An optimal $ Z $-eigenvalue inclusion interval for a sixth-order tensor and its an application

<abstract><p>An optimal $ Z $-eigenvalue inclusion interval for a sixth-order tensor is presented. As an application, a sufficient condition for the positive definiteness of a sixth-order real symmetric tensor (also a homogeneous polynomial form) is obtained, which is used to judge the asymptotically stability of time-invariant polynomial systems.</p></abstract>

Analysis of measurement uncertainty of a surface acoustic wave micro-pressure sensor

As an important support for test and control projects, sensor’s performance is directly related to the accuracy of the measurement. To fully analyze the sources of measurement uncertainty for a surface acoustic wave micro-pressure sensor, in this study the Monte Carlo method and Guide to the Expression of Uncertainty in Measurement to evaluate measurement uncertainty of sensors are used, the sensing experiment was conducted and the measurement addition model was established. We determined the source of measurement uncertainty for a surface acoustic wave micro-pressure sensor. The results show that the Monte Carlo method can obtain a more reliable and accurate inclusion interval in the measurement uncertainty evaluation of a surface acoustic wave micro-pressure sensor.

A Note on Inclusion Intervals of Matrix Singular Values

We establish an inclusion relation between two known inclusion intervals of matrix singular values in some special case. In addition, based on the use of positive scale vectors, a known inclusion interval of matrix singular values is also improved.