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The purpose of this paper is to investigate how leader humility affects the engagement of employees in creative processes, using perceived organizational support (POS) as a mediator and leader competence as a moderator.

Data were collected from a two-wave sampling of 113 dyads of leaders and subordinates in China.

A curvilinear relationship was found between leader humility and employee engagement in creative processes. Further, POS partially mediates this relationship, and leader competence positively moderates the relationship between leader humility and POS.

First, organizations should select and train leaders who show humility as a character trait and foster a supportive organizational climate. Second, managers should study the benefits of moderate and harms of superfluous humility, especially in the Chinese cultural context. Third, competent leaders are more effective as humble leaders.

Few studies have concentrated on leader humility in the eastern cultural context. The results challenge traditional views of the impact of leader humility and shed light on its mechanism and the conditions under which it promotes employee engagement in creation. This study also clarifies the nonlinear influence of leader humility, building a fine-grained theoretical framework integrating the motivation-opportunities-abilities model and Chinese Zhong-Yong theory.

With the rapid advancement in the automotive industry, the friction coefficient (FC), wear rate (WR) and weight loss (WL) have emerged as crucial parameters to measure the performance of automotive braking systems, so the FC, WR and WL of friction material are predicted and analyzed in this work, with an aim of achieving accurate prediction of friction material properties.

Genetic algorithm support vector machine (GA-SVM) model is obtained by applying GA to optimize the SVM in this work, thus establishing a prediction model for friction material properties and achieving the predictive and comparative analysis of friction material properties. The process parameters are analyzed by using response surface methodology (RSM) and GA-RSM to determine them for optimal friction performance.

The results indicate that the GA-SVM prediction model has the smallest error for FC, WR and WL, showing that it owns excellent prediction accuracy. The predicted values obtained by response surface analysis are closed to those of GA-SVM model, providing further evidence of the validity and the rationality of the established prediction model.

The relevant results can serve as a valuable theoretical foundation for the preparation of friction material in engineering practice.

This paper aims to study the transient flow characteristics in a mixed-flow pump during the start-up period.

In this study, numerical calculation of the internal flow field in a mixed-flow pump using the sliding mesh method was carried out. The regulation of the pressure, streamline and the relative speed during the start-up period was analyzed.

The trend of the simulated head is consistent with the experimental results, and the calculated head is around 0.3 m higher than the experimental head when the rotation speed reached the stable stage, indicating that the numerical method for the start-up process simulation of the mixed-flow pump has a high accuracy. At the beginning, the velocity inside the impeller changes little along the radius direction and the flow rate increases slowly during the start-up process. As the rotation speed reached the stable stage, the flow inside the impeller became steady, the vortex reduced and transient effects disappeared gradually.

The study results have significant value for revealing the internal unsteady flow characteristics of the mixed-flow pump and providing the reference for the design optimization of the mixed-flow pump.

The purpose of this paper is to experimentally and numerically study the transient hydraulic impact and overall performance during startup accelerating process of mixed-flow pump.

In this study, the impeller rotor vibration characteristics during the starting period under the action of fluid–structure interaction was investigated, which is based on the bidirectional synchronization cooperative solving method for the flow field and impeller structural response of the mixed-flow pump. Experimental transient external characteristic and the transient dimensionless head results were compared with the numerical calculation results, to validate the accuracy of numerical calculation method. Besides, the deformation and dynamic stress distribution of the blade under the stable rotating speed and accelerating condition were studied based on the bidirectional fluid–structure interaction.

The results show that the combined action of complex hydrodynamic environment and impeller centrifugal force in the startup accelerating process makes the deformation and dynamic stress of blade have the rising trend of reciprocating oscillation. At the end of acceleration, the stress and strain appear as transient peak values and the transient effect is nonignorable. The starting acceleration has a great impact on the deformation and dynamic stress of blade, and the maximum deformation near the rim of impeller outlet edge increases 5 per cent above the stable condition. The maximum stress value increases by about 68.7 per cent more than the steady-state condition at the impeller outlet edge near the hub. The quick change of rotating speed makes the vibration problem around the blade tip area more serious, and then it takes the excessive stress concentration and destruction at the blade root.

This study provides basis and reference for the safety operation of pumps during starting period

This paper aims to apply fractional variational iteration method using He's polynomials (FVIMHP) to obtain exact solutions for variable-coefficient fractional heat-like and wave-like equations with fractional order initial and boundary conditions.

The approach is based on FVIMHP. The authors choose as some examples to illustrate the validity and the advantages of the method.

The results reveal that the FVIMHP method provides a very effective, convenient and powerful mathematical tool for solving fractional differential equations.

The variable-coefficient fractional heat-like and wave-like equations with fractional order initial and boundary conditions are solved first. Illustrative examples are included to demonstrate the validity and applicability of the method.

This paper applies a volume-price probability wave differential equation to propose a conceptual theory and has innovative behavioral interpretations of intraday dynamic market equilibrium price, in which traders' momentum, reversal and interactive behaviors play roles.

The authors select intraday cumulative trading volume distribution over price as revealed preferences. An equilibrium price is a price at which the corresponding cumulative trading volume achieves the maximum value. Based on the existence of the equilibrium in social finance, the authors propose a testable interacting traders' preference hypothesis without imposing the invariance criterion of rational choices. Interactively coherent preferences signify the choices subject to interactive invariance over price.

The authors find that interactive trading choices generate a constant frequency over price and intraday dynamic market equilibrium in a tug-of-war between momentum and reversal traders. The authors explain the market equilibrium through interactive, momentum and reversal traders. The intelligent interactive trading preferences are coherent and account for local dynamic market equilibrium, holistic dynamic market disequilibrium and the nonlinear and non-monotone V-shaped probability of selling over profit (BH curves).

The authors will understand investors' behaviors and dynamic markets through more empirical execution in the future, suggesting a unified theory available in social finance.

The authors can apply the subjects' intelligent behaviors to artificial intelligence (AI), deep learning and financial technology.

Understanding the behavior of interacting individuals or units will help social risk management beyond the frontiers of the financial market, such as governance in an organization, social violence in a country and COVID-19 pandemics worldwide.

It uncovers subjects' intelligent interactively trading behaviors.

The purpose of this paper is to develop a fully discrete local discontinuous Galerkin (LDG) finite element method for solving a time‐fractional advection‐diffusion equation.

The method is based on a finite difference scheme in time and local discontinuous Galerkin methods in space.

By choosing the numerical fluxes carefully the authors' scheme is proved to be unconditionally stable and gets L² error estimates of O(h^k+1+(Δt)²+(Δt)^α/2h^k+(1/2)). Finally Numerical examples are performed to illustrate the effectiveness and the accuracy of the method.

The proposed method is different from the traditional LDG method, which discretes an equation in spatial direction and couples an ordinary differential equation (ODE) solver, such as Runger‐Kutta method. This fully discrete scheme is based on a finite difference method in time and local discontinuous Galerkin methods in space. Numerical examples prove that the authors' method is very effective. The present paper is the authors' first step towards an effective approach based on the discontinuous Galerkin method for the solution of fractional‐order problems.

The main goal of the physical education (PE) environment is that each individual trained should achieve self-fulfillment with the large group of students involved with their own efforts. Deep learning is applying transferrable knowledge in new situations to help the students master in tough circumstances. In PE training, injuries occur when working together as a team. Safety measures are taken immediately as an emergency response to reduce the potential risk in students by providing first aid. To provide safety measures for the injured student immediately, the environment is monitored in real-time using a GPS.

Theory of Humanities Education (ToHE) infers that it has less collection of theories and a wide range of applications than the state-of-the-art systems. ToHE allows students to think creatively and play a vital role in one’s health which is a critical aspect in PE. The ToHE theory focuses on two main concepts, i.e. by using a methodological approach to analyse and deep learning to solve the problem. PE motivates college students to follow a healthy and active lifestyle.

The proposed system is deployed in real time for monitoring the student’s performance and provides an emergency response with an accuracy rate of 90%.

The deep learning offers solutions to the injuries by using the deep convolutional neural network to provide interpretability of the consequence by training it with various injuries that occur in the playground and inappropriate use of sports equipment. A case study provided in this paper outlines an emergency response scenario to an injured student in sports training.

In this article, the authors aim to present the homotopy analysis method (HAM) for obtaining the approximate solutions of space‐time fractional differential equations with initial conditions.

The series solution is developed and the recurrence relations are given explicitly. The initial approximation can be determined by imposing the initial conditions.

The comparison of the HAM results with the exact solutions is made; the results reveal that the HAM is very effective and simple. The HAM contains the auxiliary parameter h, which provides a simple way to adjust and control the convergence region of series solution. Numerical examples demonstrate the effect of changing homotopy auxiliary parameter h on the convergence of the approximate solution. Also, they illustrate the effect of the fractional derivative orders a and b on the solution behavior.

The idea can be used to find the numerical solutions of other fractional differential equations.

The purpose of this study is to explore the transient characteristics of mixed-flow pumps during startup process.

This study uses a full-flow field transient calculation method of mixed-flow pump based on a closed-loop model.

The findings show the hydraulic losses and internal flow characteristics of the piping system during the start-up process.

Large computational cost.

Improve the accuracy of current numerical simulation results in transient process of mixed-flow pump.

Simplify the setting of boundary conditions in the transient calculation.