Constructing the Lyapunov Function through Solving Positive Dimensional Polynomial System

We propose an approach for constructing Lyapunov function in quadratic form of a differential system. First, positive polynomial system is obtained via the local property of the Lyapunov function as well as its derivative. Then, the positive polynomial system is converted into an equation system by adding some variables. Finally, numerical technique is applied to solve the equation system. Some experiments show the efficiency of our new algorithm

Sciences for The 2.5-meter Wide Field Survey Telescope (WFST)

The Wide Field Survey Telescope (WFST) is a dedicated photometric survey facility under construction jointly by the University of Science and Technology of China and Purple Mountain Observatory. It is equipped with a primary mirror of 2.5m in diameter, an active optical system, and a mosaic CCD camera of 0.73 Gpix on the main focus plane to achieve high-quality imaging over a field of view of 6.5 square degrees. The installation of WFST in the Lenghu observing site is planned to happen in the summer of 2023, and the operation is scheduled to commence within three months afterward. WFST will scan the northern sky in four optical bands (u, g, r, and i) at cadences from hourly/daily to semi-weekly in the deep high-cadence survey (DHS) and the wide field survey (WFS) programs, respectively. WFS reaches a depth of 22.27, 23.32, 22.84, and 22.31 in AB magnitudes in a nominal 30-second exposure in the four bands during a photometric night, respectively, enabling us to search tremendous amount of transients in the low-z universe and systematically investigate the variability of Galactic and extragalactic objects. Intranight 90s exposures as deep as 23 and 24 mag in u and g bands via DHS provide a unique opportunity to facilitate explorations of energetic transients in demand for high sensitivity, including the electromagnetic counterparts of gravitational-wave events detected by the second/third-generation GW detectors, supernovae within a few hours of their explosions, tidal disruption events and luminous fast optical transients even beyond a redshift of 1. Meanwhile, the final 6-year co-added images, anticipated to reach g about 25.5 mag in WFS or even deeper by 1.5 mag in DHS, will be of significant value to general Galactic and extragalactic sciences. The highly uniform legacy surveys of WFST will also serve as an indispensable complement to those of LSST which monitors the southern sky.Comment: 46 pages, submitted to SCMP

High-emitting vehicle identification by on-road emission remote sensing with scarce positive labels

On-road emission remote sensing (OERS) is an ideal means to identify the on-road high-emitting vehicles, which can scan thousands of vehicles within a day without interfering the normal driving. Due to the complex and varying measuring environments and vehicular operating states, it is reasonable to determine the high-emitters not only by the OERS-output pollutant concentration, but also the other information, such as meteorological and vehicular conditions. This paper aims to establish a high-emitter identification model by machine learning technologies to combine the OERS outputs and periodic emission inspection results. The periodic emission inspection, which is conducted in vehicular inspection stations (VIS), is relatively accurate since the measuring environments and vehicular operating states are controllable, and thereby the periodic emission inspection results are considered as the truth values (or labels). However, VIS is extremely inefficient compared with OERS, thus resulting in scarce labels. Moreover, due to some practical issues, such as staff cheating, only the positive labels (high-emitters) are reliable. Therefore, this paper studies the possibility of employing the one-class classification and graph-based label propagation to solve the problem of scarce positive labels. The experimental results show that the high-emitter identification model based on one-class classification can achieve satisfactory performance, which could be further improved by the application of graph-based label propagation

Price strategy of community fresh food e-commerce considering the heterogeneous needs of consumers and fresh quality transparency

High online operating costs and low consumer utility still need to be addressed in the sales of community fresh e-commerce. Herein, we develop a new community fresh marketing model composed of retailers for online operating costs and consumers for low consumer utility by dividing community consumers into essential type and expectant type in this study. Then, the profit functions of community fresh retailers are developed in this study according to utility theory. Finally, a revised model of the fresh quality transparency (FQT) factor is conducted and discussed in this study. The results suggest that the profits obtained from essential consumers and expectant consumers by the community fresh e-commerce retailers are higher within a certain range of freshness costs compared to the basic model’s projection; meanwhile, the profits from expectant consumers contribute more than those from essential consumers. However, if the freshness cost exceeds a certain critical value, the abovementioned profits predicted from the new model will be lower. This study enriches the supply chain theory of community fresh food and provides retailers with theoretical guidance on differentiated services and pricing to better match the needs of community consumers