent Raman scattering that takes place in pairs of interacting molecules. Spectral scattering intensities are given on an absolute scale. Zero order spectral moments are measured and are found higher than their long-range interaction value.     

Lithiation of 2-chloro- and 2-methoxypyridine with lithium dialkylamides: initial ortho-direction or subsequent lithium ortho-stabilization?

The lithiation pathway of 2-chloro and 2-methoxypyridine with LDA and LTMP has been investigated using deuterated probes. The availability of both H-6 and H-3 protons on the pyridine nucleus was found to be critical to ensure complete C-3 lithiation. We thus concluded that the C-3 lithiation was not a straightforward process. A mechanism involving precomplexation of lithium dialkylamides near the H-6 proton and formation of a 3,6-dilithio pyridine intermediate is proposed.     

Peptides derived from two dynamically disordered proteins self-assemble into amyloid-like fibrils

Short peptides derived from p14ARF and Hdm2 (14 and 15 amino acids in length, respectively), two cancer associated proteins, have been found to co-assemble into amyloid-like structures. Larger protein domains containing these peptide segments interact in cells and also undergo a disorder-to-order transition upon binding in vitro. In contrast to the association of beta-strand assemblies with amyloid diseases, the system described herein utilizes the formation of binary, extended beta-strands as a novel mechanism of biomolecular assembly. The beta-strand-containing fibrils formed from these peptides may allow the directed assembly of decorated fibrils with applications as biological nanostructures.     

Synthesis of stable derivatives of c(62): the first nonclassical fullerene incorporating a four-membered ring

A rational synthetic approach to the first four-membered ring-containing derivatives of C(62) is reported. They were synthesized by an inverse electron demand Diels-Alder reaction of 3,6-diaryl-1,2,4,5-tetrazines with C(60) in o-dichlorobenzene, followed by visible light irradiation at reflux. The structure of these nonclassical fullerenes derivatives was determined by X-ray single-crystal diffraction.     

Ferromagnetic Coupling through Spin Polarization in a Dinuclear Copper(II) Metallacyclophane

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