A stationary point theorem characterizing metric completeness
We give a stationary point theorem for some set-valued mappings on a metric space. The existence of fixed points of such mappings characterizes the metric completeness. Our result easily yields the order-theoretic Cantor theorem of Granas and Horvath, and the famous Ekeland variational principle.
EKELAND'S VARIATIONAL PRINCIPLE FOR SET-VALUED MAPS WITH APPLICATIONS TO VECTOR OPTIMIZATION IN UNIFORM SPACES
In this paper, we introduce the concept of a weak $q$-distance and for this distance we derive a set-valued version of Ekeland's variational principle in the setting of uniform spaces. By using this principle, we prove the existence of solutions to a vector optimization problem with a set-valued map. Moreover, we define the $(p,\varepsilon)$-condition of Takahashi and the $(p,\varepsilon)$-condition of Hamel for a set-valued map. It is shown that these two conditions are equivalent. As an application, we discuss the relationship between an $\varepsilon$-approximate solution and a solution of a vector optimization problem with a set-valued map. Also, a well-posedness result for a vector optimization problem with a set-valued map is given.
The Analysis on Fire Smoke Exhausting Robot Vibration Based on Wavelet Transform
Belt relaxation, which affects a lot on operation reliability of the fire smoke exhausting robot, is hard to detect. In this paper, a new method for belt relaxation feature recognition based on continuous wavelet transform (CWT) is proposed, and a vibration model which simplified the robot as a 2-dof forced vibration system under harmonic excitation is established. The vibration acceleration signal has been collected using the IEPE sensor and data acquisition card, experimental results verified the accuracy of the vibration model, and weak impact signal caused by the belt relaxation was distinguished, that testify the practicability of the CWT method in belt relaxation feature recognition.