Polynomial fault detection filter design under adaptive event-triggered scheme via line-integral Lyapunov functions

This paper investigates the problem of polynomial fault detection filter design under an adaptive event-triggered scheme for continuous-time networked polynomial fuzzy model–based (PFMB) systems considering network transmission delays. The proposed adaptive polynomial event-triggered scheme is checked only at the sampling instant to eliminate the Zeno behavior as well as save the network bandwidth. With the consideration of the mismatched membership functions (MFs), the asynchronous problem between the physical plant and the polynomial fault detection filter (PFDF) is examined. A Lyapunov–Krasovskii (L-K) function is introduced to deal with the time delays caused by the network transmission and the zero-order holder (ZOH), and a proper line-integral Lyapunov function is also introduced to reduce the conservation of the design constraints, whose analytical procedure is rule-dependent. The design constraints are given in the form of sum of squares (SOS) to keep the PFMB fault detection system asymptotically stable with [Formula: see text] performance [Formula: see text]. Finally, an inverted pendulum example together with a numerical example is given to verify the effectiveness and superiority of the proposed scheme in terms of transfer rate and conservatism.

Computational Electromagnetics: A Miscellany

The paper presents a miscellany of unorthodox and, in some cases, paradoxical or controversial items related to computational and applied electromagnetics. The topics include a definition of the magnetic source field via a line integral, losses in electric power transmission vs. losses in photonics, homogenization of periodic electromagnetic structures, spurious modes, models of plasmonic media, and more. It is hoped that this assortment of subjects will be of interest to a broad audience of scientists and engineers.

Soft rational line integral

Soft set theory is a new area of mathematics that deals with uncertainties. Applications of soft set theory are widely spread in various areas of science and social science viz. decision making, computer science, pattern recognition, artificial intelligence, etc. The importance of soft set-theoretical versions of mathematical analysis has been felt in several areas of computer science. This paper suggests some concepts of a soft gradient of a function and a soft integral, an analogue of a line integral in classical analysis. The fundamental properties of soft gradients are established. A necessary and sufficient condition is found so that a set can be a subset of the soft gradient of some function. The inclusion of a soft gradient in a soft integral is proved. Semi-additivity and positive uniformity of a soft integral are established. Estimates are obtained for a soft integral and the size of its segment. Semi-additivity with respect to the upper limit of integration is proved. Moreover, this paper enriches the theoretical development of a soft rational line integral and associated areas for better functionality in terms of computing systems.

The pupillary light reflex (PLR) as a marker for the ability to work or drive – a feasibility study

Background The PLR (pupillary light reflex) can be a marker for pathological medical conditions, such as neurodegenerative or mental health disorders and diseases as well as marker for physiological alterations, such as age, sex or iris color. PLR alterations have been described in people after alcohol consumption, as well. However, the effect of sleep deprivation on PLR parameters is still under debate. Methods The aim of this study was to investigate the feasibility of PLR measurements in sleep-deprived and alcohol-exposed participants. In addition, we wanted to identify PLR parameters that were altered by sleep deprivation and alcohol exposure. Results Altogether n = 50 participants have been included in this study. Differences in the PLR parameters initial diameter (dinit), latency (∆tlat), acceleration (∆ta), contraction velocity (ϑcon), quarter dilatation velocity (ϑ1/4dil), half dilatation time (∆t1/2), and the line integral (L(0.3500)) have been evaluated between baseline, sleep deprivation, as well as alcohol exposure. In a generalized linear mixed models design, we could observe statistically significant associations between the type of exposure and the PLR parameters half dilatation time and half dilatation time after the first light pulse (all p < 0.05). The participants’ latency showed a significant association in dependence of the type of exposure after the second light pulse (p < 0.05). Conclusion Our study delivers first promising results to further develop devices that may identify conditions that impair the ability to work or drive.

None zero circulation of electrostatic field around a partly electrostatic shielded loop

In this article, a loop that is partly electrostatic shielded is analyzed. It is found that the line integral of electrostatic field around this loop is not zero. This is against the theorem that the line integral of electrostatic field around any closed loop is zero and the curl of electrostatic field is zero. When the loop is made of conductor wire, there is no electric current flowing around the loop although the line integral of electric field is not zero. A loop current driven by electrostatic field will break the law of energy conservation, so it is expected and reasonable that we cannot observe a current in the loop.