In this study, an ultrasonic temperature measurement system was designed with Al₂O₃ high-temperature ceramic as an acoustic waveguide sensor and preliminarily tested in a high-temperature oxidation environment. The test results indicated that the system can indeed work stably in high-temperature environments. The relationship between the temperature and delay time of 26 °C–1600 °C ceramic materials was also determined in order to fully elucidate the high-temperature oxidation of the proposed waveguide sensor and to lay a foundation for the further application of this system in temperatures as high as 2000 °C.

In this work, we study the kth local base, which is a generalization of the base, of a primitive non-powerful nearly reducible sign pattern of order n ≥ 7. We obtain the sharp bound together with a complete characterization of the equality case, of the kth local bases for primitive non-powerful nearly reducible sign patterns. We also show that there exist “gaps” in the kth local base set of primitive non-powerful nearly reducible sign patterns.