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A numerical study that uses detrended fluctuation analysis (DFA) algorithm of time series obtained from linear and nonlinear dynamical systems is presented. The DFA algorithm behavior toward periodic and chaotic signals is investigated and the effect of the time scale under analysis is discussed. The displayed results prove that the DFA algorithm response is invariant (stable performance) to initial condition and chaotic system parameters. An initial idea of DFA algorithm implementation for fine spectrum sensing (SS) is proposed under two-stage spectrum sensor approach with test statistics based on the scaling exponent value. The outcomes demonstrate a promising new SS technique that can alleviate several imperfections such as noise power uncertainty and spatial correlation between the adjacent antenna array elements.

One of the fields of applied mathematics is related to model analysis. Biomedical systems are suitable candidates for this field because of their importance in life sciences including therapeutics. Here we deal with the analysis of a model recently proposed by Espinoza-Valdez et al. (2010) for the kidney vasculature developed via angiogenesis. The graph theory allows one to model quantitatively a vascular arterial tree of the kidney in sense that (1) the vertex represents a vessels bifurcation, whereas (2) each edge stands for a vessel including physiological parameters. The analytical model is based on the two processes of sprouting and splitting angiogeneses, the concentration of the vascular endothelial growth factor (VEGF), and the experimental data measurements of the rat kidneys. The fractal dimension depends on the probability of sprouting angiogenesis in the development of the arterial vascular tree of the kidney, that is, of the distribution of blood vessels in the morphology generated by the analytical model. The fractal dimension might determine whether a suitable renal vascular structure is capable of performing physiological functions under appropriate conditions. The analysis can describe the complex structures of the development vasculature in kidney.

The measured return loss is compared with the simulated result in Figure 6; good agreement is observed. It is seen that the bandwidths for return loss >6 dB (or VSWR <3) are 687-976 MHz, 1195-1246 MHz, and 1423 MHz, covering all the frequency bands for LTE/GSM/UMTS, GPS, and WLAN/WiMAX applications. The radiation pattern, peak gain, and antenna efficiency were measured using a SATIMO antenna measurement system SG24 at the Speed Communication Technology Corporation Ltd., Huizhou, China. The measured and simulated radiation patterns at 800 MHz, 1220 MHz, 2 GHz, 3.5 GHz, and 5.5 GHz are demonstrated in Figure 7. All radiation patterns show nearly omnidirectional in the x-z plane, suitable for a mobile communications environment. The measured and simulated gains are plotted in Figure 8. The peak gain is about 1-3 dBi for the 700-MHz band, 3-5 dBi for 1220-MHz band and the 2-GHz bands, 3-6 dBi for the 3.5-GHz and the 5-GHz bands. The measured antenna efficiency is also plotted in Figure 8. We can see that the antenna efficiency is higher than 60% for all the frequency bands. CONCLUSIONA multiband uniplanar antenna has been developed for LTE/ GSM/UMTS, GPS, and WLAN/WiMAX applications. The multiband antenna covers three frequency bands: 687-976 MHz, 1195-1246 MHz, and 1423-7665 MHz. The multiband antenna has a thin uniplanar configuration, suitable for the state-of-theart ultra-slim smartphone applications.ABSTRACT: In this work, the performance of a broadband logperiodic toothed trapezoidal antenna is evaluated to know its potential for RF energy harvesting. The energy harvested by the antenna from the different wireless standards in urban areas can be converted into Direct Current and used to feed low power electronics.

We present a study on a class of interconnected nonlinear systems and give some criteria for them to behave like a filter. Some chaotic systems present this kind of interconnected nonlinear structure, which enables the synchronization of a master-slave system. Interconnected nonlinear filters have been defined in terms of interconnected nonlinear systems. Furthermore, their behaviors have been studied numerically and theoretically on different input signals.