Intégration Symplectique des Variétés de Poisson Régulières

Asymplectic integration of a Poisson manifold (M, Λ) is a symplectic groupoid (Γ,η) whichrealizes the given Poisson manifold, i.e. such that the space of units Γ₀ with the induced Poisson structure Λ₀ is isomorphic to (M, Λ). This notion was introduced by A. Weinstein in [28] in order to quantize Poisson manifolds by quantizing their symplectic integration. Any Poisson manifold can be integrated by alocal symplectic groupoid ([4], [13]) but already for regular Poisson manifolds there are obstructions to global integrability ([2], [6], [11], [17], [28]). The aim of this paper is to summarize all the known obstructions and present a sufficient topological condition for integrability of regular Poisson manifolds; we will indeed describe a concrete procedure for this integration. Further our criterion will provide necessary and sufficient if we require Γ to be Hausdorff, which is a suitable condition to proceed to Weinstein’s program of quantization. These integrability results may be interpreted as a generalization of the Cartan-Smith proof of Lie’s third theorem in the infinite dimensional case.

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Recherche supportée par D.G.I.C.Y.T. Espagne (Proyecto PB90-0765) et Xunta de Galicia (Proxecto XUGA20704B90)     

Spatio-temporal characteristics of the Portevin–Le Châtelier effect in austenitic steel with twinning induced plasticity

An experimental investigation of spatio-temporal characteristics of the Portevin–Le Châtelier (PLC) effect in austenitic steel with twinning induced plasticity (TWIP) is presented. Post-processing of high resolution digital images captured from specimens in quasi-static, room temperature tensile tests was conducted with a digital image correlation (DIC) method. This provided direct measurement of strain fields during all stages of the tests. Variable rate digital image capture, enabled with a custom image acquisition algorithm, guaranteed a suitable number of images recorded during serrations in load–time records. Nucleation, propagation, and morphology of individual PLC bands in both straight gage and tapered specimens were quantified with strain rate contours computed with a backward differentiation scheme. Time histories of strain evolution in the PLC band wakes were extracted from cumulative strain contours. Of the three types of PLC bands, only the continuously propagating Type A bands were observed. Band nucleation, which occurred at serration crests in flow curves derived from the DIC results, was not limited to regions of geometry-induced stress concentrations. Due to its importance in finite element springback predictions and to support theoretical model development of inelastic behavior in TWIP steel, we measured Young’s modulus variation with strain in periodic loading–unloading tests. Implications of the experimental results for theoretical modeling of the PLC effect in TWIP steel are discussed.     

Allyl-functionalized hybrid silica monoliths

A hybrid organosilica monolith was synthesized containing an allyl functionality. This provided a viable platform for producing silica-based, chromatographic, monolithic columns with the stationary phase bonded through a surface silicon-carbon bond rather than a conventional siloxane bond.     

Anisotropic enhancement of discrete diffraction and formation of two-dimensional discrete-soliton trains

We demonstrate anisotropic enhancement of discrete diffraction and formation of discrete-soliton trains in an optically induced photonic lattice. Such discrete behavior of light propagation was observed when a one-dimensional stripe beam was launched appropriately into a two-dimensional lattice created with partially coherent light. Our experimental results are corroborated with numerical simulations.     

Heteroclinic primary intersections and codimension one Melnikov method for volume-preserving maps

We study families of volume preserving diffeomorphisms in R(3) that have a pair of hyperbolic fixed points with intersecting codimension one stable and unstable manifolds. Our goal is to elucidate the topology of the intersections and how it changes with the parameters of the system. We show that the "primary intersection" of the stable and unstable manifolds is generically a neat submanifold of a "fundamental domain." We compute the intersections perturbatively using a codimension one Melnikov function. Numerical experiments show various bifurcations in the homotopy class of the primary intersections. (c) 2000 American Institute of Physics.     

An Algebraic Version of the Cantor-Bernstein-Schröder Theorem

The Cantor-Bernstein-Schröder theorem of the set theory was generalized by Sikorski and Tarski to -complete boolean algebras, and recently by several authors to other algebraic structures. In this paper we expose an abstract version which is applicable to algebras with an underlying lattice structure and such that the central elements of this lattice determine a direct decomposition of the algebra. Necessary and sufficient conditions for the validity of the Cantor-Bernstein-Schröder theorem for these algebras are given. These results are applied to obtain versions of the Cantor-Bernstein-Schröder theorem for -complete orthomodular lattices, Stone algebras, BL-algebras, MV-algebras, pseudo MV-algebras, ukasiewicz and Post algebras of order n.     

List of Contributors

Authors Index

List of Contributors     

Diagnosis of Impurity Levels in a Copolymerization Process

Summary: This work investigates a fault diagnosis problem in the copolymerization process of styrene and methyl methacrylate (STY/MMA). Two topics are discussed in this paper: the system observability and optimal experimental design (OED) to reduce fault misclassification. Lack of observability has been found to be one of the major causes of misclassification in fault diagnosis, which is not remediable by any means other than including the right measurements necessary for the observability. In this work, the system observability has been studied through simulation analysis. Then, two new experimental design methods are proposed to train the projection pursuit regression (PPR) algorithm for fault diagnosis purpose. The new design methods, referred to as Gaussian probability design and Fuzzy boundary design, are compared to a conventional factorial design, to evaluate their performance for the problem under study. The Gaussian probability design is based on the calculation of the probability of an experimental data point near a class boundary belonging to a specific class. The Fuzzy boundary design is based on a bootstrapping technique used in part for the learning process in developing neural network models. It investigates the insufficiency of training data based on the identification of class boundaries by a group of models, such as PPR models. Both Gaussian probability design and Fuzzy boundary design methods automatically search for the sparseness of the training data, and provide guidelines to include pairs of training data on two sides of a class boundary in the areas where the data density is the lowest. The proposed design methods outperform a conventional factorial design by reducing the fault misclassification more effectively with the same amount of additional training data.

Testing data in the process measurement space of temperature vs. conversion.