On fencing problems

Fencing problems regard the bisection of a convex body in a way that some geometric measures are optimized. We introduce the notion of relative diameter and study bisections of centrally symmetric planar convex bodies, bisections by straight line cuts in general planar convex bodies and also bisections by hyperplane cuts for convex bodies in higher dimensions. In the planar case we obtain the best possible lower bound for the ratio between the relative diameter and the area.     

Canonical Structure and Symmetries of the Schlesinger Equations

The Schlesinger equations S _(n,m) describe monodromy preserving deformations of order m Fuchsian systems with n + 1 poles. They can be considered as a family of commuting time-dependent Hamiltonian systems on the direct product of n copies of m × m matrix algebras equipped with the standard linear Poisson bracket. In this paper we present a new canonical Hamiltonian formulation of the general Schlesinger equations S _(n,m) for all n, m and we compute the action of the symmetries of the Schlesinger equations in these coordinates.     

Lightly crosslinked,mesomorphic networks obtained through the reaction of dimeric,liquid‐crystalline epoxy–imine monomers and heptanedioic acid

We reacted various dimeric, liquid‐crystalline epoxy–imine monomers, differing in the length of the central aliphatic spacer or the dipolar moments, with heptanedioic acid. The resulting systems showed a liquid‐crystalline phase in some cases, depending on the dimer and on the reaction conditions. The systems were characterized with respect to their mesomorphic properties and then were submitted to dynamic mechanical thermal analysis in both fixed‐frequency and frequency‐sweep modes in the shear sandwich configuration. The arrangement in the liquid‐crystalline phase seemed to be mainly affected both by the polarization of the mesogen and by the reaction temperature, which favored the liquid‐crystalline arrangement when it was lying in the range of stability of the dimer mesophase. In agreement with other recent literature data, dynamic mechanical thermal analysis results suggested that the presence of the mesogen directly incorporated into the main chain increased the lifetimes of the elastic modes both in the isotropic phase and in the liquid‐crystalline phase with respect to side‐chain liquid‐crystalline elastomers and that the time–temperature superposition principle did not hold through the liquid‐crystalline‐to‐isotropic transition. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44:6270–6286, 2006     

Vinyl‐terminated side‐chain liquid‐crystalline polyethers containing mesogenic benzylideneaniline moieties

The synthesis of two vinyl‐terminated side‐chain liquid‐crystalline polyethers containing benzylideneaniline moieties as mesogenic cores was approached in two different ways: by chemically modifying poly(epichlorohydrin) with suitable mesogenic acids or by polymerizing analogous glycidyl ester or glycidyl ether derivatives. In all the conditions tested, the first approach led to materials in which the imine group was hydrolyzed. The second approach led to the desired polymers PG2a and PG2b , but only from the glycidyl ether derivatives and when the initiator was the system that combined polyiminophosphazene base t‐Bu‐P₄ and 3,5‐di‐t‐butylphenol. These polymers were chemically characterized by IR and ¹H and ¹³C NMR spectroscopies. The estimated degrees of polymerization ranged from 30 to 36. The liquid crystalline behavior of the synthesized polymers was studied by differential scanning calorimetry, polarized optical microscopy (POM) and X‐ray diffraction. Both polymers behave like liquid crystals and exhibited a single mesophase, which was recognized as a smectic C mesophase, probably with a bilayer arrangement, i.e., a smectic C₂ mesophase. The crosslinking of both polymers was performed with dicumyl peroxide as initiator, which led to liquid crystalline thermosets. POM and X‐ray diffraction confirmed that the mesophase organization mantained on the crosslinked materials. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 1877–1889, 2006     

Time reversal for infinite-dimensional diffusions

Summary In this paper we analize the reversibility of the diffusion property for the solution of certain infinite-dimensional systems of stochastic differential equations. Necessary and sufficient conditions ensuring this reversibility are given. The proofs use the techniques of the stochastic calculus of variations.This work was partly done when the first author was visiting the Centre de Recerca Matemàtica at Barcelona     

Calorimetric approach to tetronic/water interactions

Tetronic^®comprises X-shaped copolymers formed by four poly(propylene oxide) (PPO) andpoly(ethylene oxide) (PEO) block chains bonded to an ethylene diamine centralgroup. Micellization behaviour of three representative Tetronics (T304, T904and T1307) was characterized to gain an insight into the interactions betweenthe copolymer unimers and the state of water in their solutions. The enthalpyof demicellization, recorded at 37°C in an isoperibol microcalorimeter,indicated that the process was in all cases exothermic and the enthalpy rankedin the order T1307≥T904>>T304. Micellization is entropy-driven owing tohydrophobic interactions between the PPO chains.DSC analysisshowed that the crystallization and melting peaks of the free water remainingin T304 and T904 solutions were progressively shifted toward lower temperaturesas the surfactant proportion increased, owing to a colligative effect. Boundwater corresponded to 3 water molecules per EO repeating unit. In the caseof T1307, which has longer PEO chains, a splitting of the melting peak wasobserved, one peak appearing around 0°C due to free water and anotherat –15°C due to interfacial water. As T1307 proportion raised, theenthalpy of the former decreased, whilst the enthalpy of the latter increased.In 40% T1307 solutions, interfacial water overcame the proportion of freewater; there being 1 interfacial and 3 bound water molecules per EO repeatingunit. Gaussian deconvolution of FTIR spectra also enabled to characterizethe evolution of free water as a function of Tetronic proportion. The dependenceof micellization and water interaction behaviour on Tetronics structure shouldbe taken into account to use these copolymers as drug solubilizers and micellarcarriers.     

THE α-OXIDASE SYSTEM OF YOUNG PEA LEAVES (Pisum sativum) AS GENERATOR OF ELECTRONICALLY EXCITED STATES. EXCITATION IN THE DARK UNDER NATURAL CONDITIONS

Abstract. The aerobic oxidation of saturated long chain fatty acids to the lower aldehyde and CO₂ catalyzed by the α-oxidase system of young leaves from germinating Pisum sativum results in concomitant excitation of the chloroplasts or/and fractions present in the α-oxidase preparation. The excitation is attested to by both chlorophyll emission and Hill activity. This is the first case of photobiochemistry without light within a natural system.     

Accreditation of reference material producers: the example of IRMM's Reference Materials Unit

The potential approaches for third-party assessment of reference material producers are revisited and the activities of the Reference Materials (RM) Unit of the Institute for Reference Materials and Measurements (IRMM) to obtain accreditation to ISO Guide 34 and ISO 17025 are described. Accreditation was related to the Unit as all matrix RM activities of the institute are concentrated there. A management system was established that allows sufficient flexibility to be applicable to a wide range of RMs while being precise enough to ensure compliance with ISO Guides 30, 31 and especially 34 and 35. Accreditation was achieved in 2004 with independent scopes for testing and RM production and was confirmed and extended in 2005. The key aspects of the RM Unit's management system for RM production are presented. Presented at BERM-10, April 2006, Charleston, SC, USA     

Molecular modeling study of the differential ligand–receptor interaction at the μ, δ and κ opioid receptors

3D models of the opioid receptors , and were constructed using BUNDLE, an in-house program to build de novo models of G-protein coupled receptors at the atomic level. Once the three opioid receptors were constructed and before any energy refinement, models were assessed for their compatibility with the results available from point-site mutations carried out on these receptors. In a subsequent step, three selective antagonists to each of three receptors (naltrindole, naltrexone and nor-binaltorphamine) were docked onto each of the three receptors and subsequently energy minimized. The nine resulting complexes were checked for their ability to explain known results of structure-activity studies. Once the models were validated, analysis of the distances between different residues of the receptors and the ligands were computed. This analysis permitted us to identify key residues tentatively involved in direct interaction with the ligand.     

High mobility of dithiophene-tetrathiafulvalene single-crystal organic field effect transistors

Single-crystal field effect transistors of the organic semiconductor dithiophene-tetrathiafulvalene (DT-TTF) were prepared by drop casting. Long, thin crystals connected two microfabricated gold electrodes, and a silicon substrate was used as a back gate. The highest hole mobility observed was 1.4 cm2/Vs, which is the highest reported for an organic semiconductor not based on pentacene. A high ON/OFF ratio of at least 7 x 105 was obtained for this device.