Theory of nonlinear Gaussian noise

We consider stochastic differential equations of the Langevin type in which the noise enters nonlinearly. In particular we study quadratic gaussian noise and we derive equations for the probability density under different approximations. In the limit of small intensity and small correlation time of the noise we obtain a Fokker-Planck equation which accounts for the main effects of the nonlinear noise. We present some examples and we discuss the consequences of our results in the analysis of an electrohydrodynamic instability in liquid crystals in the presence of external noise.     

Hydrogen sulphide doping of GaAs and AlxGa1−xAs grown by molecular beam epitaxy (MBE)

H₂S gas has been used during molecular beam epitaxy (MBE) growth of GaAs and Al _x Ga_1–x As as sulphur vector forn-type doping. Doping efficiencies are less than 10^–3 at usual growth temperatures, and are limited by an incorporation competitive surface process, probably 2Ga+H₂SGa₂S+H₂. In Al_xGa_1–x As forx0.2 the doping efficiency is further reduced by carrier freeze-out at deep levels. Measured thermal activation energies depend on growth conditions and remain relatively low even up to the direct-indirect bandgap crossover for substrate temperatures in the 585–645 C range.     

Optimal frequency-response sensitivity of compressible flow over roughness elements*

Compressible flow over a flat plate with two localised and well-separated roughness elements is analysed by global frequency-response analysis. This analysis reveals a sustained feedback loop consisting of a convectively unstable shear-layer instability, triggered at the upstream roughness, and an upstream-propagating acoustic wave, originating at the downstream roughness and regenerating the shear-layer instability at the upstream protrusion. A typical multi-peaked frequency response is recovered from the numerical simulations. In addition, the optimal forcing and response clearly extract the components of this feedback loop and isolate flow regions of pronounced sensitivity and amplification. An efficient parametric-sensitivity framework is introduced and applied to the reference case which shows that first-order increases in Reynolds number and roughness height act destabilising on the flow, while changes in Mach number or roughness separation cause corresponding shifts in the peak frequencies. This information is gained with negligible effort beyond the reference case and can easily be applied to more complex flows.     

Determination of Paint Solvents by Vapour Phase Fourier Transform Infrared Spectrometry.

A fast procedure has been developed for the direct determination of paint solvents. The method is based on the injection of small volumes of untreated solvent mixtures into a heated Pyrex glass reactor in which the sample is volatilized and introduced by means of a flow of nitrogen into an IR multiple pass gas cell and the spectrum in the mid-IR region is registered as a function of time. Data found for samples are interpolated in calibration graphs obtained by injecting different volumes of pure compounds which constitute the solvent mixture. A methylisobutylketone (MIBK) toluene mixture was used as test system to develop the proposed procedure. The method provides a limit of detection of the order of 1–4 μg, a relative standard deviation of the order of 0.4 to 2% for five independent measurements, and recovery percentage values from 99.8 till 103.6 %. A commercial sample of polyurethane paint solvent has been analysed by the developed procedure.     

Symmetries of the heat equation on the lattice

Discrete versions of the heat equation on two-dimensional uniform lattices are shown to possess the same symmetry algebra as their continuum limits. Solutions with definite symmetry properties are presented.     

Ultrasonic velocity and amplitude characterization of magnetorheological fluids under magnetic fields

Variations in velocity of sound and amplitude of the signal of a commercial magnetorheological fluid under different magnetic fields are studied experimentally. Different factors such as orientation, uniformity, geometry and intensity of the magnetic field are investigated. An increase in the change of MR fluid acoustical properties is obtained when the magnetic field intensity is risen. In addition, these properties show an opposite behavior when a magnetic field is applied parallel or perpendicular to the ultrasound propagation. Experiments using an electromagnet and permanent magnets as the source of magnetic field are also compared. Properties such as anisotropy in sound velocity and amplitude make these materials interesting regarding applications.     

Prime ideals and radicals of centred extensions and tensor products

In this paper, we study prime ideals and radicals of centred extensions of rings. Obtained results are applied to tensor products of algebras over commutative rings. This research was partially supported by Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), Brazil. The second-named author was also supported by KBN grant 2 P301 035 06.     

Plethystic Exponential Polynomials and Plethystic Stirling Numbers

In this article we introduce a plethystic generalization of the exponential polynomials and their umbral inverses. We obtain recursive formulas for both families of polynomials, and use them to get recursions for the plethystic Stirling numbers of the first and second kind and for the plethystic Bell numbers. Finally, we apply Bergeron's S-species to obtain a Dobinsky formula for the plethystic exponential polynomials and a close formula for the plethystic Stirling numbers of the second kind.     

Acoustic voice analysis in patients with essential tremor

To quantify several acoustic features of the voice in patients with essentialtremor (ET), 28 patients and 28 age- and sex-matched controls were studied. ET severity was assessed with the rating scale for tremor of Fahn, Tolosa, and Marín. The Computerized Speech Lab 4300 program (Kay Elemetrics) was used. Two-second samples of a sustained /a/ and a sentence were captured with a microphone and laryngograph equipment. Measures included fundamental frequency (F₀), frequency perturbation (fitter, Koike algorithm), intensity perturbation (shimmer, Horii algorithm), and harmonic-to-noise ratio (H/N, Yumoto algorithm) of the vowel /a/, and the frequency and intensity variability of the sentence, phonational range, and dynamic range at the natural frequency, maximum phonational time, and s/z ratio. All subjects underwent indirect laryngoscopy and/or laryngeal fibroscopy. When compared with controls, ET patients showed higher jitter, lower H/N ratio (the last one only with laryngographic signal), of the vowel /a/, lower frequency variability in the microphonc signal, lower intensity variability in the laryngographic signal of the sentence, and significantly lower dynamic range at natural frequency of phonation. ET patients reported higher frequency of the presence of high voice intensity, tremor, and struggle. Several acoustic parameters were influenced by the severity of the disease, including shimmer, jitter, H/N ratio, frequency variability of the sentence, and s/z ratio, although neither of the acoustic analysis values or the phonetometric measurements were affected by the presence of voice tremor or by a successful pharmacological treatment of ET.