The irreducible unitary representations of the extended Poincare group in (1+1) dimensions

We prove that the extended Poincare group in (1+1) dimensions is non-nilpotent solvable exponential, and therefore that it belongs to type I. We determine its first and second cohomology groups in order to work out a classification of the two-dimensional relativistic elementary systems. Moreover, all irreducible unitary representations of the extended Poincare group are constructed by the orbit method. The most physically interesting class of irreducible representations corresponds to the anomaly-free relativistic particle in (1+1) dimensions, which cannot be fully quantized. However, we show that the corresponding coadjoint orbit of the extended Poincare group determines a covariant maximal polynomial quantization by unbounded operators, which is enough to ensure that the associated quantum dynamical problem can be consistently solved, thus providing a physical interpretation for this particular class of representations.Comment: 12 pages, Revtex 4, letter paper; Revised version of paper published in J. Math. Phys. 45, 1156 (2004

Semidirect products and the Pukanszky condition

We study the general geometrical structure of the coadjoint orbits of a semidirect product formed by a Lie group and a representation of this group on a vector space. The use of symplectic induction methods gives new insight into the structure of these orbits. In fact, each coadjoint orbit of such a group is obtained by symplectic induction on some coadjoint orbit of a "smaller" Lie group. We study also a special class of polarizations related to a semidirect product and the validity of Pukanszky's condition for these polarizations. Some examples of physical interest are discussed using the previous methods.Comment: 33 pages, including special macros and fonts (JGPpaper.tex is the source TeX file), to appear in J. Geom. Phys., also available via anonymous ftp or via gopher gopher://cpt.univ-mrs.fr

Decreased oxygen permeability of EVOH through molecular interactions

Poly(ethylene-co-vinyl alcohol) of 48 mol% ethylene content was modified with N,N'-bis(2,2,6,6-tetramethyl-4-piperidyl)-isophthalamide (Nylostab SEED) to decrease the oxygen permeability of the polymer. The additive was added in a wide concentration range from 0 to 10 wt%. The structure and properties of the polymer were characterized with various methods including differential scanning calorimetry, X-ray diffraction, mechanical testing, optical measurements and oxygen permeation. Interactions were estimated by molecular modeling and infrared spectroscopy. The results showed that oxygen permeation decreased considerably when the additive was added at less than 2.0 wt% concentration. The decrease resulted from the interaction of the hydroxyl groups of the polymer and the amide groups of the additive. The dissolution of the additive in the polymer led to decreased crystallinity, but also to decreased mobility of amorphous molecules. Stiffness and strength, but also deformability increased as a result. Above 2 wt% the additive forms a separate phase leading to the deterioration of properties. The success of the approach represents a novel way to control oxygen permeation in EVOH and in other polymers with similar functional groups capable of strong interactions

Improvement of the impact resistance of natural fiber–reinforced polypropylene composites through hybridization

Polypropylene (PP) hybrid composites were prepared by the combination of naturalreinforcements and poly(ethylene terephthalate) (PET) fibers. Wood, flax, and sugarpalm fibers were used to increase stiffness and strength, while PET fibers served toimprove impact resistance. Interfacial adhesion was increased by using a maleated PP(MAPP) coupling agent. The hybrid composites containing 20 wt% of the naturalfibers were homogenized in a twin-screw compounder and then injection moldedinto standard tensile specimens. The amount of PET fibers was changed from 0 to40 wt% in the composites. Tensile and impact testing, acoustic emission measure-ments, and scanning electron microscopy (SEM) were used for the characterizationof the composites as well as to follow deformation and failure processes. The resultsproved that the concept of using PET fibers to improve impact resistance works withall natural fibers. Local deformations, the debonding or pullout of the PET fibers, initi-ate the plastic deformation of the matrix, which consumes considerable energy. Thefracture of PET fibers might also contribute to energy absorption. The type of naturalfiber does not influence the effect; the amount of PET fibers determines fractureresistance. The improvement of interfacial adhesion by coupling increases strengthand slightly improves impact resistance. The overall properties of the hybrid compos-ites prepared are acceptable, sufficiently large stiffness and impact resistance beingachieved for a large number of structural application

Plancherel formula for Berezin deformation of L2L^2 on Riemannian symmetric space

Consider the space B of complex $p\times q$ matrces with norm <1. There exists a standard one-parameter family $S_a$ of unitary representations of the pseudounitary group U(p,q) in the space of holomorphic functions on B (i.e. scalar highest weight representations). Consider the restriction $T_a$ of $S_a$ to the pseudoorthogonal group O(p,q). The representation of O(p,q) in $L^2$ on the symmetric space $O(p,q)/O(p)\times O(q)$ is a limit of the representations $T_a$ in some precise sence. Spectrum of a representation $T_a$ is comlicated and it depends on $\alpha$. We obtain the complete Plancherel formula for the representations $T_a$ for all admissible values of the parameter $\alpha$. We also extend this result to all classical noncompact and compact Riemannian symmetric spaces

Notes on Stein-Sahi representations and some problems of non L2L^2 harmonic analysis

We discuss one natural class of kernels on pseudo-Riemannian symmetric spaces.Comment: 40p

Stein--Sahi complementary series and their degenerations

The aim of the paper is an introduction to Stein--Sahi complementary series, holomorphic series, and 'unipotent representations'. We also discuss some open problems related to these objects. For the sake of simplicity, we consider only the groups U(n,n).Comment: 40pp, 7fig, revised versio