QDYBE: some explicit formulas for exchange matrix and related objects in case of sl(2), q=1

This mainly tutorial paper is intended as a somewhat larger example for parts of the theory exposed in the Lectures on the dynamical Yang-Baxter equations by P. Etingof and O. Schiffmann, math.QA/9908064. We explicitly compute the matrix entries of the intertwining operator, fusion matrix and exchange matrix associated to sl(2,R) for q=1. We also consider the weighted trace function and the dual Macdonald-Ruijsenaars equation for this particular case. As expected, the matrix entries of the exchange matrix turn out to be Racah polynomials. However, the road to their explicit formula via the fusion matrix is quick, and it also yields an interesting way to derive their orthogonality relations.Comment: 19 page

Confidence Regions for Calibrated Parameters in Computable General Equilibrium Models

We consider the problem of assessing the uncertainty of calibrated parameters in computable general equilibrium (CGE) models through the construction of confidence sets (or intervals) for these parameters. We study two different setups under which this can be done. The first one extends earlier work from Abdelkhalek and Dufour (1998) and is based on a projection technique which allows the construction of confidence sets for calibrated parameters from confidence sets on the free parameters of a (deterministc) CGE model. We discuss in detail how this approach can be applied to CES (Armington-type) function parameters frequently used in CGE models and illustrate it on models of the Moroccan economy. The second method allows one to extend the usual deterministic specification of CGE models by adding stochastic disturbances to the equations of the model and then to construct corresponding confidence sets for calibrated parameters using simulation techniques. This method uses the classical concept of a pivotal function for a parameter. We discuss in detail how this method can be applied to the calibrated parameters of a Cobb-Douglas production function. Nous considérons le problème de la prise en compte de l'incertitude sur les paramètres calibrés de modèles calculables d'équilibre général (MCEG) en construisant des régions (ou des intervalles) de confiance pour ces paramètres. Nous étudions en détail deux méthodes qui permettent de ce faire. La première est une extension des travaux de Abdelkhalek et Dufour (1998) et repose sur une technique de projection qui permet de construire des régions de confiance pour les paramètres calibrés à partir de régions de confiance pour les paramètres libres d'un MCEG déterministe. Nous discutons en détail comment cette approche peut être appliquée aux paramètres d'une fonction CES (de type Armington) d'usage fréquent dans les MCEG et nous l'illustrons sur des modèles de l'économie marocaine. La seconde méthode permet de dépasser le cadre déterministe usuel des MCEG en ajoutant des perturbations aléatoires à certaines équations du modèle pour construire des régions de confiance pour les paramètres calibrés en utilisant des techniques de simulation. Cette méthode utilise aussi le concept classique de fonction pivotale d'un paramètre. Nous discutons en détail comment cette méthode peut être appliquée aux paramèrtes calibrés d'une fonction de production de type Cobb-Douglas.Computable general equilibrium models, calibration, sensitivity analysis, confidence set, confidence interval, projection, Morocco, Modèles calculables d'équilibre général, calibration, région de confiance, intervalle de confiance, projection, analyse de sensibilité, Maroc

Parameter identification of a mechanical ductile damage using Artificial Neural Networks in sheet metal forming.

In this paper, we report on the developed and used of finite element methods, have been developed and used for sheet forming simulations since the 1970s, and have immensely contributed to ensure the success of concurrent design in the manufacturing process of sheets metal. During the forming operation, the Gurson–Tvergaard–Needleman (GTN) model was often employed to evaluate the ductile damage and fracture phenomena. GTN represents one of the most widely used ductile damage model. In this investigation, many experimental tests and finite element model computation are performed to predict the damage evolution in notched tensile specimen of sheet metal using the GTN model. The parameters in the GTN model are calibrated using an Artificial Neural Networks system and the results of the tensile test. In the experimental part, we used an optical measurement instruments in two phases: firstly during the tensile test, a digital image correlation method is applied to determinate the full-field displacements in the specimen surface. Secondly a profile projector is employed to evaluate the localization of deformation (formation of shear band) just before the specimen’s fracture. In the validation parts of this investigation, the experimental results of hydroforming part and Erichsen test are compared with their numerical finite element model taking into account the GTN model. A good correlation was observed between the two approaches

Circumstellar Disks Around Rapidly Rotating Be-Type Stars

Be stars are rapidly rotating B-type stars that eject large amounts of material into a circumstellar disk. Evidence of the presence of a disk is found through hydrogen emission lines in their spectra, IR excess flux, and linear intrinsic polarization. In this dissertation, we report the first simultaneous interferometric and spectroscopic observations of circumstellar disks around 24 bright Be stars made using the techniques of long baseline interferometry and moderate resolution spectroscopy in the near infrared. The goal of the project is to characterize the fundamental geometrical and physical properties of the emitting regions that are responsible for the IR flux excesses detected in the K-band in our sample stars. This observational work has been conducted with both the Center for High Angular Resolution Astronomy (CHARA) Array at Mount Wilson Observatory, and the Mimir spectrograph at Lowell Observatory. The visibility measurements were interpreted with different geometrical and physical disk models in order to determine the spatial extension of the disk, the inclination angle, the position angle, and the density profile of the disk. We find that the spatial extension of the circumstellar disk in the K-band is only about a few stellar radii, and that the density structure of the disk is consistent with a radially decreasing function with a density exponent that ranges between 2.5 and 3.5. The resulting disk densities are in a good agreement with those derived from the Infrared Astronomical Satellite (IRAS) measurements, and the resulting disk geometries are consistent with previous polarimetric measurements. We find that the K-band sizes of the emitting regions in the disk are smaller by a factor of two than the Hα sizes, and we show that this is due to the lower opacity of the continuum in the disk. By combining recent measurements of the projected rotational velocities with the disk inclination angles derived from interferometry, we were able to estimate the actual equatorial linear rotational velocities of the Be stars in our sample. The obtained linear rotational velocities indicate that Be stars are rapid rotators with an equatorial velocity that is about 0.7 - 0.9 of their critical velocities

Biosensors and Nanobiosensors: Design and Applications

The goal of this chapter is to cover the full scope of biosensors. It offers a survey of the principles, design, operation, and biomedical applications of the most popular types of biosensing devices in use today. By discussing recent research and future trends based on many excellent books and reviews, it is hoped to give the readers a comprehensive view on this fast growing field