Combinatorial Expansions of Kazhdan-Lusztig Polynomials

We introduce two related families of polynomials, easily computableby simple recursions into which any Kazhdan–Lusztig (andinverse Kazhdan–Lusztig) polynomial of any Coxeter groupcan be expanded linearly, and we give combinatorial interpretationsto the coefficients in these expansions. This yields a combinatorialrule for computing the Kazhdan–Lusztig polynomials interms of paths in a directed graph, and a completely combinatorialreformulation of the nonnegativity conjecture [15, p. 166].     

Properties of fluoroelastomer/semicrystalline perfluoropolymer nano-blends

Properties of blends of semicrystalline perfluoropolymers in fluoroelastomers strongly depend on the size of the dispersed phase and are at the best when dispersed phase dimension is well below 0.1 μm, i.e. in the nano-scale region. This fine dispersion is obtained with an innovative mixing technology based on microemulsion polymerization. Further increase of properties can be obtained by generating chemical links between fluoroelastomer and semicrystalline fluoropolymer. Nano-blends combine the performing properties of fluoroelastomers with those of semicrystalline perfluoropolymers. For example, these nano-blends have at the same time the sealing and mechanical properties of fluoroelastomers and the exceptional thermal and chemical resistance, low permeability and low friction coefficient of semicrystalline perfluoropolymers. In addition, as dispersed phase size is below visible light wavelength, finished items made with these nano-blends are optically transparent even when they contain as much as 40 wt.% of semicrystalline perfluoropolymer.     

Polycondensed nitrogen heterocycles. Part 24. Pyrrolo[3,4-c]isoquinolinone by thermal rearrangement of a pyrrolylbenzotriazinone

Rearrangement under acidic conditions of the pyrrolylbenzotriazinone 7 afforded the pyrrolylbenzamides 10 and 11 . By thermal rearrangement instead, the first fully aromatic derivative of the pyrrolo[3,4-c]isoquinoline ring system 9 was obtained.     

Chemical mechanisms in C3F8-H2 radiofrequency discharges

Discharges fed with C₃F₈-H₂ mixtures have been studied by means of mass spectrometry in a tubular reactor operated at 0.5 torr and 50 W. Comparison of the results with those obtained with emission actinometry give additional evidence that emission actinometry and mass spectrometry are powerful diagnostic tools to monitor stable and unstable species in discharges utilized for dry etching and polymer depositions. Mechanisms for end product formation and polymer deposition are also discussed.     

Classical “freezing” of plane rotations: A proof of the Boltzmann-Jeans conjecture

Using simple known methods and results of classical perturbation theory, especially those due to Nekhoroshev and Neishtadt, we study the energy exchanges between the rotational and the translational degrees of freedom in a particular model representing the planar motion of a rigid body in a bounded analytic potential. We prove that, if the angular velocity is initially large, then the energy exchanges are small,O( ^–1), for times growing exponentially with, |t|exp. We also deduce that in a scattering process from a (smooth) potential barrier, the overall change in the rotational energy of the incoming body is exponentially small in, exp(–. The results are interpreted in the light of an old conjecture by Boltzmann and Jeans on the existence of very large time scales for equilibrium in statistical systems containing high-frequency degrees of freedom (purely classical freezing of the high-frequency degrees of freedom); the rotating object is, in this interpretation, a (classical) molecule, which moves in an external field, or collides with the wall of a container. Two different limits of large are considered, namely the limit of large rotational energy, and (as is interesting for the molecular interpretation) the limit of point mass, at finite rotational energy.     

Cantor spectrum and singular continuity for a hierarchical Hamiltonian

We study the spectrum of the HamiltonianH onl ₂() given by (H)(n)=(n+1)+(n–1)+V(n)(n) with the hierarchical (ultrametric) potentialV(2 ^m (2l+1))=(1–R ^m )/(1–R), corresponding to 1-, 2-, and 3-dimensional Coulomb potentials for 0<R<1,R=1 andR>1, respectively, in a suitably chosen valuation metric. We prove that the spectrum is a Cantor set and gaps open at the eigenvaluese _n (1)<e _n (2)<...<e _n (2 ⁿ –1) of the Dirichlet problemH=E, (0)=(2 ⁿ )=0,n1. In the gap opening ate _n (k) the integrated density of states takes on the valuek/2 ⁿ . The spectrum is purely singular continuous forR1 when the potential is unbounded, and the Lyapunov exponent vanishes in the spectrum. The spectrum is purely continuous forR<1 in (H)[–2, 2] and =0 here, but one cannot exclude the presence of eigenvalues near the border of the spectrum. We also propose an explicit formula for the Green's function.Work supported by the Fonds National Suisse de la Recherche Scientifique, Grant No. 2.042-0.86 (H.K. and R.L.) and 2.483-0.87 (A.S.)On leave from the Dipartimento di Fisica, Università degli Studi di Firenze, Largo E. Fermi 2, I-50125 Firenze, Italy     

The spectrum of a one-dimensional hierarchical model

The spectrum of a discrete Schrödinger operator with a hierarchically distributed potential is studied both by a renormalization group technique and by numerical analysis. A suitable choice of the potential makes it possible to reduce the original problem to a two-dimensional map. Scaling laws for the band-edge energyE _be and for the integrated density of states are predicted together with the global properties of the spectrum. Different scaling regimes are obtained depending on a hierarchy positive parameterR: for R<1/2 the usual scaling laws for the periodic case are obtained, while forR>1/2 the scaling behavior depends explicitly onR.     

Light Electrospun Polyvinylpyrrolidone Blanket for Low Frequencies Sound Absorption

Light polymeric soundproofing materials(density = 63 kg/m~3) of interest for the transportation industry were fabricated through electrospinning. Blankets of electrospun polyvinylpyrrolidone(average fiber diameter =(1.6 ± 0.5) or(2.8 ± 0.5) μm) were obtained by stacking disks of electrospun mats. The sound absorption coefficients were measured using the impedance tube instrument based on ASTM E1050 and ISO 10534-2. For a given set of disks(from a minimum of 6) the sound absorption coefficient changed with the frequency(in the range 200–1600 Hz) following a bell shape curve with a maximum(where the coefficient is greater than 0.9) that shifts to lower frequencies at higher piled disks number and greater fiber diameter. This work showed that electrospinning produced sound absorbers with reduced thickness(2–3 cm) and excellent sound-absorption properties in the low and medium frequency range.     

Effect of the introduction of an alcohol-soluble conjugated polyelectrolyte as cathode interlayer in solution-processed organic light-emitting diodes and photovoltaic devices

Interfacial engineering provides an important tool for optimizing the performances of optoelectronic devices. We show that poly[(2,7-(9,9′-dioctyl)fluorene)-alt-(2,7-(9,9′-bis(5″-trimethylammonium bromide)pentyl)fluorene)])], an alcohol-soluble π-conjugated polymer based on polyfluorene backbone and ammonium groups on the alkyl side chains, is capable of modifying the interface between the organic layer and the metal cathode in both organic solar cells and light-emitting diodes based on commercial materials and conventional architectures, improving their performances. The introduction of the cathode interlayer enhances the efficiency of a red-emitting phosphorescent OLED by 15% and decreases its turn-on voltage. The same polymer improves the power conversion efficiency of a PTB7/PC₇₁BM solar cell by 55% and shows a beneficial effect in terms of device stability.