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This study aims to use the polynomial approximation method based on the Pascal polynomial basis for obtaining the numerical solutions of partial differential equations. Moreover, this method does not require establishing grids in the computational domain.

In this study, the authors present a meshfree method based on Pascal polynomial expansion for the numerical solution of the Sobolev equation. In general, Sobolev-type equations have several applications in physics and mechanical engineering.

The authors use the Crank-Nicolson scheme to discrete the time variable and the Pascal polynomial-based (PPB) method for discretizing the spatial variables. But it is clear that increasing the value of the final time or number of time steps, will bear a lot of costs during numerical simulations. An important purpose of this paper is to reduce the execution time for applying the PPB method. To reach this aim, the proper orthogonal decomposition technique has been combined with the PPB method.

The developed procedure is tested on various examples of one-dimensional, two-dimensional and three-dimensional versions of the governed equation on the rectangular and irregular domains to check its accuracy and validity.

Due to social transformation in China, more than 100,000,000 people are migrating within the country. Many parents are forced to leave their children behind when they migrate. In 2008, 58,000,000 children were living as left‐behind children, mainly in the rural parts of China (Zhang, 2009).Migration and its accompanying stressors may affect the mental health of the left‐behind children. This unique literature review of Chinese literature summarises the present state of knowledge and reviews the influential factors. Possible approaches to intervention and system reforms are discussed.A literature review was performed of published studies between 2001 and 2008. Databases used were Fujian Medical University Library Interface, Chinese National Knowledge Infrastructure, Wanfang Data, and VIP Information. The Chinese word for ‘left‐behind’ was used as a key word. Books, book chapters, monographs and studies on caring were searched electronically and by hand. Altogether, 53 items were found, discussed and grouped together. Migration affected the mental health of the left‐behind children in a passive way, especially their emotions and social behaviour.There is still controversy over how serious mental health problems are among children who have been left behind. Life events, personality, coping strategies and social suppor t can be regarded as four main factors that are predictive of mental health, which provides theoretical guidance for intervention. Suppor t and prevention of mental health problems in schools, in families and in primary care should be developed and studied.

This paper aims to develop a method for evaluating the failure probability and global sensitivity of multiple failure modes based on convex-probability hybrid uncertainty.

The uncertainty information of the input variable is considered as convex-probability hybrid uncertainty. Moment-independent variable global sensitivity index based on the system failure probability is proposed to quantify the effect of the input variable on the system failure probability. Two-mode sensitivity indices are adopted to characterize the effect of each failure mode on the system failure probability. The method based on active learning Kriging (ALK) model with a truncated candidate regions (TCR) is adopted to evaluate the systems failure probability, as well as sensitivity index and this method is termed as ALK-TCR.

The results of five examples demonstrate the effectiveness of the sensitivity index and the efficiency of the ALK-TCR method in solving the problem of multiple failure modes based on the convex-probability hybrid uncertainty.

Convex-probability hybrid uncertainty is considered on system reliability analysis. Moment-independent variable sensitivity index based on the system failure probability is proposed. Mode sensitivity indices are extended to hybrid uncertain reliability model. An effective global sensitivity analysis approach is developed for the multiple failure modes based on convex-probability hybrid uncertainty.

The purpose of this paper is to introduce error ellipse into the bootstrap method to improve the reliability of small samples and the credibility of the S-N curve.

Based on the bootstrap method and the reliability of the original samples, two error ellipse models are proposed. The error ellipse model reasonably predicts that the discrete law of expanded virtual samples obeys two-dimensional normal distribution.

By comparing parameters obtained by the bootstrap method, improved bootstrap method (normal distribution) and error ellipse methods, it is found that the error ellipse method achieves the expansion of sampling range and shortens the confidence interval, which improves the accuracy of the estimation of parameters with small samples. Through case analysis, it is proved that the tangent error ellipse method is feasible, and the series of S-N curves is reasonable by the tangent error ellipse method.

The error ellipse methods can lay a technical foundation for life prediction of products and have a progressive significance for the quality evaluation of products.

Although high-order smooth reproducing kernel mesh-free approximation enables the analysis of structural vibrations in an efficient collocation formulation, there is still a lack of systematic theoretical accuracy assessment for such approach. The purpose of this paper is to present a detailed accuracy analysis for the reproducing kernel mesh-free collocation method regarding structural vibrations.

Both second-order problems such as one-dimensional (1D) rod and two-dimensional (2D) membrane and fourth-order problems such as Euler–Bernoulli beam and Kirchhoff plate are considered. Staring from a generic equation of motion deduced from the reproducing kernel mesh-free collocation method, a frequency error measure is rationally attained through properly introducing the consistency conditions of reproducing kernel mesh-free shape functions.

This paper reveals that for the second-order structural vibration problems, the frequency accuracy orders are p and (p − 1) for even and odd degree basis functions; for the fourth-order structural vibration problems, the frequency accuracy orders are (p − 2) and (p − 3) for even and odd degree basis functions, respectively, where p denotes the degree of the basis function used in mesh-free approximation.

A frequency accuracy estimation is achieved for the reproducing kernel mesh-free collocation analysis of structural vibrations, which can effectively underpin the practical applications of this method.

The water-lubricated hydrodynamic herringbone groove journal bearing (HGJB) is capable of running at high speed. However, when running at a low speed, it suffers from a low load-carrying capacity due to the weak hydrodynamic effect. To overcome this problem, this study proposes a hybrid water-lubricated HGJB and aims to investigate its dynamic characteristics.

A hybrid lubrication model applicable to the hybrid water-lubricated HGJB is established based on the boundary fitted coordinate system, which considers the turbulent, thermal and tilting effects, and the finite difference method is used to calculate the dynamic characteristics of the hybrid water-lubricated HGJB.

The result shows that the hybrid HGJB has larger dynamic coefficients and better system stability compared with the hydrodynamic HGJB when running at low speed. Furthermore, the stiffness of hybrid HGJB are mainly governed by the hydrodynamic effect rather than the hydrostatic effect when running at high speed.

The proposed hybrid water-lubricated HGJB shows excellent dynamic characteristics at either low speed or high speed; and the hybrid water-lubricated HGJB has a large load-carrying capacity when running at low speed and has a good dynamic stability when running at high speed.

The peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-06-2024-0233/

Intuitionistic linguistic fuzzy information (ILFI), characterized by linguistic terms and intuitionistic fuzzy sets (IFSs), can easily express the fuzzy information in the process of muticriteria decision making (MCDM) and muticriteria group decision making (MCGDM) problems. The purpose of this paper is to provide an overview of aggregation operators (AOs) and applications of ILFI.

First, some meaningful AOs for ILFI are summarized, and some extended MCDM approaches for intuitionistic uncertain linguistic variables (IULVs), such as extended TOPSIS, extended TODIM, extended VIKOR, are discussed. Then, the authors summarize and analyze the applications about the AOs of IULVs.

IULVs, characterized by linguistic terms and IFSs, can more detailed and comprehensively express the criteria values in the process of MCDM and MCGDM. Therefore, lots of researchers pay more and more attention to the MCDM or MCGDM methods with IULVs.

The authors summarize and analyze the applications about the AOs of IULVs Finally, the authors point out some possible directions for future research.

The purpose of this study is to evaluate the profit efficiency of decision-making units (DMUs) based on predicted future information to solve the lag problem of improvement benchmarks given by the traditional profit efficiency model.

This paper proposes a two-step profit efficiency evaluation method. The first step predicts the future input and output information of DMUs through the past time-series data, obtaining a likely production possibility set (PPS) and profit frontier for the next period. The second step calculates DMUs' profit efficiency based on the predictions obtained in the first step and provides predictive benchmarking for DMUs.

The empirical results show that the proposed method yields good solutions for the lag problem of benchmarks given in ex-post evaluation, enabling bank managers to use predicted future information to achieve better improvement. Besides, compared with the technical efficiency measure, profit efficiency can better reflect the financial situation of DMUs and give the specific gap between the evaluated and optimal DMU.

For bank managers, the authors' new technique is advantageous for grasping the initiative of development because this technique accounts for the future development of the whole industry and sets forward-looking targets. These advantages can help banks improve in a more favorable direction and improve the asset management ability of banks.

This paper combines the data envelopment analysis (DEA) profit efficiency model with performance prediction and proposes a new two-step profit efficiency model, filling a gap in previous studies.

This paper aims to develop a method to improve the accuracy of tolerance analysis considering the spatial distribution characteristics of part surface morphology (SDCPSM) and local surface deformations (LSD) of planar mating surfaces during the assembly process.

First, this paper proposes a skin modeling method considering SDCPSM based on Non-Gaussian random field. Second, based on the skin model shapes, an improved boundary element method is adopted to solve LSD of nonideal planar mating surfaces, and the progressive contact method is adopted to obtain relative positioning deviation of mating surfaces. Finally, the case study is given to verify the proposed approach.

Through the case study, the results show that different SDCPSM have different influences on tolerance analysis, and LSD have nonnegligible and different influence on tolerance analysis considering different SDCPSM. In addition, the LSD have a greater influence on translational deviation along the z-axis than rotational deviation around the x- and y-axes.

The surface morphology with different spatial distribution characteristics leads to different contact behavior of planar mating surfaces, especially when considering the LSD of mating surfaces during the assembly process, which will have further influence on tolerance analysis. To address the above problem, this paper proposes a tolerance analysis method with skin modeling considering SDCPSM and LSD of mating surfaces, which can help to improve the accuracy of tolerance analysis.

This study aims to propose an improved affine interval truncation algorithm to restrain interval extension for interval function.

To reduce the occurrence times of related variables in interval function, the processing method of interval operation sequence is proposed.

The interval variable is evenly divided into several subintervals based on correlation analysis of interval variables. The interval function value is modified by the interval truncation method to restrain larger estimation of interval operation results.

Through several uncertain displacement response engineering examples, the effectiveness and applicability of the proposed algorithm are verified by comparing with interval method and optimization algorithm.