Defense Budget Growth and Inflation: A Wavelet-Based Study of the U.S. and Britain

Despite the extensive theoretical connections between defense budget growth and inflation, empirical findings based on traditional time-domain methods have been inconclusive. This study reexamines the issue from a time–frequency perspective. Applying continuous wavelet analysis to the U.S. and Britain, it shows empirical evidence in support of positive bilateral effects in both cases. In the bivariate context, U.S. defense budget growth promoted inflation at 2- to 4-year cycles in the 1840s and at 8- to 24-year cycles between 1825 and 1940. Conversely, inflation accelerated defense spending growth at 5- to 7-year cycles in the 1830s and at 25- to 64-year cycles between 1825 and 1940. Similarly, British defense budget growth spurred inflation at 8- to 48-year cycles between 1890 and 1940 and at 50- to 65-year cycles between 1790 and 1860. Inflation fueled the growth of defense spending at 7- to 20-year cycles between 1840 and 1870, in the 1940s, and in the 1980s. Preliminary results from multivariate analyses are also supportive, though there is a need for further research that is contingent on advancements in the wavelet method in the direction of simulation-based significance tests.

Repetitive Transient Extraction Using the Optimized SES Entropy Wavelet for Fault Diagnosis of Rotating Machinery

Repetitive transients are usually generated in the monitoring data when a fault occurs on the machinery. As a result, many methods such as kurtogram and optimized Morlet wavelet and kurtosis method are proposed to extract the repetitive transients for fault diagnosis. However, one shortcoming of these methods is that they are constructed based on the index of kurtosis and are sensitive to the impulsive noise, leading to failure in accurately diagnosing the fault of the machinery operating under harsh environment. To address this issue, an optimized SES entropy wavelet method is proposed. In the proposed method, the optimized parameters including bandwidth and central frequency of Morlet wavelets are selected. Then, based on the wavelet coefficients decomposed using the optimized Morlet wavelet, the SES entropy is calculated to select the scales of wavelet coefficients. Finally, the repetitive transients are reconstructed based on the denoising wavelet coefficients of the selected scales. One simulation case and vibration data collected from the experimental setup are used to verify the effectiveness of the proposed method. The simulated and experimental analyses showed that the signal-to-noise ratio (SNR) of the proposed method has the largest value. Specifically, the SNR in the experimental analysis of the proposed method is 0.6, while that of the other three methods is 0.043, 0.0065, and 0.0045, respectively. Therefore, the result shows that the proposed method is superior to the traditional methods for repetitive transient extraction from the vibration data suffered from impulsive noise.

A Wavelet-Galerkin Method for the Nonlinear Schrödinger Equation

A general implementation is presented for constructing a wavelet method for solving the nonlinear equation of Schr¨odinger. An explicit formula is derived which yields a stability in of the numerical solution. A simulation is elaborated to show the general behavior of the distribution function. Numerical results and comparison with classical algorithms are provided. This approach prove an attractive scheme for solving such equation.

Pilot Study of Blood Perfusion Changes at PC4 and Its Surrounding Points Induced by Acupuncture and Moxibustion

Acupuncture and moxibustion are widely used in clinical practice; however, the differences between their mechanisms are unclear. In the present study, the response of blood perfusion resulting from acupuncture or moxibustion at Ximen (PC4) and its surrounding points was explored. Using the wavelet method, the differences in the frequency interval of blood flux were observed. Furthermore, the correlations between these points were analyzed. The results suggested that moxibustion could significantly improve blood flow perfusion at PC4 compared to acupuncture; however, there was no significant difference around PC4. The response of blood flux at PC4 to different stimulations was related to the frequency V (0.4–1.6 Hz) component. However, a difference in response at other points was not observed. Correlation analysis showed that both acupuncture and moxibustion could cause a decline in the correlation of blood flux signals at these recorded points, but there was no significant difference between these techniques. The results suggested that, at least in the forearm, the acupuncture or moxibustion only influenced the level of blood perfusion locally.

PLANAR SCINTIGRAPHY IMAGE DE-NOISING USING COIFLET WAVELET

The planar scintigraphic image usually has poor resolution and contains noise. This noise can be removed using the coiflet wavelet method so that the image quality gets better. This coiflet wavelet method is a noise reduction method based on frequency analysis. The planar scintigraphy image is the reconstructed image of the gamma radiation count data (phantom with the Cs-137 source in it). The original image is 15×15 pixel. Before the de-noising process, the image went through an interpolation process, which is to increase the pixel size of the image. The original image enlarged to 70×70, 480×480, and 1200×1200 pixel. After de-noising with coiflet wavelet, the image quality is measured based on MSE and PSNR parameters. The resulting images are quite good, with MSE values are close to zero and PSNR values of more than 60 dB. The smaller the MSE and the bigger the PSNR, is getting the better the image quality. In this study, the results show that the 1200×1200 pixel image has the best quality. It means that the image enlargement process has a good effect on the de-noising process, especially if the original image has a low resolution.

Solving Nonlinear Boundary Value Problems Using the Higher Order Haar Wavelet Method

The current study is focused on development and adaption of the higher order Haar wavelet method for solving nonlinear ordinary differential equations. The proposed approach is implemented on two sample problems—the Riccati and the Liénard equations. The convergence and accuracy of the proposed higher order Haar wavelet method are compared with the widely used Haar wavelet method. The comparison of numerical results with exact solutions is performed. The complexity issues of the higher order Haar wavelet method are discussed.