Sharp determinants

We introduce a sharp trace Tr^# and a sharp determinant Det^#(1-z) for an algebra of operators acting on functions of bounded variation on the real line. We show that the zeroes of the sharp determinant describe the discrete spectrum of . The relationship with weighted zeta functions of interval maps and Milnor-Thurston kneading determinants is explained. This yields a result on convergence of the discrete spectrum of approximated operators.Oblatum 8-V-1995 & IX-1995On leave from CNRS, UMR 128, ENS Lyon, France     

Semileptonic decays B → (π, )eν in relativistic quark model

Quark model results for the B → π, decays are analysed, making use of the dispersion formulation of the model: The form factors at q² > 0 are expressed as relativistic invariant double spectral representation over invariant masses of the initial and final mesons through their light-cone wave functions. The dependence of the results on the quark model parameters is studied. For various versions of the quark model the ranges

Full-size image

,

Full-size image

, and Γ_L/Γ_T = 0.7 ± 0.08 are found. The effects of the constituent quark transition form factor are briefly discussed.     

Analysis and design of highly broad-band,planar evanescent couplers

It is shown that by taking advantage of the maximum in the spectral dependence of the coupling coefficient, very broad-band symmetric and asymmetric single-mode planar couplers can be designed. The symmetric coupler allows at least 95.6% coupling between the two cores over the wavelength range 1.3–1.58 m, while the asymmetric coupler can act as a 3 dB splitter with only ±1.6% variation in the splitting ratio over the wavelength range 1.3–1.67 m. In both cases, the design includes the curved input-output arms, and the estimated bend loss is approximately 0.1 dB.     

Influence of mixture design on multivariate prediction of PAHs in mixture spectra

This work describes a simulation study aimed at establishing the impact of mixture design on the prediction ability of PLS regression models. Data sets are formed by multiplying UV absorbance spectra of 12 PAHs by their concentration profiles. In these case studies, either all possible mixtures of 1-12 components are used or randomly chosen selections of the mixtures. The effects of the number of samples and the number of concentration levels in the mixture designs on the results of the calibration are assessed. Comparisons are made between models formed using orthogonal fractional factorial mixture designs and those based on random designs. The applicability limits of the orthogonal designs are analysed in terms of actual concentration ranges of individual components in the mixtures.     

Applications of laser-induced breakdown spectrometry (LIBS) in surface analysis

The applicability of laser-induced breakdown spectrometry (LIBS) for surface analysis is presented in terms of its lateral and depth resolution. A pulsed N(2) laser at 337.1 nm (3.65 J/cm(2)) was used to irradiate solar cells employed for photovoltaic energy production. Laser produced plasmas were collected and detected using a charge-coupled device. An experimental device developed in the laboratory permits an exact synchronization of sample positioning using an XY motorized system with laser pulses. Multielement analysis with lateral resolution of up to 30 microm is feasible with the present system. Three-dimensional capabilities of the system are used for studies on the distribution of carbon impurities at the surface of the solar cells.     

Microwave sputtering of conductors and insulators for optical emission and mass spectrometry

A microwave-powered slab-line cavity was used to excite a discharge in low pressure argon or neon and to demonstrate the sputtering of conducting and non-conducting samples by a microwave excited discharge. Both optical emission spectroscopy and mass spectrometry were used as detection systems. The dependence of the signals on gas pressure and net microwave power was investigated.     

Some aspects of the interactions of orthopositronium with perfect and defect surfaces of insulating materials

ETLA (Elastic Thermalisation Lifetime Analysis) is a new model function for the fitting of lifetime spectra of slowly thermalising orthopositronium in the free space between the grains of insulating oxide powders. From this model one can obtain three fundamental parameters; the mass of the cluster of atoms which scatters the o-Ps, the probability that the o-Ps is forced into two-quantum decay at each collision and the emission energyE(0) of the o-Ps from the powder surface. As a consequence of full thermalisation of the Ps it is shown that the o-Ps quenching constant _q () follows atT ^1/2 dependency for MgO, Al₂O₃ and SiO₂ and for temperatures between 77 and 500 K. In MgO powder at low temperatures the irradiation by the positrons induces surface paramagnetic defects which are identified as Mg⁺ sites. These surface defects do not affect the thermalisation, but they induce paramagnetic o-p conversion i.e., an increase in , and they are also responsible for an increase in the emission energyE(0) of the o-Ps.     

Spectral transport model for turbulence

The spectrum of inhomogeneous turbulence is modeled by an approach that is not limited to regimes of large Reynolds numbers or small mean-flow strain rates. In its simplest form and applied to incompressible flow, the model depends on five phenomenological constants defining the strength of turbulence coupling to mean flow, turbulence transport in physical and wave-number space, and mixing of stress-tensor components. The implications for homogeneous isotropic turbulence are investigated in detail and found to correspond well to the conclusions from more fundamental theories. Under appropriate limiting conditions, a turbulent system described by the model will relax over time into a state of approximate spectral equilibrium permitting a reduction to a one-point model for the system that is substantially like the familiar K- model. This yields preliminary estimates of the present model's parameters and points to the way to improved modeling of flows beyond the applicability of the K- method.