The “Essential Tension” at Work in Qualitative Analysis: A Case Study of the Opposite Points of View of Poincaré and Enriques on the Relationships between Analysis and Geometry

An analysis of the different philosophic and scientific visions of Henri Poincaré and Federigo Enriques relative to qualitative analysis provides us with a complex and interesting image of the “essential tension” between “tradition” and “innovation” within the history of science. In accordance with his scientific paradigm, Poincaré viewed qualitative analysis as a means for preserving the nucleus of the classical reductionist program, even though it meant “bending the rules” somewhat. To Enriques's mind, qualitative analysis represented the affirmation of a synthetic, geometrical vision that would supplant the analytical/quantitative conception characteristic of 19th-century mathematics and mathematical physics. Here, we examine the two different answers given at the turn of the century to the question of the relationship between geometry and analysis and between mathematics, on the one hand, and mechanics and physics, on the other.Copyright 1998 Academic Press.Un'analisi delle diverse posizioni filosofiche e scientifiche di Henri Poincaré e Federigo Enriques nei riguardi dell'analisi qualitativa fornisce un'immagine complessa e interessante della “tensione essenziale” tra “tradizione” e “innovazione” nell'ambito della storia della scienza. In linea con il proprio paradigma scientifico, Poincaré vedeva nell'analisi qualitativa un mezzo per preservare il nucleo del programma riduzionista calssico, anche se cio comportava una lieve “distorsione delle regole”. Nella mente di Enriques, l'analisi qualitativa rappresentava l'affermazione di un punto di vista sintetico e geometrico che avrebbe soppiantato la concezione analitico-quantitativa caratteristica della matematica e della fisica matematica del 19° secolo. Il nostro scopo principale è di esaminare due diverse risposte date a cavallo del secolo alla questione dei rapporti tra geometria e analisi e tra matematica da un lato e meccanica e fisica dall'altro.Copyright 1998 Academic Press.AMS subject classification: 01A55     

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     

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.     

Characterization of Mercury – Humic Acids Interaction by Potentiometric Titration with a Modified Carbon Paste Mercury Sensor

Stability constant for mercury binding by commercial and natural humic acids (HA) were determined using a new potentiometric mercury(II) sensor based on dithiosalicylic acid modified carbon paste electrode. The sensor present a high selective and sensitive response to mercury(II) ions, and a low detection limit of 1.8×10^?8 M. The potentiometric titrations curves of humic acids against mercury(II) ions were modeled. For 1.00×10^?7 to 3.00×10^?4 M mercury(II) ion concentration levels the results are consistent with the presence of two different binding sites in the humic acid macromolecule. The strongest binding sites (log K₁ ranging from 10.1 to 6.8) are probably due to interaction with carboxylic acid and amine groups in the molecule, whereas weakest binding sites (log K₂ ranging from 8.8 to 4.5) can be associated to phenolic groups.     

Complex formation of isocytosine tautomers with PdII and PtII

Isocytosine (ICH) exists in solution as two major tautomers, the keto form with N1 carrying a proton (1a) and the keto form with N3 being protonated (1b). In water, 1a and 1b exist in equilibrium with almost equal amounts of both forms present. Reactions with a series of Pd(II) and Pt(II) am(m)ine species such as (dien)Pd(II), (dien)Pt(II), and trans-(NH(3))(2)Pt(II) reveal, however, a distinct preference of these metals for the N3 site, as determined by (1)H NMR spectroscopy. Individual species have been identified by the pD dependence of the ICH resonances. pK(a) values (calculated for H(2)O) for deprotonation of the individual tautomers complexes are 6.5 and 6.4 for the N3 linkage isomers of dienPd(II) and dienPt(II), respectively, as well as 6.2 and 6.0 for the N1 linkage isomers. The dimetalated species [(dienM)(2)(IC-N1,N3)](3+) (M = Pd(II) or Pt(II)) are insensitive over a wide range of pD. The crystal structure analysis of [(dien)Pd(ICH-N3)](NO(3))(2) is reported. Ab initio calculations have been performed for tautomer compounds of composition [(NH(3))(3)Pt(ICH)](2+), cis- and trans-[(NH(3))(2)PtCl(ICH)](+), as well as trans-[(NH(3))(2)Pt(ICH)(2)](2+). Without exception, N3 linkage isomers are more stable, in agreement with experimental findings. As to the reasons for this binding preference, an NBO (natural bond orbital) analysis for [(NH(3))(3)Pt(ICH-N3)](2+)strongly suggests that intramolecular hydrogen bonding between trans-positioned NH(3) ligands and the two exocyclic groups of the ICH is of prime importance. The calculations furthermore show a marked pyramidalization of the NH(2) group of ICH in the complex once the heterocyclic ligand forms a dihedral angle <90 degrees with the Pt coordination plane.     

Photogeneration and quenching of reactive oxygen species by urocanic acid

Urocanic acid, UCA, is characterized by two electronic transitions in the UV-B (280-320 nm) which comprise its broad absorption spectrum and give rise to wavelength-dependent isomerization quantum yields. The absorption spectrum of UCA extends into the UV-A (320-400 nm). Given the UV-A component of sunlight is significantly greater than the UV-B component it is hypothesized even weak UV-A photochemistry of UCA could be important for in vivo responses to UV radiation. Degenerate pump-probe experiments performed on t-UCA at several wavelengths in the UV-A reveal an excited-state absorption that undergoes a rapid, approximately 1 ps decay. Photoacoustic experiments performed on both the cis and trans isomers reveal the formation of a long-lived intermediate following UV-A excitation. The efficiency and action spectra for this latter photoactive process are presented and are similar for both isomers of UCA. Cholesterol hydroperoxide assays designed to investigate the nature of the UV-A photoreactivity of t-UCA confirm the production of reactive oxygen species. The bimolecular rate constant for the quenching of singlet oxygen by t-UCA is determined to be 3.5 x 10(6) M(-1) s(-1). Taking into consideration recent theoretical calculations and jet expansion studies of the electronic structure of gas-phase t-UCA, a model is proposed to explain the isomerization and photoreactivity of t-UCA in solution over the UV-A region.     

Evaluation of isothermal kinetic of sweetener

Summary Sulfonylureas are widely used for the treatment of non-insulin dependent diabetes mellitus. Glibenclamide belongs to the group of substituted arylsulfonylureas. Many representative of this group shows polymorphism. The purpose of this work was to investigate the thermal behaviour and compatibility between glibenclamide and some excipients using thermoanalytical techniques (TG-DTG/DSC). The thermal and isothermal kinetics data showed incompatibility between glibenclamide and magnesium stearate.