Missed detection probability is a critical metric for the integrity performance of receiver autonomous integrity monitoring (RAIM) in the presence of faults. The traditional missed detection probability evaluation method for RAIM is limited by impractical time consumption because of the absence of accurate searching interval for the magnitude of a worst-case fault. To address this issue, the searching interval for the magnitude of a worst-case fault is constructed by the combination of minimum detectable magnitude and minimum hazardous magnitude, and the searching interval adjustment is designed to avoid the absence of worst-case fault magnitude so that the maximum missed detection probability can be accurately evaluated. The simulation result indicates that the proposed method can achieve higher accuracy for the worst-case fault magnitude searching. Furthermore, the accuracy of worldwide evaluated missed detection rate can achieve an improvement of 57·66% at most by the proposed method for the different classical RAIM algorithms.

For a wide range of insect species, the microbiota has potential roles in determining host developmental programme, immunity and reproductive biology. The tea geometrid moths Ectropis obliqua and E. grisescens are two closely related species that mainly feed on tea leaves. Although they can mate, infertile hybrids are produced. Therefore, these species provide a pair of model species for studying the molecular mechanisms of microbiotal involvement in host reproductive biology. In this study, we first identified and compared the compositions of microbiota between these sibling species, revealing higher microbiotal diversity for E. grisescens. The microbiota of E. obliqua mainly comprised the phyla Firmicutes, Proteobacteria and Cyanobacteria, whereas that of E. grisescens was dominated by Proteobacteria, Actinobacteria and Firmicutes. At the genus level, the dominant microbiota of E. grisescens included Wolbachia, Enterobacter and Pseudomonas and that of E. obliqua included Melissococcus, Staphylococcus and Enterobacter. Furthermore, we verified the rate of Wolbachia to infect 80 samples from eight different geographical populations, and the results supported that only E. grisescens harboured Wolbachia. Taken together, our findings indicate significantly different microbiotal compositions for E. obliqua and E. grisescens, with Wolbachia possibly being a curial factor influencing the reproductive isolation of these species. This study provides new insight into the mechanisms by which endosymbiotic bacteria, particularly Wolbachia, interact with sibling species.

In this paper, we consider a two-point boundary value problem with Caputo fractional derivative, where the second order derivative of the exact solution is unbounded. Based on the equivalent form of the main equation, a finite difference scheme is derived. The L∞ convergence of the difference system is discussed rigorously. The convergence rate in general improves previous results. Numerical examples are provided to demonstrate the theoretical results.

Mechanisms of herbicide resistance were studied in a quizalofop–ethyl-resistant barnyardgrass biotype. Acetyl-coenzyme A carboxylase (ACCase) sensitivity to quizalofop-p-ethyl was measured by high-performance liquid chromatography and the trend in ACCase gene expression over time was determined using real-time polymerase chain reaction. The results showed that an insensitive ACCase was present in Geqiushan resistant plants (R), with a resistance index of 106. The basal ACCase activities in Geqiushan R and Geqiushan susceptible plants (S) were similar, at 1.20 and 1.17 ng malonyl-CoA min−1 µg−1 extract protein, respectively. Basal ACCase gene expression in Geqiushan R was similar to that in Geqiushan S. The relative expression of ACCase gene decreased after spraying quizalofop–ethyl at 60 g ai ha−1 in Geqiushan S, whereas it was almost not changed in Geqiushan R. From these results we concluded that plastid ACCase sensitivity change might be responsible for the resistance and gene overexpression does not play a role in this resistance.

A compact finite difference scheme is derived for a time fractional differential equation subject to Neumann boundary conditions. The proposed scheme is second-order accurate in time and fourth-order accurate in space. In addition, a high order alternating direction implicit (ADI) scheme is also constructed for the two-dimensional case. The stability and convergence of the schemes are analysed using their matrix forms.

In this paper, we study a high-order compact difference scheme for the fourth-order fractional subdiffusion system. We consider the situation in which the unknown function and its first-order derivative are given at the boundary. The scheme is shown to have high order convergence. Numerical examples are given to verify the theoretical results.

We observed with the Submillimeter Array and IRAM 30 m telescope three high-mass star-forming regions in different evolutionary stages in the W3 high-mass star formation complex. These regions, i.e. W3 SMS1 (W3 IRS5), SMS2 (W3 IRS4) and SMS3, are located within the same large-scale environment, which allows us to study rotation and outflows as well as chemical properties in an evolutionary sense. While we find multiple mm continuum sources toward all regions, these three subregions exhibit different dynamical and chemical properties, which indicates that they are in different evolutionary stages. Even within each sub-region, massive cores of different ages are found, e.g. in SMS2, sub-sources from the most evolved UCHii region to potential starless cores exist within 30 000 AU (left panel, Fig. 1). Outflows and rotational structures are found in SMS1 and SMS2. Evidence for interactions between the molecular cloud and the HII regions is found in the 13CO channel maps (right panel, Fig. 1), which may indicate triggered star formation.