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The main purpose of this work is to develop a novel algorithm based on Scale-3 Haar wavelets (S-3 HW) and quasilinearization for numerical simulation of dynamical system of ordinary differential equations.

The first step in the development of the algorithm is quasilinearization process to linearize the problem, and then Scale-3 Haar wavelets are used for space discretization. Finally, the obtained system is solved by Gauss elimination method.

Some numerical examples of fractional dynamical system are considered to check the accuracy of the algorithm. Numerical results show that quasilinearization with Scale-3 Haar wavelet converges fast even for small number of collocation points as compared of classical Scale-2 Haar wavelet (S-2 HW) method. The convergence analysis of the proposed algorithm has been shown that as we increase the resolution level of Scale-3 Haar wavelet error goes to zero rapidly.

To the best of authors’ knowledge, this is the first time that new Haar wavelets Scale-3 have been used in fractional system. A new scheme is developed for dynamical system based on new Scale-3 Haar wavelets. These wavelets take less time than Scale-2 Haar wavelets. This approach extends the idea of Jiwari (2015, 2012) via translation and dilation of Haar function at Scale-3.

This paper aims to find the numerical solution of planar and non-planar Burgers’ equation and analysis of the shock behave.

First, the authors discritize the time-dependent term using Crank–Nicholson finite difference approximation and use quasilinearization to linearize the nonlinear term then apply Scale-2 Haar wavelets for space integration. After applying this scheme on partial differential, the equation transforms into a system of algebraic equation. Then, the system of equation is solved using Gauss elimination method.

Present method is the extension of the method (Jiwari, 2012). The numerical solutions using Scale-2 Haar wavelets prove that the proposed method is reliable for planar and non-planar nonlinear Burgers’ equation and yields results better than other methods and compatible with the exact solutions.

The numerical results for non-planar Burgers’ equation are very sparse. In the present paper, the authors identify where the shock wave and discontinuity occur in planar and non-planar Burgers’' equation.

This paper aims to propose a novel approach based on uniform scale-3 Haar wavelets for unsteady state space fractional advection-dispersion partial differential equation which arises in complex network, fluid dynamics in porous media, biology, chemistry and biochemistry, electrode – electrolyte polarization, finance, system control, etc.

Scale-3 Haar wavelets are used to approximate the space and time variables. Scale-3 Haar wavelets converts the problems into linear system. After that Gauss elimination is used to find the wavelet coefficients.

A novel algorithm based on Haar wavelet for two-dimensional fractional partial differential equations is established. Error estimation has been derived by use of property of compactly supported orthonormality. The correctness and effectiveness of the theoretical arguments by numerical tests are confirmed.

Scale-3 Haar wavelets are used first time for these types of problems. Second, error analysis in new work in this direction.

The purpose of this paper is to identify significant factors of environmental variables and pollutants that have an effect on PM_2.5 through wavelet and regression analysis.

In order to provide stable data set for regression analysis, multiresolution analysis using wavelets is conducted. For the sampled data, multicollinearity among the independent variables is removed by using principal component analysis and multiple linear regression analysis is conducted using PM_2.5 as a dependent variable.

It is found that few pollutants such as NO₂, NO_x, SO₂, benzene and environmental factors such as ambient temperature, solar radiation and wind direction affect PM_2.5. The regression model developed has high R² value of 91.9 percent, and the residues are stationary and not correlated indicating a sound model.

The research provides a framework for extracting stationary data and other important features such as change points in mean and variance, using the sample data for regression analysis. The work needs to be extended across all areas in India and for various other stationary data sets there can be different factors affecting PM_2.5.

Control measures such as control charts can be implemented for significant factors.

Rules and regulations can be made more stringent on the factors.

The originality of this paper lies in the integration of wavelets with regression analysis for air pollution data.

The purpose of this paper is to examine the extent to which the capital control measures implemented by the Malaysian central bank in late 1998 had an influence on segmenting the Malaysian equity market from other major equity markets.

The S&P 500, the Nikkei 225 Index, the STI Index and the KLSE Composite Index are considered. The discrete wavelet transform technique – “Haar” is employed to decompose the series into various time scales during the pre‐ and post‐capital control periods in Malaysia. The decomposed series are then used to estimate the interdependence between KLSE Composite Index with the other three markets at various time scales.

The empirical findings support three conclusions. First, in the pre‐capital control period, Singapore is the most influential market followed by the US across all time scales in transmitting news into Malaysia. Second, after the imposition of capital controls, the spillover effects from Singapore to Malaysia have declined substantially, suggesting a reduced integration between these two markets. Finally, in the post‐capital control period, all three markets appear to be imparting a similar but moderate level of influence on the Malaysian market.

To explore the return and volatility spillovers, the use of return and volatility series at different time scales provided a greater level of insight into the dynamics than the standard approaches which employ only one series in the time domain.

The results from this paper will have potential implications for asset allocation, the pricing of domestic securities, the implementation of global hedging and trading strategies and the evaluation of regulatory proposals to restrict international capital flows.

When designing the electrode widths of the electrode-width-weighted (EWW) input interdigital transducers (IDTs) according to the envelope amplitudes of the wavelet function, the EWW wavelet transform processor (WTP) using surface acoustic wave (SAW) devices can be fabricated. The electrode widths have influence on the frequency characteristic of the EWW WTP using SAW devices. The purpose of this research is to solve the influence of the electrode width accuracy on the frequency characteristic of the EWW WTP using SAW devices.

In order to solve the influence of the electrode width accuracy on the frequency characteristics of the EWW WTP using SAW devices, the function between the electrode widths and the −3 dB bandwidth is derived. That the −3 dB bandwidth varies as the electrode widths is known according to this function so that the exposure time and the etching are presented as the two key problems.

Solutions to these problems are achieved in this study. As long as there is accurate exposure time, the precision IDTs (i.e. the precision electrode widths) will be obtained. The accuracy of the exposure time for the EWW WTP using SAW devices is ±1 per cent. Because the dry etching is a type of etching technology in gas medium, it can etch nanometer lines, even more fine lines, so that the dry etching is used in EWW WTP using SAW devices.

Research highlights solving the influence of the electrode width accuracy on the frequency characteristic for the EWW WTP using SAW devices; deriving the function between the electrode widths and the −3 dB bandwidth (it is known from this function that the −3 dB bandwidth varies as the electrode widths); and presenting the exposure time and the etching as two key problems.

This study aims to explore the linkage between fluctuations in the global crude oil price and equity market in fast emerging economies of India and China.

The present research uses wavelet decomposition and maximal overlap discrete wavelet transform (MODWT), which decompose the time series into various frequencies of short, medium and long-term nature. The paper further uses continuous and cross wavelet transform to analyze the variance among the variables and wavelet coherence analysis and wavelet-based Granger causality analysis to examine the direction of causality between the variables.

The continuous wavelet transform indicates strong variance in WTIR (return series of West Texas Instrument crude oil price) in short, medium and long run at various time periods. The variance in CNX Nifty is observed in the short and medium run at various time periods. The Chinese stock index, i.e. SCIR, experiences very little variance in short run and significant variance in the long and medium run. The causality between the changes in crude oil price and CNX Nifty is insignificant and there exists a bi-directional causality between global crude oil price fluctuations and the Chinese equity market.

To the best of the authors’ knowledge, very limited work has been done where the researchers have analyzed the linkage between the equity market and crude oil price fluctuations under the framework of discrete wavelet transform, which overlooks the bottleneck of non-stationarity nature of the time series. To bridge this gap, the present research uses wavelet decomposition and MODWT, which decompose the time series into various frequencies of short, medium and long-term nature.

Fabric defects detection is vital in the automation of textile industry. The purpose of this paper is to develop and implement a new fabric defects detection method based on adaptive wavelet.

Fabric defects can be regarded as the abrupt features of textile images with uniform background textures. Wavelets have compact support and can represent these textures. When there is an abrupt feature existed, the response is totally different with the response of the background textures, so wavelets can detect these abrupt features. This method designs the appropriate wavelet bases for different fabric images adaptively. The defects can be detected accurately.

The proposed method achieves accurate detection of fabric defects. The experimental results suggest that the approach is effective.

This paper develops an appropriate method to design wavelet filter coefficients for detecting fabric defects, which is called adaptive wavelet. And it is helpful to realize the automation of textile industry.

The purpose of this paper is to study the application of feature‐based image matching algorithm for PCB matching without using special fiducial marks.

Speed‐up robust feature (SURF) is applied to extract the interest points in PCB images. An advanced threshold is set to reject the interest points with low responses to speed up feature computation. In order to improve the performance for rotation, the descriptors are based on multi‐orientations. The many‐to‐many tentative correspondences are determined with a maximum distance. Hough transform is used to reject the mismatches and the affine parameters are computed with a square‐least solution.

Results show that the method proposed in this paper can match the PCB images without using special fiducial marks effectively. The image matching algorithm shows a better performance for image rotation than the standard SURF and it succeeds in matching the image including repetitive patterns which will deteriorate the distinctiveness of feature descriptors.

Additional orientations produce more descriptors so that it takes extra time for feature description and matching.

The paper proposes a SURF‐based image matching algorithm to match the PCB images without special fiducial marks. This can reduce the complexity of PCB production. The image matching algorithm is robust to image rotation and repetitive patterns and can be used in other applications of image matching.

Extracting suitable features to represent an image based on its content is a very tedious task. Especially in remote sensing we have high-resolution images with a variety of objects on the Earth's surface. Mahalanobis distance metric is used to measure the similarity between query and database images. The low distance obtained image is indexed at the top as high relevant information to the query.

This paper aims to develop an automatic feature extraction system for remote sensing image data. Haralick texture features based on Contourlet transform are fused with statistical features extracted from the QuadTree (QT) decomposition are developed as feature set to represent the input data. The extracted features will retrieve similar images from the large image datasets using an image-based query through the web-based user interface.

The developed retrieval system performance has been analyzed using precision and recall and F1 score. The proposed feature vector gives better performance with 0.69 precision for the top 50 relevant retrieved results over other existing multiscale-based feature extraction methods.

The main contribution of this paper is developing a texture feature vector in a multiscale domain by combining the Haralick texture properties in the Contourlet domain and Statistical features using QT decomposition. The features required to represent the image is 207 which is very less dimension compare to other texture methods. The performance shows superior than the other state of art methods.