The actions ofS n+1 andS n on the cohomology ring of a coxeter arrangement of typeA n−1

Let be the complexified Coxeter arrangement of hyperplanes of typeA _n−1. In this paper we construct anS _n+1 extension of the naturalS _n action on the complex cohomology ring of the complement ofA _n−1. Recurrence formulas connecting characters with respect to theS _n and theS _n+1 action are given.     

Packing T-joins

A consequence of Seymour's characterization of binary clutters with the Max Flow Min Cut property is that the minimum cardinality of a T-cut is equal to the largest number of edge-disjoint T-joins in every graph that cannot be T-contracted to an odd K_2,3. We give a simple “graphic” proof of this fact. © 1996 John Wiley & Sons, Inc.     

Tuning the phase transition of ZnO thin films through lithography: an integrated bottom‐up and top‐down processing

An innovative approach towards the physico‐chemical tailoring of zinc oxide thin films is reported. The films have been deposited by liquid phase using the sol–gel method and then exposed to hard X‐rays, provided by a synchrotron storage ring, for lithography. The use of surfactant and chelating agents in the sol allows easy‐to‐pattern films made by an organic–inorganic matrix to be deposited. The exposure to hard X‐rays strongly affects the nucleation and growth of crystalline ZnO, triggering the formation of two intermediate phases before obtaining a wurtzite‐like structure. At the same time, X‐ray lithography allows for a fast patterning of the coatings enabling microfabrication for sensing and arrays technology.     

Firing-Induced Microstructural Properties of Quasi-Diamagnetic Carbonate-Based Porous Ceramics: a <Superscript>1</Superscript>H NMR Relaxation Correlation Study

This study deals with the application of two-dimensional proton nuclear magnetic resonance relaxometry (2D ¹H NMR-R) to the characterization of porous ceramics nearly free of magnetic compounds. Different microstructural properties were obtained by firing a diamagnetic mixture of kaolin, calcium, and magnesium carbonate over a wide range of maximum temperatures (600–1100 °C) and firing times at the maximum temperature (soaking times) (0–10 h). The 2D ¹H NMR-R method relies on the correlated measurement of ¹H longitudinal (T ₁) and transverse (T ₂) relaxation times of pore-filling water by which the properties of the interconnected pore space may be investigated. In the absence of significant magnetic susceptibility effect due to para- and ferro-magnetic compounds, the 2D ¹H NMR-R maps allow studying the conjoint effects on pore size distribution and inter-pore coupling due to the variations in both time and temperature of firing. The NMR experiments were performed with a low-field ¹H NMR sensor, which allows non-destructive and in situ analysis. For ceramic specimens fired at 600 and 700 °C, the fraction of smallest pores increases with firing time at the expenses of those with intermediate size. The pore shrinkage occurring at this stage, and likely associated with the transformation of kaolinite in metakaolinite, is affected in a similar way by soaking time and firing temperature, in line with the concept of equivalent firing temperature. At temperatures from 800 to 1100 °C, the structural modifications involving interconnectivity and average pore size are driven primarily by firing temperature and, secondarily, by soaking time. The 2D ¹H NMR-R results are confirmed by more traditional, but destructive, mineralogical, and structural analyses like X-ray powder diffraction, helium pycnometry, mercury intrusion porosimetry, and nitrogen adsorption/desorption method.     

Covariant Sectors with Infinite Dimension¶and Positivity of the Energy

Let ? be a local conformal net of von Neumann algebras on S ¹ and ρ a M?bius covariant representation of ?, possibly with infinite dimension. If ρ has finite index, ρ has automatically positive energy. If ρ has infinite index, we show the spectrum of the energy always to contain the positive real line, but, as seen by an example, it may contain negative values. We then consider nets with Haag duality on ℝ, or equivalently sectors with non-solitonic extension to the dual net; we give a criterion for irreducible sectors to have positive energy, namely this is the case iff there exists an unbounded M?bius covariant left inverse. As a consequence the class of sectors with positive energy is stable under composition, conjugation and direct integral decomposition. Received: 21 April 1997 / Accepted: 23 September 1997     

Nonlinear behavior of vocal fold vibration: The role of coupling between the vocal folds

Coupling between the vocal folds is one of the nonlinear mechanisms allowing regulation and synchronization of mucosal vibration. The purpose of this study was to establish that modulations such as diplophonia and abnormalities observed in vocal signals that may be observed in some cases of laryngeal pathology can be considered as nonlinear behavior due to the persistence of some physical interaction (coupling). An experimental model using excised porcine larynx was designed to create tension asymmetry between the vocal folds and to obtain vocal signals with modulations. Signals were analyzed by spectral analysis and the phase portrait method. Results were compared with computer-generated synthetic signals corresponding to nonlinear combinations of sinusoid signals. Under these conditions, evidence of nonlinear behavior was detected in 85% of experimental signals. These findings were interpreted as a demonstration of vocal fold interaction. Based on these findings, the authors conclude that (1) coupling must be taken into account in physical models of laryngeal physiology, and that (2) methods of nonlinear dynamics may be used for objective voice analysis.     

Nonrelativistic Geodesic Motion

We show that any second-order dynamic equationon a configuration space X R ofnonrelativistic time-dependent mechanics can be seen asa geodesic equation with respect to some (nonlinear)connection on the tangent bundle TX X of relativisticvelocities. We compare relativistic and nonrelativisticgeodesic equations, and study the Jacobi vector fieldsalong nonrelativistic geodesics.     

Noise-Induced Drift in Stochastic Differential Equations with Arbitrary Friction and Diffusion in the Smoluchowski-Kramers Limit

We consider the dynamics of systems with arbitrary friction and diffusion. These include, as a special case, systems for which friction and diffusion are connected by Einstein fluctuation-dissipation relation, e.g. Brownian motion. We study the limit where friction effects dominate the inertia, i.e. where the mass goes to zero (Smoluchowski-Kramers limit). Using the Itô stochastic integral convention, we show that the limiting effective Langevin equations has different drift fields depending on the relation between friction and diffusion. Alternatively, our results can be cast as different interpretations of stochastic integration in the limiting equation, which can be parametrized by α∈?. Interestingly, in addition to the classical Itô (α=0), Stratonovich (α=0.5) and anti-Itô (α=1) integrals, we show that position-dependent α=α(x), and even stochastic integrals with α?[0,1] arise. Our findings are supported by numerical simulations.     

The surface layers dual to hydrodynamic boundaries

The AdS/hydrodynamics correspondence provides a 1–1 map between large wavelength features of AdS black branes and conformal fluid flows. In this note we consider boundaries between nonrelativistic flows, applying the usual boundary conditions for viscous fluids. We find that a naive application of the correspondence to these boundaries yields a surface layer in the gravity theory whose stress tensor is not equal to that given by the Israel matching conditions. In particular, while neither stress tensor satisfies the null energy condition and both have nonvanishing momentum, only Israel's tensor has stress. The disagreement arises entirely from corrections to the metric due to multiple derivatives of the flow velocity, which violate Israel's finiteness assumption in the thin wall limit.