Nonlinear oscillations beyond caustics

This paper studies the focusing of high-frequency solutions of semilinear hyperbolic equations. In previous papers, we studied two opposite phenomena. First, the focusing of nonlinear waves can force the solutions to blow up, even before reaching the caustics. Second, for strongly dissipative equations, nonlinear oscillations can be completely absorbed when they reach the caustic set. In this paper, we study the intermediate case of equations with globally Lipschitz nonlinearities. The nonlinear oscillations persist after crossing the caustic set. The solutions are described using oscillatory integrals, which are associated with Lagrangian manifolds in the cotangent bundle. The equations of nonlinear geometric optics lift to these manifolds. In contrast to the linear case, the transport equations for amplitudes living above the same points of spacetime are coupled. © 1996 John Wiley & Sons, Inc.     

Fredholm Modules on P.C.F. Self-Similar Fractals and Their Conformal Geometry

The aim of the present work is to show how, using the differential calculus associated to Dirichlet forms, it is possible to construct non-trivial Fredholm modules on post critically finite fractals by regular harmonic structures (D, r). The modules are (d _S , ∞)–summable, the summability exponent d _S coinciding with the spectral dimension of the generalized Laplacian operator associated with (D, r). The characteristic tools of the noncommutative infinitesimal calculus allow to define a d _S -energy functional which is shown to be a self-similar conformal invariant. Thiswork has been supported by the project “Teoria ellittica e forme di Dirichlet su spazi frattali” G.N.A.M.P.A. 2008 and by the G.R.E.F.I.-G.E.N.C.O. French-Italian Research Group.     

On the moments and distribution of discrete Choquet integrals from continuous distributions

We study the moments and the distribution of the discrete Choquet integral when regarded as a real function of a random sample drawn from a continuous distribution. Since the discrete Choquet integral includes weighted arithmetic means, ordered weighted averaging functions, and lattice polynomial functions as particular cases, our results encompass the corresponding results for these aggregation functions. After detailing the results obtained in [J.-L. Marichal, I. Kojadinovic, Distribution functions of linear combinations of lattice polynomials from the uniform distribution, Statistics & Probability Letters 78 (2008) 985–991] in the uniform case, we present results for the standard exponential case, show how approximations of the moments can be obtained for other continuous distributions such as the standard normal, and elaborate on the asymptotic distribution of the Choquet integral. The results presented in this work can be used to improve the interpretation of discrete Choquet integrals when employed as aggregation functions.     

Minimal arithmetic thickness connecting discrete planes

While connected arithmetic discrete lines are entirely characterized, only partial results exist for the more general case of arithmetic discrete hyperplanes. In the present paper, we focus on the three-dimensional case, that is on arithmetic discrete planes. Thanks to arithmetic reductions on a vector , we provide algorithms either to determine whether a given arithmetic discrete plane with as normal vector is connected, or to compute the minimal thickness for which an arithmetic discrete plane with normal vector is connected.     

Evaluation of solid-phase microextraction desorption parameters for fast GC analysis of cocaine in coca leaves

By its simplicity and rapidity, solid-phase microextraction (SPME) appears as an interesting alternative for sample introduction in fast gas chromatography (fast GC). This combination depends on numerous parameters affecting the desorption step (i.e., the release of compounds from the SPME fiber coating to the GC column). In this study, different liner diameters, injection temperatures, and gas flow rates are evaluated to accelerate the thermal desorption process in the injection port. This process is followed with real-time direct coupling a split/splitless injector to a mass spectrometer by means of a short capillary. It is shown that an effective, quantitative, and rapid transfer of cocaine (COC) and cocaethylene (CE) is performed with a 0.75-mm i.d. liner, at 280 degrees C and 4 mL/min gas flow rate. The 7-microm polydimethylsiloxane (PDMS) coating is selected for combination with fast GC because the 100-microm PDMS fiber presents some limitations caused by fiber bleeding. Finally, the developed SPME-fast GC method is applied to perform in less than 5 min, the quantitation of COC extracted from coca leaves by focused microwave-assisted extraction. An amount of 7.6 +/- 0.5 mg of COC per gram of dry mass is found, which is in good agreement with previously published results.     

Orientation of native cellulose in an electric field

Native cellulose has been oriented in an ac electric field at both the macroscopic and colloidal level. Ramie fiber fragments suspended in chloroform have been shown to point along the field. Cellulose microcrystal suspensions in cyclohexane have also been allowed to evaporate in an electric field and have exhibited a high degree of orientation when further examined by TEM and electron diffraction. Similarly, cellulose whisker suspensions showed increasing birefringence with increasing field strength and displayed interference Newton colors that saturated at around 2000 V cm(-)(1). A high degree of order of this suspension was also obtained by evaluating the induced birefringence with color charts.     

Vibronic coupling in organic semiconductors: the case of fused polycyclic benzene-thiophene structures

The nature of vibronic coupling in fused polycyclic benzene-thiophene structures has been studied using an approach that combines high-resolution gas-phase photoelectron spectroscopy measurements with first-principles quantum-mechanical calculations. The results indicate that in general the electron-vibrational coupling is stronger than the hole-vibrational coupling. In acenedithiophenes, the main contributions to the hole-vibrational coupling arise from medium- and high-frequency vibrations. In thienobisbenzothiophenes, however, the interaction of holes with low-frequency vibrations becomes significant and is larger than the corresponding electron-vibrational interaction. This finding is in striking contrast with the characteristic pattern in oligoacenes and acenedithiophenes in which the low-frequency vibrations contribute substantially only to the electron-vibrational coupling. The impact of isomerism has been studied as well.     

Thermal system identification using fractional models for high temperature levels around different operating points

This work aims at the preparation of an experiment for the thermal modeling of an ARMCO iron sample (iron of the American Rolling Mill COmpany) for small temperature variations around different operating points. Fractional models have proven their efficacy for modeling thermal diffusion around the ambient temperature and for small variations. Due to their compactness, as compared to rational models and to finite element models, they are suitable for modeling such diffusive phenomena. However, for large temperature variations, thermal characteristics such as thermal conductivity and specific heat vary along with the temperature. In this context, the thermal diffusion obeys a nonlinear partial differential equation and cannot be modeled by a single linear model. In this paper, thermal diffusion of the iron sample is modeled around different operating points for temperatures ranging from 400 to 1070?K, which is above the Curie point (In physics and materials science, the Curie temperature (T _C), or Curie point, is the temperature at which a ferromagnetic or a ferrimagnetic material becomes paramagnetic.) showing that for a large range of temperature variations, a nonlinear model is required. Identification and validation data are generated by finite element methods using COMSOL Software.     

A Facile Synthesis and Crystallographic Analysis of Seven Trityl Phosphorus Compounds and Two Nickel(II) Phosphine Side-Products

Abstract  The syntheses and X-ray analyses of triphenylmethyl (trityl=Tr) phosphorus compounds are reported and the structural similarities, differences and ³¹P chemical shifts compared. A series of seven trityl-substituted phosphorus-containing compounds have been characterized by single crystal X-ray diffraction. Ph₃CPPh₂, 1, a bulky P(III) compound crystallizes in the triclinic space group , a = 7.5624(6) ?, b = 9.5470(8) ?, c = 16.9722(14) ?, α = 83.4720(10)°, β = 80.541(2)°, γ = 68.1580(10)°, the borane complex of 1, 2, Ph₃CPPh₂(BH₃) crystallizes as monoclinic colorless crystals, P2₁/c, a = 10.0972(12) ?, b = 9.6955(12) ?, c = 25.197(3) ?, β = 90.258(2)°. The analogous methyl substituted, 3, Ph₃CPMe₂(BH₃) is monoclinic, C₂/c, a = 15.628(3) ?, b = 12.770(3) ?, c = 18.406(4) ?, β = 103.968(3)°. Compounds 4–7 are trityl substituted P(V) compounds: Ph₃CP(Ph)(O)(OH), 4, crystallizes in the triclinic space group , a = 8.9847(18) ?, b = 9.7443(19) ?, c = 12.786(3) ?, α = 72.045(3)°, β = 72.031(3)°, γ = 78.769(3)°. Esterification of 4 affords TrCP(O)(Ph)OBn 5, space group, P2₁/c, a = 7.9196(5) ?, b = 31.701(2) ?, c = 19.8062(13) ?, β = 99.7750(10)°. A phosphonate diester was also characterized, Ph₃CP(O)(OEt)₂, 6, triclinic, , a = 7.9521(17) ?, b = 9.2205(19) ?, c = 14.471(3) ?, α = 85.906(4)°, β = 83.031(4)°, γ = 68.283(4)°. Treatment of the trityl H-phosphinic acid, Ph₃CPO₂H_2, with elemental selenium yields yellow crystals of 7, [Ph₃CP(O)(OH)Se]_2, P2₁/c, a = 9.0603(4) ?, b = 22.3652(11) ?, c = 16.9134(7) ?, β = 107.035(2)°. In our efforts to isolate a nickel-phosphine complex, two Ni(II) complexes were crystallographically analyzed, [Ni(OP(H)Ph₂)₆]₂BF₄ ⁻ 8 and 9. Complex 8 with an uncoordinated BF₄ ⁻ ion crystallizes as yellow orthorhombic crystals, Pbca, a = 18.8247(12) ?, b = 18.5518(12) ?, c = 21.0976(14) ?, while crystals of 9 are trigonal, , a = b = 13.1545(12) ?, c = 68.461(9) ?. Graphical Abstract  The syntheses and X-ray analyses of triphenylmethyl (trityl=Tr) phosphorus compounds are reported and the structural similarities, differences and ³¹P chemical shifts compared.