Discontinuous Observers, in particular those based in the Super-Twisting Algorithm, are able to estimate the unknown input of a system in finite time when the relative degree is one for all the time and the input is a Lipschitz function of time. The authors extend in this study this result for the case when the relative degree is not well defined for all the time because of the fact that the unknown input has a time-varying coefficient that can be zero for some time intervals and that can also change its sign. The authors propose a discontinuous observer able to estimate the input in finite time and despite of its bounded but unknown velocity of change during the times the relative degree is well defined and one. They also provide a Lyapunov-like analysis to show the convergence of the observer using multiple instead of a single Lyapunov function. It is shown that if the signal to be estimated is Persistently Exciting and its number of changes of signs is bounded in any bounded interval of time, then the observer converges globally, uniformly and in finite time to the true value. The authors use the observer as estimator of a time-varying parameter and illustrate in an example its performance.

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Low-dimensional thermoelectricity opens the possibility of improving the performance and the efficiency of thermoelectric devices by redistributing the electron density of states through the reduction of dimensionality. In this work, we explore this possibility in silicene by reducing its dimensionality through the periodic arrangement of gated electrodes, the so-called gated silicene superlattices. Silicene electrons were described quantum relativistically. The transmission, conductance, and thermoelectric properties were obtained with the transfer matrix method, the Landauer-Büttiker formalism, and the Cutler-Mott formula, respectively. We find that the redistribution of the density of states together with the intrinsic characteristics of silicene, the local bandgap and the large spin-orbit coupling, contribute to the enhancement of the thermoelectric properties. In particular, the Seebeck coefficient and the power factor reach values of a few mV/K and nW/K2. These findings in conjunction with the low thermal conductivity of silicene indicate that silicene-based nanostructures could be the basis of more efficient thermoelectric devices.

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A new method for image compression based on morphological associative memories (MAMs) is presented. We used the MAM to implement a new image transform and applied it at the transformation stage of image coding, thereby replacing such traditional methods as the discrete cosine transform or the discrete wavelet transform. Autoassociative and heteroassociative MAMs can be considered as a subclass of morphological neural networks. The morphological transform (MT) presented in this paper generates heteroassociative MAMs derived from image subblocks. The MT is applied to individual blocks of the image using some transformation matrix as an input pattern. Depending on this matrix, the image takes a morphological representation, which is used to perform the data compression at the next stages. With respect to traditional methods, the main advantage offered by the MT is the processing speed, whereas the compression rate and the signal-to-noise ratio are competitive to conventional transforms.

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This paper theoretically investigates the impact of aperiodic sequences in the ballistic transport and thermoelectric effect in silicene gated superlattices. In our analysis, we have implemented the well-known Fibonacci, Thue–Morse, and triadic Cantor type sequences. The transfer matrix technique and the Landauer–Bütikker formalism are used to calculate the transmission probability and the conductance, respectively. The Cutler–Mott formula is employed to estimate the Seebeck coefficient, and the thermoelectric power factor is then obtained. We found that the transmission minibands of aperiodic superlattices exhibit a much more fragmented structure in comparison to that reported in the periodic case. Consequently, the conductance curve presents a more pronounced oscillating shape, which improves the thermoelectric properties. In particular, the Seebeck coefficient has reached values up to 78.2 mV/K for Fibonacci, 233.0 mV/K for Thue–Morse, and 436.3 mV/K for Cantor. In addition, the power factor has been substantially increased, reaching peaks of approximately 8.2, 50.2, and 2.1 nW/K2 for the mentioned sequences, respectively. The best results were obtained for spindown (spinup) charge carriers in the K (K′) valley. Besides, an additional improvement is obtained by considering superior generations of the aperiodic sequences. Finally, our findings are supported through the redistribution of the density of the states, which is induced by the aperiodicity of the nanostructure as well as by the low-dimensionality of the thermoelectric device.

A new method for image compression based on Morphological Associative Memories (MAM) is proposed. We used MAM at the transformation stage of image coding, thereby replacing the traditional methods such as Discrete Cosine Transform or Wavelet Transform. After applying the MAM, the informative image data are concentrated in a minimum of values. The next stages of image coding can be obtained by taking advantage of this new representation of the image. The main advantage offered by the MAM with respect to the traditional methods is the speed of processing, whereas the compression rate and the obtained signal to noise ratios compete with the traditional methods.