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The purpose of this paper is to develop a novel multivariate fractional grey model termed GM(a, n) based on the classical GM(1, n) model. The new model can provide accurate prediction with more freedom, and enrich the content of grey theory.

The GM(α, n) model is systematically studied by using the grey modelling technique and the forward difference method. The optimal fractional order a is computed by the genetic algorithm. Meanwhile, a stochastic testing scheme is presented to verify the accuracy of the new GM(a, n) model.

The recursive expressions of the time response function and the restored values of the presented model are deduced. The GM(1, n), GM(a, 1) and GM(1, 1) models are special cases of the model. Computational results illustrate that the GM(a, n) model provides accurate prediction.

The GM(a, n) model is used to predict China’s total energy consumption with the raw data from 2006 to 2016. The superiority of the GM(a, n) model is more freedom and better modelling by fractional derivative, which implies its high potential to be used in energy field.

It is the first time to investigate the multivariate fractional grey GM(α, n) model, apply it to study the effects of China’s economic growth and urbanization on energy consumption.

Sand production is a challenging issue during hydrocarbon production in the oil and gas industry. This paper aims to investigate one sand production process, i.e. transient sand production, using a novel bonded particle lattice Boltzmann method. This mesoscopic technique provides a unique insight into complicated sand erosion process during oil exploitation.

The mesoscopic fluid-particle coupling is directly approached by the immersed moving boundary method in the framework of lattice Boltzmann method. Bonded particle method is used for resolving the deformation of solid. The onset of grain erosion of rocks, which are modelled by a bonded particle model, is realised by breaking the bonds simulating cementation when the tension or tangential force exceeds critical values.

It is proved that the complex fluid–solid interaction occurring at the pore/grain level can be well captured by the immersed moving boundary scheme in the framework of the lattice Boltzmann method. It is found that when the drawdown happens at the wellbore cavity, the tensile failure area appears at the edge of the cavity. Then, the tensile failure area gradually propagates inward, and the solid particles at the tensile failure area become fluidised because of large drag forces. Subsequently, some eroded particles are washed out. This numerical investigation is demonstrated through comparison with the experimental results. In addition, through breaking the cementation, which is simulated by bond models, between bonded particles, the transient particle erosion process is successfully captured.

A novel bonded particle lattice Boltzmann method is used to investigate the sand production problem at the grain level. It is proved that the complex fluid–solid interaction occurring at the pore/grain level can be well captured by the immersed moving boundary scheme in the framework of the lattice Boltzmann method. Through breaking the cementation, which is simulated by bond models, between bonded particles, the transient particle erosion process is successfully captured.

The use of removable complete dentures is a selectable restorative procedure for edentulous patients. To improve the fabrication quality and efficiency of removable complete dentures, this paper aims to introduce a new method to fabricate customized wax complete dentures with additive manufacturing. This process uses complementary digital technologies, and allows faster and better manufacture of complete dentures.

In the study, a dental scanner was used to obtain surface data from edentulous casts and rims made by the dentist. A parameterized three-dimensional graphic database of artificial teeth was pre-established. Specialized computer-aided design software was used to set up the artificial dentition and design the esthetic gingiva and base plate. A selective laser sintering machine was used to transfer the data from stereolithography files into a wax base plate with location holes for each artificial tooth.

Under this method, a set of wax base plates with 28 location holes available for the placement of the artificial teeth were designed and fabricated within 6 h. The try-in wax dentures fitted the patient’s mouth well, besides occlusion relationships. Then, the occlusion relationships can be adjusted manually to achieve a balanced centric occlusion.

This method can be used to design and fabricate wax try-in removable complete dentures semi-automatically and rapidly; however, the algorithm for the occlusion contact design needs to be improved.

The business world today is witnessing ever-growing disruption. This study highlights corporate social responsibility (CSR) as an effective strategy for firms in disrupted industries to consider in order to differentiate themselves and to increase their chance of survival facing disruption.

In this study, the authors test the hypotheses using a multilevel modeling (MLM) design to capture the group and intergroup effects at the industry level and at the firm level. The empirical analysis is based on a panel sample of 1,193 firms over the 10-year period from 2010 to 2019.

The empirical analysis indicates that CSR has a positive impact on corporate financial stability and the effect is especially significant for firms in disrupted industries. Further investigation suggests that this positive effect largely runs through traits of the social pillar, such as human rights, employee relations, customer protection, product responsibility and community impact. The results are robust after controlling for other firm-specific characteristics and after addressing endogeneity concerns.

This study examines whether, and through which channel, CSR helps enhance corporate financial stability and mitigate bankruptcy risk in disrupted industries. To the best of the authors' knowledge, this study is the first attempt to explore the use of CSR as an effective strategic response to disruption. Further analysis indicates that the social capital built through CSR plays an important role in helping enhance corporate financial stability.

The purpose of this paper is to investigate the interfacial conductivity and corrosion resistance of the Ni–P/Ti₄O₇ composite coating that is deposited on a carbon steel substrate as bipolar plates for proton exchange membrane fuel cells.

The Ni–P/Ti₄O₇ coating was prepared by electroless plating. Scanning electron microscopy, white light interference, energy dispersive spectrometry and X-ray diffraction were used, respectively, to study the surface morphology, chemical composition and phase composition of coated samples. Electrochemical impedance spectroscopy, potentiodynamic and potentiostatic polarization were used to test the electrochemical performance and corrosion behavior. The interfacial contact resistance (ICR) was measured via the standard method.

The surface of the Ni–P/Ti₄O₇ coating is complete and dense and without obvious defects. The electrochemical test results show that the Ni–P/Ti₄O₇ coating provides better corrosion resistance than the Ni–P coating and substrate. Compared with the Ni–P coating, the ICR of the Ni–P/Ti₄O₇ coating is lower by about 82.7%. This is because the coating has more conductive contact points. The more exciting thing is that the ICR of the Ni–P/Ti₄O₇ coating only increases to 12.38 mΩ·cm² after 5 h of polarization.

This paper provides a method for achieving surface modification of metal bipolar plates. Introducing Ti₄O₇ particles in the Ni–P layer reduces the contact resistance before and after polarization while ensuring good corrosion resistance.

The purpose of this paper is to study a fractional grey model FAGM(1,1,t^α) based on the GM(1,1,t^α) model and the fractional accumulated generating operation, and then predict the national health expenditure, the government health expenditure and the out-of-pocket health expenditure of China.

The presented univariate grey model is systematically studied by using the grey modelling technique, the fractional accumulated generating operation and the trapezoid approximation formula of definite integral. The optimal system parameters r and α are evaluated by the particle swarm optimisation algorithm.

The expressions of the time response function and the restored values of this model are derived. The GM(1,1), NGM(1,1,k,c) and GM(1,1,t^α) models are particular cases of the FAGM(1,1,t^α) model with deterministic r and α. Compared with other forecasting models, the results of the FAGM(1,1,t^α) model have higher precision.

The superiority of the new model has high potential to be used in the medicine and health fields and others. Results can provide a guideline for government decision making.

The univariate fractional grey model FAGM (1,1,t^α) successfully studies the China’s health expenditure.

Training remains an important factor in developing the managerial effectiveness and capability of small and medium-sized enterprises (SMEs), yet there are concerns regarding the quality of training provided to SME managers in Ghana, hence the weak managerial capabilities observed in SME management. This study, therefore, examines the impact of managerial training on the effectiveness of SME managers in Ghana.

Drawing on the human capital theory (Becker, 1962; Rosen, 1977), this study employs the variance-based estimating technique, partial least square structural equation modelling (PLS-SEM) in estimating the effects of training on the managerial effectiveness of SME managers. Adopting a stratified random sampling technique, the study uses primary data collected from 506 SMEs in Ghana to test 4 hypothesised paths.

First, the model result indicates that training accessibility and training content are statistically significant in explaining managerial effectiveness at a 1% level. However, both training efficiency and training frequency are statistically insignificant in explaining managerial effectiveness in Ghana. Second, while the industry category is found to influence the relationship between training and managerial effectiveness, gender, manager's age and education are insignificant in explaining any effects.

Though the sample size is large, the findings from this study could not be generalised to the whole of Ghana since it is regionally based. The study could benefit immensely from a triangulated method where a qualitative dimension could provide deeper insight into some of the findings in this study.

Studies of this nature focussing on the managerial effectiveness of SME managers in the Ghanaian context is rare. This is one of the few studies in the Ghanaian research context which focuses on the capability development approach in the delivery of managerial training to SMEs.

Based on theories related to coopetition, the purpose of this paper is to examine the patterns of business-to-business digital referrals inscribed in businesses’ digital content.

A complete industry-wise digital data set is formed by extracting digital referrals in all the content pages. The authors outline how digital referrals are strategically used among peer businesses in the peer-to-peer digital network and in the augmented digital network, taking into consideration geographical framing and physical distance.

The authors reveal how geographical framing and physical distance influence peer-to-peer referral patterns in the digital space. Quite counter-intuitively, businesses are more likely to give digital referrals for peers residing in the same region, as well as for peers located in closer proximity. Further, results from the augmented digital network show that peer businesses in closer proximity exhibit greater strategic similarity in their digital referring strategy.

The findings extend the understanding of business-to-business coopetition to the digital space and suggest that geographical framing and physical distance can induce reciprocated relationships between peers by offering each other digital referrals.

The findings shed light on the formation of a business-to-business digital coopetition strategy using digital referral marketing.

This study highlights the impact of digital referrals in business-to-business relationship management, especially in the digital coopetition context.