In this paper, the mathematical model of a kind of two-robot security system with an early warning function is studied. By using strongly continuous operator semigroup theory and Volterra integral equation theory, the properties of the semigroup of the system operator, the existence and uniqueness of nonnegative solution, and the well-posedness of solution are discussed, respectively. Under the assumption that the failure rate and repair rate of the system are constants, the equations of the robot system are transformed into an ordinary differential equation group, and then the instantaneous reliability and stable-state reliability of the system are obtained. The reliability and zero-state controllability of the system are proved. Finally, the numerical solution of the system model is obtained by using MATLAB mathematical software, and the corresponding numerical simulation diagram is given. The results show that the conclusions of numerical calculation and numerical simulation are in accordance with the results of reliability theory, thereby the reliability of the robot safety system is verified.
This paper filters out the sport quality evaluation indicators of taekwondo athletes' special physical stamina through the questionnaire and mathematical statistics method and finally determines the specific evaluation indicator to measure Taekwondo special physical stamina through the process of mathematical statistics. Taking the sport quality indicators of Taekwondo athletes' special physical stamina for example, this paper uses principal component analysis method, evaluates the comprehensive evaluation level of each sport quality indicator of taekwondo athletes' special physical stamina, determines the importance and weight of each indicator, establishes the indicator evaluation criteria of Taekwondo Athletes' sport quality, and provides a theoretical basis for the daily training of taekwondo coaches and athletes.
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