Convolution of operators and applications

Supported by the Grant C.A.I.C.Y.T. n 85-0338     

Bilinear Hilbert Transform on Measure Spaces

In this article we obtain the boundedness of the periodic, discrete and ergodic bilinear Hilbert transform, from , where 1$, and $p_3\ge 1$" align="middle" border="0"> . The main techniques are a bilinear version of the transference method of Coifman and Weiss and certain discretization of bilinear operators. In the periodic case, we also obtain the boundedness for      

Integrable perturbations of the N-dimensional isotropic oscillator

Two new families of completely integrable perturbations of the N-dimensional isotropic harmonic oscillator Hamiltonian are presented. Such perturbations depend on arbitrary functions and N free parameters and their integrals of motion are explicitly constructed by making use of an underlying h₆-coalgebra symmetry. Several known integrable Hamiltonians in low dimensions are obtained as particular specializations of the general results here presented. An alternative route for the integrability of all these systems is provided by a suitable canonical transformation which, in turn, opens the possibility of adding (N−1) ‘Rosochatius’ terms that preserve the complete integrability of all these models.     

In vitro mouse model in Duchenne muscular dystrophy diagnosis using 50-MHz ultrasound waves

Duchenne muscular dystrophy (DMD) is caused by the absence of dystrophin, the protein that plays a key mechanical role in maintaining muscle membrane integrity. One of the major consequences of dystrophin deficiency is the degeneration of muscle fibres, with a progressive loss in muscle strength. The objective of this research was to find an ultrasonic parameter sensitive to DMD, which could give relevant information related to microstructure if compared to traditional investigations such as morphometrical analysis. This “in vitro” study focused on the Mdx mouse model and investigated the potential differences between wild-type and dystrophin-deficient mice diaphragms. Using a 50 MHz ultrasonic sensor built in our group, we recorded an increase in ultrasonic wave attenuation in the dystrophin-deficient samples in comparison with normal muscles. A correlation between attenuation, mouse age and the percentage of non-muscular proportion in muscle was observed. As Mdx mouse is the best animal model for DMD and reproduces the degenerative pattern observed in human DMD muscles, this approach could be a powerful tool for in vitro DMD investigation and, more generally, for the characterisation of muscle properties.     

High efficiency fiber coupling to silicon sandwiched slot waveguides

The design of a fiber coupler for high efficiency light coupling to silicon sandwiched slot waveguides is reported. The proposed fiber coupler is based on the inverted taper approach. Parameters have been optimized to maximize coupling efficiency for λ = 1550 nm and TM polarization. Maximum coupling efficiencies of 93% for a inverted taper length of 150 μm and a inverted taper tip width of 40 nm have been obtained by means of the overlap integral and 3D beam propagation method (BPM) simulations.     

Lichens biomonitoring as feasible methodology to assess air pollution in natural ecosystems: Combined study of quantitative PAHs analyses and lichen biodiversity in the Pyrenees Mountains

The air quality in the Aragón valley, in the central Pyrenees, has been assessed by evaluation of lichen biodiversity and mapped by elaboration of the Index of Air Purity (IAP) based on observations of the presence and abundance of eight kinds of lichen with different sensitivity to air pollution. The IAP values obtained have been compared with quantitative analytical measures of 16 PAHs in the lichen Evernia prunastri, because this species was associated with a wide range of traffic exposure and levels of urbanization. Analyses of PAHs were carried out by the DSASE method followed by an SPE clean-up step and GC–MS analysis. The concentration of total PAHs found in lichen samples from the Aragón valley ranged from 692 to 6420 ng g⁻¹ and the PAHs profile showed predominance of compounds with three aromatic rings. The influence of the road traffic in the area has been shown because values over the median concentration of PAHs (>1092 ng g⁻¹), percentage of combustion PAHs (>50%), and equivalent toxicity (>169) were found in lichens collected at places exposed to the influence of traffic. The combination of both methods suggests IAP as a general method for evaluating the air pollution referenced to PAHs because it can be correlated with the content of combustion PAHs and poor lichen biodiversity can be partly explained by the air pollution caused by specific PAHs. Figure Map of the air pollution level in the Aragón valley (Pyrenees) based on the Index of Air Purity (IAP) calculation (lichen biodiversity)