Bounded coherent states and excitonic systems

New bounded coherent state construction, based in a Keldysh conjecture, is presented. The particular group structure arising from the model leads a new symmetry transformations for the coherent state system. The emergent new symmetry transformations are reminiscent of the Bogoliubov ones. This construction is applied to describe an excitonic system. We discuss how the symmetry of these transformations is intrinsically related with the stability and the behavior of the physical systems as in the excitonic case.     

Should Epstein strip arrangement be changed?

The paper describes effect of texture on the anisotropy of magnetic properties and shows that an Epstein strip arrangement including strips cut in a direction 45° to the rolling direction gives property values that are closer to the average values than the traditional RD+TD arrangement.     

Bounded rank-one perturbations in sampling theory

Sampling theory concerns the problem of reconstruction of functions from the knowledge of their values at some discrete set of points. In this paper we derive an orthogonal sampling theory and associated Lagrange interpolation formulae from a family of bounded rank-one perturbations of a self-adjoint operator that has only discrete spectrum of multiplicity one.     

Thermal monitoring of morphology in triblock terpolymers with crystallizable blocks

The bulk morphology of poly(1,4‐butadiene)–block–polystyrene–block–poly (ethylene oxide) (PB‐b‐PS‐b‐PEO) and polyethylene–block–polystyrene–block–poly (ethylene oxide) (PE‐b‐PS‐b‐PEO) triblock terpolymers is analyzed under a thermal protocol. This allows the investigation of the morphology during the occurrence of thermal transitions, such as crystallization and melting, which is a neat way of studying the competition between microphase separation and crystallization for the morphology formation. Only one of the studied systems presented a morphological transition upon melting of the PEO and the PE blocks, attributed to the crystallization of the PE block in finite interconnected domains. All the other systems presented no morphological transitions during the thermal scan. The results prove that the crystallization only disrupt the microphases generated in the molten state under very specific circumstances for these block copolymers. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 3197–3206, 2007     

Flow injection preconcentration by chemofiltration and spectrophotometric determination of Gd

A new on-line Gd preconcentration and determination system associated to flow injection (FI) method was developed. 2,2′-(1,8-dihydroxy-3,6-disulfonaphthylene-2,7-bisazo) bisbenzenearsonic acid (Arsenazo III) was used as a complexing agent at pH 2.5. A reactor containing the polyamide membrane was used for the retention of the Gd complex by chemofiltration. The complex was then removed from the reactor with buffer solution pH 9. The variables affecting the combined on-line preconcentration-absorptiometric method have been evaluated and optimised. The coupling of the on-line preconcentration and spectrophotometric flow through detection led to a detection limit of 15 μg l⁻¹ for a preconcentration time of 5 min at 2 ml/min. The method was successfully applied to biological samples.     

Algorithm for the Semigroup of a Space Curve Singularity

The semigroup of values of irreducible space curve singularities is the set of intersection multiplicities among hypersurfaces and the given curve. It is an invariant of the singularity, and for plane curves it characterizes the equisingularity type considered by Zariski. For space curve singularities the semigroup of values is a numerical semigroup and it can not be computed by means of the exponents of any Puiseux parametrization, as in the plane case. We obtain an algorithm for calculating the semigroup of values of a space curve singularity, which determines the generators of the semigroup and the valuation ideals associated with the semigroup. We give a Maple version of the algorithm.     

Minimal, rigid foliations by curves on ℂℙ n

We prove the existence of minimal and rigid singular holomorphic foliations by curves on the projective space ℂℙ ⁿ for every dimension n≥2 and every degree d≥2. Precisely, we construct a foliation ℱ which is induced by a homogeneous vector field of degree d, has a finite singular set and all the regular leaves are dense in the whole of ℂℙ ⁿ . Moreover, ℱ satisfies many additional properties expected from chaotic dynamics and is rigid in the following sense: if ℱ is conjugate to another holomorphic foliation by a homeomorphism sufficiently close to the identity, then these foliations are also conjugate by a projective transformation. Finally, all these properties are persistent for small perturbations of ℱ.?This is done by considering pseudo-groups generated on the unit ball 𝔹 ⁿ ⊆ℂ ⁿ by small perturbations of elements in Diff(ℂ ⁿ ,0). Under open conditions on the generators, we prove the existence of many pseudo-flows in their closure (for the C ⁰-topology) acting transitively on the ball. Dynamical features as minimality, ergodicity, positive entropy and rigidity may easily be derived from this approach. Finally, some of these pseudo-groups are realized in the transverse dynamics of polynomial vector fields in ℂℙ ⁿ . Received March 7, 2002 / final version received November 26, 2002?Published online February 7, 2003 Most of this work has been carried out during a visit of the first author to IMPA/RJ and a visit of the second author to the University of Lille 1. We would like to thank these institutes for hospitality and express our gratitude to CNPq-Brazil and CNRS-France for the financial support which made these visits possible. We are also indebted to Paulo Sad, Marcel Nicolau and the referee whose comments helped us to improve on the preliminary version. Finally, the second author has partially conducted this research for the Clay Mathematics Institute.