Numerical solution of nth‐order integro‐differential equations using trigonometric wavelets

The main aim of this paper is to apply the trigonometric wavelets for the solution of the Fredholm integro‐differential equations of nth‐order. The operational matrices of derivative for trigonometric scaling functions and wavelets are presented and are utilized to reduce the solution of the Fredholm integro‐differential equations to the solution of algebraic equations. Furthermore, we get an estimation of error bound for this method. Copyright © 2011 John Wiley & Sons, Ltd.     

Leak detection in water-filled plastic pipes through the application of tuned wavelet transforms to Acoustic Emission signals

A new method to detect leakage in a water-filled plastic pipe is proposed. In this method, a leakage signal-signature in time domain is first captured by monitoring the Short Time Fourier Transforms (STFT) of AE (Acoustic Emission) signals over a relatively long time-interval. The captured signal is then used to find a mother wavelet (tuned wavelet) for the best signal localization in time and frequency domains. The technique for AE signal detection using tuned wavelet is then described. Practical application of the method proposed herein is then presented using a water-filled plastic pipe as a case study. Signals generated from this experimental setup are collected to identify leakage signal-signatures from other interfering signals (background, pipe natural frequency, splash and environmental noise). The results of the experiment prove that using tuned wavelet, AE events can be detected and identified precisely in time. In addition, sources of signals due to leakage and their respective energy levels can also be recognized.     

Ultrasonic degradation of Rhodamine B in the presence of hydrogen peroxide and some metal oxide

In this research, degradation of Rodamine B in the presence of (hydrogen peroxide), (hydrogen peroxide + ultrasound), (hydrogen peroxide + aluminum oxide), (hydrogen peroxide + aluminum oxide + ultrasound with different ultrasound power), (hydrogen peroxide + iron oxide) and (hydrogen peroxide + iron oxide + ultrasound with different ultrasound power) were investigated at 25 °C. The apparent rate constants for the examined systems were calculated by pseudo-first-order kinetics. The results indicate that the rate of degradation was accelerated by ultrasound. The rate of degradation was increased by increasing power ultrasound. The efficiency of the (hydrogen peroxide + iron oxide + ultrasound) system for degradation of Rodamine B was higher than the others examined.