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This meshless collocation method is applicable not only to the Helmholtz equation with Dirichlet boundary condition but also mixed boundary conditions. It can calculate not only the high wavenumber problems, but also the variable wave number problems.

In this paper, the authors developed a meshless collocation method by using barycentric Lagrange interpolation basis function based on the Chebyshev nodes to deduce the scheme for solving the three-dimensional Helmholtz equation. First, the spatial variables and their partial derivatives are treated by interpolation basis functions, and the collocation method is established for solving second order differential equations. Then the differential matrix is employed to simplify the differential equations which is on a given test node. Finally, numerical experiments show the accuracy and effectiveness of the proposed method.

The numerical experiments show the advantages of the present method, such as less number of collocation nodes needed, shorter calculation time, higher precision, smaller error and higher efficiency. What is more, the numerical solutions agree well with the exact solutions.

Compared with finite element method, finite difference method and other traditional numerical methods based on grid solution, meshless method can reduce or eliminate the dependence on grid and make the numerical implementation more flexible.

The Helmholtz equation has a wide application background in many fields, such as physics, mechanics, engineering and so on.

This meshless method is first time applied for solving the 3D Helmholtz equation. What is more the present work not only gives the relationship of interpolation nodes but also the test nodes.

The paper aims to accurately measure the key motion parameters, such as velocity, azimuth and pitch angle, of the small flying object with a non-uniform curve trajectory. It proposes a measurement method and its calculation model of non-uniform curve trajectory using a photoelectric sensor array.

First, the basic composition of the measurement system and mechanism of photoelectric sensor array are described, respectively. Second, a non-uniform curve mathematical measurement model is constructed differently from the traditional linear trajectory, taking into account the influence of gravity and air resistance. Third, the measurement error of the system is analyzed through numerical simulation. Finally, the accuracy and feasibility of the approach are verified by live-ammunition experiments.

The results show that the systematic error of the hitting point coordinates can be reduced by 9% compared to the traditional linear measurement model. Consequently, this method can meet the higher measurement requirement for the key motion parameters of the small flying object under the non-uniform curve trajectory. Research limitations/implications (if applicable)- although the approach itself is generalizable, the method is unable to detect the motion parameters of multiple small flying objects.

Although the approach itself is generalizable, the method is unable to detect the motion parameters of the multiple small flying objects.

It is evident that the proposed non-uniform curve measurement model is more precise in quantifying the essential characteristics of the small flying object, particularly in consideration of the environmental conditions.

The precise measurement of the key motion parameters of the small flying object can facilitate the enhancement of the protective performance of protective materials.

A novel approach to measurement is proposed, which differs from the conventional uniform trajectory model. To this end, the space construction of the photoelectric sensor array is optimized. The number of the sensors is revised.

Traditional Chinese medicine (TCM) prescriptions have always relied on the experience of TCM doctors, and machine learning(ML) provides a technical means for learning these experiences and intelligently assists in prescribing. However, in TCM prescription, there are the main (Jun) herb and the auxiliary (Chen, Zuo and Shi) herb collocations. In a prescription, the types of auxiliary herbs are often more than the main herb and the auxiliary herbs often appear in other prescriptions. This leads to different frequencies of different herbs in prescriptions, namely, imbalanced labels (herbs). As a result, the existing ML algorithms are biased, and it is difficult to predict the main herb with less frequency in the actual prediction and poor performance. In order to solve the impact of this problem, this paper proposes a framework for multi-label traditional Chinese medicine (ML-TCM) based on multi-label resampling.

In this work, a multi-label learning framework is proposed that adopts and compares the multi-label random resampling (MLROS), multi-label synthesized resampling (MLSMOTE) and multi-label synthesized resampling based on local label imbalance (MLSOL), three multi-label oversampling techniques to rebalance the TCM data.

The experimental results show that after resampling, the less frequent but important herbs can be predicted more accurately. The MLSOL method is shown to be the best with over 10% improvements on average because it balances the data by considering both features and labels when resampling.

The authors first systematically analyzed the label imbalance problem of different sampling methods in the field of TCM and provide a solution. And through the experimental results analysis, the authors proved the feasibility of this method, which can improve the performance by 10%−30% compared with the state-of-the-art methods.

The sustainable development of the platform economy has been hindered by the absence and alienation of platform corporate social responsibility. Previous studies have mainly focused on the contents and governance models for platform corporate social responsibility. This study seeks to explore which strategy participants choose in the governance of platform corporate social responsibility and their influencing factors.

Using a platform ecosystem approach, a quadrilateral evolutionary game model was developed, and the stabilities of subjects’ behavioral strategies and their combinations in various scenarios were analyzed. Additionally, the effects of key parameters on the system’s evolutionary path were simulated.

The ideal steady state system is achieved when platform enterprises, complementors and consumers adopt positive strategies while the government adopts lax regulation. Moreover, the evolutionary strategies of the subjects are influenced by several factors, including the participation costs of governance, the rewards and punishments imposed by platform enterprises, as well as the reputational losses of platform enterprises and complementors due to media coverage.

This study offers insights into improving the governance effectiveness of platform corporate social responsibility for managers and practitioners.

This study contributes to existing literature by considering the rational orientation of platform ecosystem members and revealing the interaction mechanisms among members. Furthermore, this study combines collective action theory and reputation theory to clarify the influencing factors on members’ behaviors.

Online health monitoring of large complex equipment has become a trend in the field of equipment diagnostics and prognostics due to the rapid development of sensing and computing technologies. The purpose of this paper is to construct a more accurate and stable grey model based on similar information fusion to predict the real-time remaining useful life (RUL) of aircraft engines.

First, a referential database is created by applying multiple linear regressions on historical samples. Then similarity matching is conducted between the monitored engine and historical samples. After that, an information fusion grey model is applied to predict the future degradation trajectory of the monitored engine considering the latest trend of monitored sensory data and long-term trends of several similar referential samples, and the real-time RUL is obtained correspondingly.

The results of comparative analysis reveal that the proposed model, which is called similarity-based information fusion grey model (SIFGM), could provide better RUL prediction from the early degradation stage. Furthermore, SIFGM is still able to predict system failures relatively accurately when only partial information of the referential samples is available, making the method a viable choice when the historical whole life cycle data are scarce.

The prediction of SIFGM method is based on a single monotonically changing health indicator (HI) synthesized from monitoring sensory signals, which is assumed to be highly relevant to the degradation processes of the engine.

The SIFGM can be used to predict the degradation trajectories and RULs of those online condition monitoring systems with similar irreversible degradation behaviors before failure occurs, such as aircraft engines and centrifugal pumps.

This paper introduces the similarity information into traditional GM(1,1) model to make it more suitable for long-term RUL prediction and also provide a solution of similarity-based RUL prediction with limited historical whole life cycle data.

Grey modeling technique is an important element of grey system theory, and academic articles applied to agricultural science research have been published since 1985, proving the broad applicability and effectiveness of the technique from different aspects and providing a new means to solve agricultural science problems. The analysis of the connotation and trend of the application of grey modeling technique in agricultural science research contributes to the enrichment of grey technique and the development of agricultural science in multiple dimensions.

Based on the relevant literature selected from China National Knowledge Infrastructure, the Web of Science, SpiScholar and other databases in the past 37 years (1985–2021), this paper firstly applied the bibliometric method to quantitatively visualize and systematically analyze the trend of publication, productive author, productive institution, and highly cited literature. Then, the literature is combed by the application of different grey modeling techniques in agricultural science research, and the literature research progress is systematically analyzed.

The results show that grey model technology has broad prospects in the field of agricultural science research. Agricultural universities and research institutes are the main research forces in the application of grey model technology in agricultural science research, and have certain inheritance. The application of grey model technology in agricultural science research has wide applicability and precise practicability.

By analyzing and summarizing the application trend of grey model technology in agricultural science research, the research hotspot, research frontier and valuable research directions of grey model technology in agricultural science research can be more clearly grasped.

This study examines the effect of employees' perceptions of political connections on performance measurement systems (PMS) design choice and firm performance. In addition, this study explores the moderating effect of social networking, a very common and widely used factor by domestic and foreign multinational firms operating in China, and its joint effect with political connections or PMS design choice on firm performance. We collected survey responses from a sample of 110 managers from manufacturing firms in China. Our results reveal that highly politically connected managers use nonfinancial measures, leading to improved firm performance. Our results suggest that social networking interacts significantly with political connections, and nonfinancial and financial measures on firm performance. The theoretical and practical implications of our findings are discussed.

Currently, conjugated nonlinear optical (NLO) materials suffer from the drawbacks of complex manufacturing process and high cost. To further study the NLO materials with cost-effective, it is necessary to prepare new NLO materials with satisfactory performance.

Pyrene derivatives with good third-order NLO properties were synthesized by combining pyrene compounds with TCNE, TCNQ, F4-TCNQ and other molecular systems by clicking chemical method.

The pyrene derivatives were characterized by ultraviolet spectrum and Z-scan. The charge-transfer of the D-p-A structures plays a key role in the absorption peak shifts. And the third-order nonlinear absorption of the products revealed good third-order NLO susceptibilities.

The synthesis technology of pyrene derivatives is not mature enough and is in the preliminary exploration stage. So, the authors produced a relatively small number of samples and did not conduct a very comprehensive test.

This novel pyrene derivative is suggestive and can promote the exploration and development of the third-order nonlinear materials.

Four new pyrene derivatives were synthesized by selecting new molecular systems. Because of its good chemical properties and stable properties, it can be a reference for the development of third-order nonlinear materials in the future.