In this article, we propose a nonlinear Proportional+Derivative (PD) tracking controller with adaptive Fourier series compensation. The proposed controller uses a regressor-free adaptive scheme that relies on a trigonometric polynomial with varying coefficients to solve the control problem. Asymptotic convergence of the position and velocity errors is proven via a formal stability analysis based on Lyapunov and LaSalle theory for discontinuous systems. The proposed controller is validated on a 2-degrees of freedom robot manipulator. The experimental results validate the theoretically obtained results and reflect the effect of certain parameters in the transient behavior of the error dynamics. Certain robustness properties are also observed.

The nanostructural features of the gas-phase displacement reaction 2Mg(g)+SiO2→2MgO(s)+{Si}, where SiO2 is in the form of diatom shells were studied via X-ray diffraction and Fourier methods. Diatomaceous powder heated to 700 °C in a sealed graphite cell in the presence of Mg vapor formed MgO via a displacement reaction. Warren-Averbach analysis performed on samples reacted for different times showed an initial sharp MgO grain size distribution which broadened with time. New MgO crystallization was shown to occur until about 60 min, whereafter only MgO grain growth occurred. Median MgO crystallite size increased from 7.5 to 24.9 nm during this period, whereas microstrain decreased dramatically past 60 min annealing time.

This paper focuses on the demand for money in the United States in the context of two globally flexible functional forms—the Fourier and the asymptotically ideal model (AIM)—estimated subject to full regularity, using methods suggested over 20 years ago. We provide a comparison in terms of violations of the regularity conditions for consumer maximization and in terms of output in the form of a full set of elasticities. We also provide a policy perspective, using (for the first time) parameter estimates that are consistent with global regularity, in that a very strong case can be made for abandoning the simple-sum approach to monetary aggregation, on the basis of the low elasticities of substitution among the components of the popular M2 aggregate of money.

The aim of this study was to assess the error made by violating the assumption of stationarity when using Fourier analysis for spectral decomposition of heart period power. A comparison was made between using Fourier and Wavelet analysis (the latter being a relatively new method without the assumption of stationarity). Both methods were compared separately for stationary and nonstationary segments. An ambulatory device was used to measure the heart period data of 40 young and healthy participants during a psychological stress task and during periods of rest. Surprisingly small differences (<1%) were found between the results of both methods, with differences being slightly larger for the nonstationary segments. It is concluded that both methods perform almost identically for computation of heart period power values. Thus, the Wavelet method is only superior for analyzing heart period data when additional analyses in the time-frequency domain are required.