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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 contagion among the major world markets during the last 25 years and propose a new way to analyze contagion with wavelet methods.

The analysis uses a novel way to study contagion using wavelet methods. The comparison is made between co‐movements at different time scales. Co‐movement methods of the discrete wavelet transform and the continuous wavelet transform are applied.

Clear signs of contagion among the major markets are found. Short time scale co‐movements increase during the major crisis while long time scale co‐movements remain approximately at the same level. In addition, gradually increasing interdependence between markets is found.

Because of the chosen method, the approach is limited to large data sets.

The research has practical implications to portfolio managers etc. who wish to have better view of the dynamics of the international equity markets.

The research uses novel wavelet methods to analyze world equity markets. These methods allow the markets to be analyzed in the whole state space.

This study aims to present a novel hydrostatic squeeze film-metal mesh journal bearing (HS-MMJB), which uses both hydrostatic squeeze film damper (HSFD) and metal mesh damper (MMD), to suppress the vibration of rotor-bearing systems.

The lubrication equations were introduced to calculate the dynamic characteristics of HS-MMJB, and the response analyses of rotor systems were carried out. Experiments were conducted to study the vibration reduction of a rotor system with HS-MMJB. In addition, experiments for different oil supply pressures in the HS-MMJB were conducted.

The theoretical and experimental results show that the HS-MMJB exhibits excellent damping and vibration attenuation characteristics. Moreover, the stability of the rotor system can be improved by controlling the oil supply pressure.

There is a dearth of research on vibration characteristics of rotor system support by journal bearing combining HSFD and MMD. Moreover, the active oil pressure control is implemented to improve the stability of rotor system.

To develop an overview of generalized scales based on pansystems‐relative quantification.

This is a discussion paper exploring the key issues surrounding generalized measures.

The concrete contents of the study include generalized measure views, dimension theory, concepts, logic, theories, Einstein's relativity, quality‐quantity‐degree, methodology of physics, theorems in pansystems mathematics and physics explained within the framework of pan‐scale transformations.

Provides an overview of generalized scales based on pansystems‐relative quantification.

This paper presents a novel framework for solving elliptic partial differential equations (PDEs) over irregularly spaced meshes on bounded domains.

Second‐generation wavelet construction gives rise to a powerful generalization of the traditional hierarchical basis (HB) finite element method (FEM). A framework based on piecewise polynomial Lagrangian multiwavelets is used to generate customized multiresolution bases that have not only HB properties but also additional qualities.

For the 1D Poisson problem, we propose – for any given order of approximation – a compact closed‐form wavelet basis that block‐diagonalizes the stiffness matrix. With this wavelet choice, all coupling between the coarse scale and detail scales in the matrix is eliminated. In contrast, traditional higher‐order (n>1) HB do not exhibit this property. We also achieve full scale‐decoupling for the 2D Poisson problem on an irregular mesh. No traditional HB has this quality in 2D.

Similar techniques may be applied to scale‐decouple the multiresolution finite element (FE) matrices associated with more general elliptic PDEs.

By decoupling scales in the FE matrix, the wavelet formulation lends itself particularly well to adaptive refinement schemes.

The paper explains second‐generation wavelet construction in a Lagrangian FE context. For 1D higher‐order and 2D first‐order bases, we propose a particular choice of wavelet, customized to the Poisson problem. The approach generalizes to other elliptic PDE problems.

In this chapter we perform a Monte Carlo simulation study of the errors-in-variables model examined in Ramsey, Gallegati, Gallegati, and Semmler (2010) by using a wavelet multiresolution approximation approach. Differently from previous studies applying wavelets to errors-in-variables problem, we use a sequence of multiresolution approximations of the variable measured with error ranging from finer to coarser scales. Our results indicate that multiscale approximations to the variable observed with error based on the coarser scales provide an unbiased asymptotically efficient estimator that also possess good finite sample properties.

Multiresolution representations of data are classical tools in image processing applications. The purpose of this paper is to discuss a particular problem, obtaining good reconstructions of noise images.

A nonlinear multiresolution scheme within Harten's framework corresponding to a nonlinear cell‐average technique is used for color image denoising.

This paper finds it is possible, for example, to apply the theoretical framework to case studies in internationally operating companies delivering a mix of goods and services.

The present study provides a starting point for further research in the denoising problems using nonlinear techniques.

Moreover, the proposed framework has proven to be useful in improving the classical linear multiresolution approaches.

Limited geometric accuracy is one of the major challenges that hinder the wider application of additive manufacturing (AM). This paper aims to predict in-plane shape deviation for online inspection and compensation to prevent error accumulation and improve shape fidelity in AM.

A sequence-to-sequence model with an attention mechanism (Seq2Seq+Attention) is proposed and implemented to predict subsequent layers or the occluded toolpath deviations after the multiresolution alignment. A shape compensation plan can be performed for the large deviation predicted.

The proposed Seq2Seq+Attention model is able to provide consistent prediction accuracy. The compensation plan proposed based on the predicted deviation can significantly improve the printing fidelity for those layers detected with large deviations.

Based on the experiments conducted on the knee joint samples, the proposed method outperforms the other three machine learning methods for both subsequent layer and occluded toolpath deviation prediction.

This work fills a research gap for predicting in-plane deviation not only for subsequent layers but also for occluded paths due to the missing scanning measurements. It is also combined with the multiresolution alignment and change point detection to determine the necessity of a compensation plan with updated G-code.

To provide several comparisons between linear and nonlinear approaches in denoising applications.

The comparison is based on the peak signal noise ratio (PSNR) image quality measure. Which one of the algorithms gives higher PSNR and then denoises more the original picture is studied.

Nonlinear reconstruction operators can improve the accuracy of the prediction in the vicinity of isolated singularities. A better treatment of the singularities corresponding to the image edges and, therefore, an improvement on the sparsity of the multiresolution representation of images are then expected.

In this paper the point‐value framework is considered. Other frameworks, as the cell‐average discretization, are more suitable for image processing where noise and texture appear. But, the point value schemes can be adapted to the cell‐average discretization using primitive function.

People can use the new denoising algorithm presented in the paper.

In this paper nonlinear schemes in the Harten's multiresolution framework that improve the results of the classical linear schemes are presented.

An automated way of revealing the diagnostic character of discontinuous adventitious sounds (DAS), i.e. crackles and squawks, by isolating them from vesicular sounds (VS), based on their nonstationarity, is presented in this paper. The proposed algorithm combines multiresolution analysis with hard thresholding in order to compose a wavelet‐based stationary‐non‐stationary filter (WTST‐NST). Applying the WTST‐NST filter to fine/coarse crackles and squawks, selected from three lung sound databases, the coherent structure of the DAS is revealed and they are separated from VS. When compared to other separation tools, in noiseless case, the WTST‐NST filter performed more accurately, objectively, and with lower computational cost. Owing to its simple implementation it can easily be used in clinical medicine.