Spectral theory for commutative algebras of differential operators on Lie groups

The joint spectral theory of a system of pairwise commuting self-adjoint left-invariant differential operators L₁,…,Ln on a connected Lie group G is studied, under the hypothesis that the algebra generated by them contains a “weighted subcoercive operator” of ter Elst and Robinson (1998) [52]. The joint spectrum of L₁,…,Ln in every unitary representation of G is characterized as the set of the eigenvalues corresponding to a particular class of (generalized) joint eigenfunctions of positive type of L₁,…,Ln. Connections with the theory of Gelfand pairs are established in the case L₁,…,Ln generate the algebra of K-invariant left-invariant differential operators on G for some compact subgroup K of Aut(G).     

Deligne��s representation theory in complex rank and objects of integral type

Working with Pierre Deligne??s category of representations of the ??symmetric group S _t with t a complex number?? we give negative answers to certain questions on ${\otimes}$ -categories raised by Bruno Kahn and Charles A. Weibel.     

Vibrational analysis of x-ray absorption fine structure thermal factors by ab initio molecular dynamics: the Zn(II) ion in aqueous solution as a case study

In this work, we consider a new combination of vibrational analysis and normal-like mode decomposition of Debye-Waller factors of solvated ions entirely based on molecular dynamics data. Such a novel time-dependent analysis procedure provides a direct link between x-ray absorption fine structure parameters and normal mode contributions for an ion-solvent system. The potentialities of such a methodology rely on two fundamental aspects which distinguish it from already available tools. First, a general vibrational analysis that does not require any Gaussian or harmonic model for describing atomic fluctuations in liquids. Second, a very accurate sampling of the short range motions around the structural probe via the recently developed atom centered density matrix propagation/general liquid optimized boundary method. This novel molecular dynamics methodology is based on an integrated ab initio/classical potential using localized basis functions and nonperiodic boundary conditions. As a case study we have chosen the Zn(II) ion in aqueous solution. The consistency of our results and the observed good agreement with experiments show how the key support to advanced structural techniques from molecular dynamics can be further expanded and investigated.     

Functionalized dibenzoborepins as components of small molecule and polymeric π-conjugated electronic materials

We present the synthesis and characterization of dibenzo[b,f]borepins (DBBs) functionalized at the para and meta position with respect to the boron center in order to understand how regiochemical issues influence photophysical and electrochemical properties. An expanded synthetic repertoire is presented, using palladium catalysis (to perform Stille, Suzuki, Buchwald-Hartwig, and Sonogashira cross-coupling reactions) and lithium-halogen exchange to synthesize a series of extended π-conjugated DBBs. These chemistries are enabled by the use of a sterically bulky Mes* (2,4,6-tri-tert-butylphenyl) group on boron and the inclusion of reactive bromide handles on the DBB core. Photophysical, electrochemical, and computational analyses of these compounds indicate that relative to the protio-DBB the installation of groups at the meta positions decreases the optical band gap while para substitution raises the electron affinity of the system. Thus, both the HOMO-LUMO gap and specific frontier molecular orbital levels can be tuned by the installation of different conjugated substituents.     

Development and validation of a liquid chromatography/electrospray ionization tandem mass spectrometry method for the quantification of latanoprost free acid in rabbit aqueous humor and ciliary body

A rapid, selective and sensitive method for quantification of latanoprost free acid in rabbit aqueous humor (AH) and ciliary body (CB) using reverse phase-high performance liquid chromatography coupled with electrospray ionization (ESI)-mass spectrometry/mass spectrometry has been developed and validated. Quantification in AH and CB was achieved by stable isotope dilution employing tetra-deuterated analog of latanoprost free acid, used as internal standard. Sample preparation was based on protein precipitation with methanol in AH, and on liquid extraction with a mixture of ethyl acetate and isopropanol 60:40 (v/v) in CB. Elution was achieved on an octylsilica (C8) column, using an isocratic elution method. Detection was performed on a triple quadrupole mass spectrometer, using ESI in positive ion selected reaction monitoring mode. Calibration curves were linear in the validated concentration ranges of 10-160 ng/mL in AH and 80-1280 ng/g in CB. The accuracy and precision values, obtained from three different sets of quality control samples, each analyzed in triplicate on three different days, were within the generally accepted criteria for analytical methods (< 15%). The limit of detection was 30.66 pg/mL in AH and 237.75 pg/g in CB. The assay proved to be accurate and precise when applied to the in vivo study of latanoprost free acid in rabbit AH and CB after single administration of an eye drops containing latanoprost.     

Understanding the role of carbamate reactivity in fatty acid amide hydrolase inhibition by QM/MM mechanistic modelling

QM/MM modelling of FAAH inactivation by O-biphenyl-3-yl carbamates identifies the deprotonation of Ser241 as the key reaction step, explaining why FAAH is insensitive to the electron-donor effect of conjugated substituents; this may aid design of new inhibitors with improved selectivity and in vivo potency.     

Nanostructured polymer assemblies formed at interfaces: applications from immobilization and encapsulation to stimuli-responsive release

In recent years, interfacial properties have been tailored with nanostructured polymer assemblies to generate materials with specific properties and functions for application in diverse fields, including biomaterials, drug delivery, catalysis, sensing, optics and corrosion. This perspective begins with a brief introduction of the assembly techniques that are commonly employed for the synthesis of nanostructured polymer materials, followed by discussions on how the interfaces influence the properties and thus the functionalities of the polymer materials prepared. Applications of the interfacial polymer nanostructures, particularly for the immobilization and encapsulation of cargo, are then reviewed, focusing on stimuli-responsive cargo release from the polymer nanostructured assemblies for controlled delivery applications. Finally, future research directions in these areas are briefly discussed.     

Halogen bonding to a divalent sulfur atom: an experimental study of the interactions of CF3X (X = Cl, Br, I) with dimethyl sulfide

Using FTIR and Raman spectroscopy, the formation of halogen bonded complexes of the trifluorohalomethanes CF(3)Cl, CF(3)Br and CF(3)I with dimethyl sulfide (DMS) dissolved in liquid krypton has been investigated. For CF(3)Br and CF(3)I, evidence was found for the formation of C-XS halogen bonded 1:1 complexes. At higher concentrations of CF(3)I weak absorptions due to a 2:1 complex were also observed. Using spectra recorded at temperatures between 118 and 163 K, the complexation enthalpies for the complexes were determined to be -9.5(5) kJ mol(-1) for CF(3)Br·DMS, -17.4(1) kJ mol(-1) for CF(3)I·DMS and -30.8(16) kJ mol(-1) for (CF(3)I·)(2)DMS. The results from the cryospectroscopic study are compared with ab initio calculations at the MP2/aug-cc-pVDZ(-PP) level. Apart from vibrational modes localized in the trifluorohalomethanes and the DMS moieties, for both CF(3)Br and CF(3)I, an additional band, which we assign as the intermolecular stretching mode in the complex, was identified in the infrared and Raman spectra.     

Gas chromatographic quantitative analysis of methanol in wine: operative conditions, optimization and calibration model choice

The influence of the wine distillation process on methanol content has been determined by quantitative analysis using gas chromatographic flame ionization (GC-FID) detection. A comparative study between direct injection of diluted wine and injection of distilled wine was performed. The distillation process does not affect methanol quantification in wines in proportions higher than 10%. While quantification performed on distilled samples gives more reliable results, a screening method for wine injection after a 1:5 water dilution could be employed. The proposed technique was found to be a compromise between the time consuming distillation process and direct wine injection. In the studied calibration range, the stability of the volatile compounds in the reference solution is concentration-dependent. The stability is higher in the less concentrated reference solution. To shorten the operation time, a stronger temperature ramp and carrier flow rate was employed. With these conditions, helium consumption and column thermal stress were increased. However, detection limits, calibration limits, and analytical method performances are not affected substantially by changing from normal to forced GC conditions. Statistical data evaluation were made using both ordinary (OLS) and bivariate least squares (BLS) calibration models. Further confirmation was obtained that limit of detection (LOD) values, calculated according to the 3sigma approach, are lower than the respective Hubaux-Vos (H-V) calculation method. H-V LOD depends upon background noise, calibration parameters and the number of reference standard solutions employed in producing the calibration curve. These remarks are confirmed by both calibration models used.     

Composing dinatural transformations: Towards a calculus of substitution

Dinatural transformations, which generalise the ubiquitous natural transformations to the case where the domain and codomain functors are of mixed variance, fail to compose in general; this has been known since they were discovered by Dubuc and Street in 1970. Many ad hoc solutions to this remarkable shortcoming have been found, but a general theory of compositionality was missing until Petri?, in 2003, introduced the concept of g-dinatural transformations, that is, dinatural transformations together with an appropriate graph: he showed how acyclicity of the composite graph of two arbitrary dinatural transformations is a sufficient and essentially necessary condition for the composite transformation to be in turn dinatural. Here we propose an alternative, semantic rather than syntactic, proof of Petri?'s theorem, which the authors independently rediscovered with no knowledge of its prior existence; we then use it to define a generalised functor category, whose objects are functors of mixed variance in many variables, and whose morphisms are transformations that happen to be dinatural only in some of their variables.We also define a notion of horizontal composition for dinatural transformations, extending the well-known version for natural transformations, and prove it is associative and unitary. Horizontal composition embodies substitution of functors into transformations and vice-versa, and is intuitively reflected from the string-diagram point of view by substitution of graphs into graphs.This work represents the first, fundamental steps towards a substitution calculus for dinatural transformations as sought originally by Kelly, with the intention then to apply it to describe coherence problems abstractly. There are still fundamental difficulties that are yet to be overcome in order to achieve such a calculus, and these will be the subject of future work; however, our contribution places us well in track on the path traced by Kelly towards a calculus of substitution for dinatural transformations.