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.     

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.     

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.     

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.     

LPI in pulsed laser space communications

A basic low-probability of intercept (LPI) study for a pulsed-laser pulse position modulated (PPM) optical link with a colocated direct detection intercepting receiver is presented. The latter is considered to be a form of optical radiometer using continuous threshold testing to detect the presence of the transmitting laser. The various design alternatives for the coded PPM link, and their effect on the communication and LPI performance, are examined. It is shown that the use of optical pulse power spreading via multiple frame symbol coding is vital for avoiding interception. It can be achieved by transmitting message symbols as repeated PPM symbols using a laser pulse of sufficiently low peak power so that the detected pulse energy is much less than the detected background energy. The possibility of the use of both wideband and narrowband radiometers by the interceptor further limits the communicator's code design choices. Some equations defining effective LIP gain parameters for the communication link are developed     

Laboratory simulation of inertial and frictional effects on barotropic rotating flows over and past obstacles: Comparison with simple numerical and analytical models

Summary This paper presents the results of laboratory experiments designed to simulate some basic process of large-scale flows interacting with obstacles, also in order to better understand details of subsynoptic disturbances that are created in the lee of large topographic features. For this event, the experimental facilities of the Istituto di Cosmogeofisica of Consiglio Nazionale delle Ricerche (CNR) were exploited, consisting in a hydraulic channel mounted on a rotating platform, along whose longitudinal axis a hemispherical obstacle was towed at various speeds. Because of the conversion of potential vorticity, the experimental results showed, as expected, the existence of a region of anticyclonic circulation, located above the obstacle; however, also an asymmetric pattern of positive vorticity located downwind of the obstacle did appear, which cannot be interpreted in terms of simple quasi-geostrophic inviscid dynamics. This behaviour is not surprising, if one considers that the real flow near the obstacle could hardly ever match the conditions of inviscid quasi-geostrophy (Ro≪1,E∼0), but was similar to that characterising the zone close to the surface of the obstacle, where inertial and viscous effects are not negligible. Finally, in order to investigate the importance of these effects on the interaction processes, simple numerical and analytical models were applied, by which the consistency of some laboratory simulations, chosen among the most significant ones, could be compared.     

Future of low-x forward physics at RHIC

Comparisons of particle production from high-energy ion collisions with next-to-leading order perturbative QCD calculations show good agreement down to moderate transverse momentum values. Distributions of azimuthal angle differences between coincident hadrons in these collisions support a partonic origin to the particle production, again down to moderate transverse momentum values. The rapidity dependence of inclusive and coincident particle production can therefore be used to probe parton distribution functions down to small momentum fractions where theory anticipates that parton saturation could be present. This paper describes how such experiments could be completed.Arrival of the final proofs: 27 July 2005PACS: 12.38 Qk, 13.88. + e, 24.85. + p