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The impedance compensation approaches have been adopted to achieve the maximum output power and transfer efficiency in many magnetic coupling resonance wireless power transfer projects. However, it remains a challenge to obtain the constant output power and transfer efficiency in a fixed-frequency mode during variations in transfer distance and orientation of the coils. In this paper, using two series transmitting coils to achieve the constant output power and transfer efficiency is used.

First, the circuit model is established and transfer characteristics are studied. Second, using the two series transmitting coils to achieve the constant output power and transfer efficiency is investigated. Finally, the experimental system is designed; it can optimize the transfer performances by itself; the constant output power and transfer efficiency are achieved in the fixed-frequency mode.

When the receiving coil moves between the two series transmitting coils, the tolerance of the output power and transfer efficiency is less than 5 per cent.

When a receiving coil is placed between the two series transmitting coils, there are space limits. The receiving coil only shifts between the two transmitting coils.

However, the rail guide vehicle may achieve constant output power and transfer efficiency when it moves on the rail guide. So, this topology may provide a practical solution.

In this research, the three-coil MCR-WPT system including two series transmitting coils is presented. In a fixed-frequency mode, the constant output power and transfer efficiency is achieved in experiments during variations in transfer distance and orientation of the coils. The fluctuation of the output power and transfer efficiency is less than 5 per cent.

The purpose of this paper is to study the wireless power transfer (WPT) system that always achieves the maximum output power at a fixed angular frequency using the dynamic impedance compensation and also the maximum transfer efficiency.

An efficient topology of the WPT system is proposed which states that the functions of the relay are transformed into the functions of the compensator in the three-coil WPT system.

Increasing the ratio of the frequency detuning factor of the compensator relative to the frequency detuning factor of the compensator also causes the curves of the normalized output power and the transfer efficiency to move toward the high frequency direction.

The scheme of the dynamic compensation for the WPT using a compensator is convenient to obtain the dynamic impedance compensation by adding or removing the capacitances or inductances from the compensator.

The functions of the relay are transformed into the functions of the compensator in the three-coil WPT system.

This paper aims to find an approach that achieves constant output power and transfer efficiency in an open space, such as charging pads.

In this study, a topology of the five-coil system including two transmitting coils is presented. Also, in a fixed-frequency mode and an open space, this study focuses on the two transmitting coils to achieve the uniform magnetic field and ultimately, attain the constant output power and transfer efficiency.

In a fixed-frequency mode and an open space, the constant output power and transfer efficiency is then achieved in experiments by inserting the relay loop into the uniform magnetic field.

An approach that achieves constant output power and transfer efficiency in an open space. The topology of the five-coil magnetically coupled resonant-wireless power transfer (MCR-WPT) system shows prospective value for various applications, which could be used at designing of wireless battery charger dedicated for cars or mobile phones.

By comparing the simulation and experimental results, the topology can be optimized in the transmission performance by itself. By doing so, the constant output power and transfer ef?ciency are achieved in the constant frequency mode.

This study focused on parents' health anxiety by proxy about their children when they started learning online during the COVID-19 pandemic, to explore the impact of academic stress by parent-proxy on parents' learning support services with the mediating role of health anxiety by parent-proxy and the moderating role of parental educational level.

In total, 8,940 primary school students' parents participated in the study. Bootstrapping was performed to test the constructed model.

(1) Academic stress by parent-proxy positively predicted health anxiety by parent-proxy. (2) Health anxiety by parent-proxy significantly positively predicted learning support services. (3) Academic stress by parent-proxy also significantly positively predicted learning support services. (4) Academic stress by parent-proxy positively predicted parents' learning support services through the mediating effect of health anxiety by parent-proxy. (5) Parental educational level moderated the relationship between academic stress by parent-proxy, health anxiety by parent-proxy, and learning support services. Academics and parents will benefit from the conclusions of this study in both theory and practice.

During the COVID-19 pandemic, offline learning has been replaced with online learning, which has brought with it many physical and mental health problems, including additional academic stress. Most studies on learning support services have focused on offline learning. However, this study explored the relationships between academic stress by parent-proxy, health anxiety by parent-proxy, learning support services, and parental educational level in the context of online learning. Results show that it is necessary to pay attention to academic stress and health to provide children with appropriate learning support services.