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The purpose of this paper is to analyze the characteristics of the factors influencing the effect of magnetic levitation, including the impedance angle of the levitated coil, number of turns, material parameter, frequency of excitation and geometric parameters. The final purpose is to provide approaches to increasing the levitation effect.

Some design principles and strategies for levitation systems are suggested, such as selecting the number of turns of the levitated coil, choosing the frequency of excitation considering the saturation phenomenon of levitation force against frequency and deciding the section area of the excitation coil and its ratio of height and thickness.

The magnetic force is not always repulsive in a cycle. Therefore, the key approach to increasing the levitation is to increase the period when the force is repulsive and decrease the time when attractive. The impedance angle of the equivalent circuit of the levitated coil determines the ratio of the two periods, and the larger the angle, the longer the repulsion period. A valuable finding is that a saturation situation exists between the levitation force and frequency; that is, when the frequency increases to a certain value, the increasing degree of force tends to decrease as the frequency increases.

Some influential characteristics were found in some factors against the effect of the levitation system, which is beneficial for improving the efficiency of systems. For example, owing to the saturation phenomenon of the frequency, it is useless to continue increasing the frequency and the copper-levitated coil does not bring much greater force effectiveness than the aluminum coil.

The purpose of this study is to elucidate the size effect (groove width, unit length and area density) of the hexagonal texture on tribological properties under lubrication.

The tribological properties of nine hexagonal textures with different hexagon lengths and groove widths have been investigated under mixed lubrication to elucidate the size effect.

Overall, the friction coefficient decreases as the groove width increases within the examined range, whereas the hexagon length shows an optimal value around 3 mm. In particular, one hexagonal texture (3 × 3 mm) exhibits lower friction coefficients and less wear losses than the others. Interestingly, two hexagonal textures of similar area density (1 × 1 mm and 3 × 3 mm) yield the worst and best tribological performances, respectively, which can be explained by the simulated distribution of equivalent stress.

The tribological properties of nine hexagonal textures are examined under lubrication. The 3 × 3 texture exhibits lower friction coefficient and wear loss than the others. Two textures of similar area density yield the worst and best tribological performances. The results agree with the simulated distribution of equivalent stress.

The effective and efficient motivation of the sales personnel affects the sales of a firm directly. The aim of this paper is to study the incentive effects of different compensation contracts under the framework of multi‐agent principal agent model, and it finds that the optimal contract is not the one that ties one salesperson's compensation to his own performance, but the one that ties his compensation to all the salespersons' performance. Factors that influence the incentive degree are also discussed. The purpose of this article is to design a reasonable incentive contract for salespersons where there are competitions between them.

A multi‐agent model where the efforts of one agent harm the performance of the other agent is established.

The optimal compensation of a salesperson is always composed of two parts: an incentive for an agent to improve his own performance and a disincentive for the agent to harm his colleague's performance, provided that there is a competition relationship between the two agents.

This model applies only to the rewards incentive of multi‐agents with competitive relationships.

The conclusion could be used anywhere when there are two agents with one's behavior harming the other's performance.

A multi‐agent model where the efforts of one agent harm the performance of the other agent is established to study the compensation design problems for agents.