We study the long-time asymptotics for the solution of the modified Camassa–Holm (mCH) equation with step-like initial data.

\begin{align*} &m_{t}+\left (m\left (u^{2}-u_{x}^{2}\right )\right )_{x}=0, \quad m=u-u_{xx}, \\[3pt] & {u(x,0)=u_0(x)\to \left \{ \begin{array}{l@{\quad}l} 1/c_+, &\ x\to +\infty, \\[3pt] 1/c_-, &\ x\to -\infty, \end{array}\right .} \end{align*}

$c_+$

$c_-$

$(y,t)$

$(\xi, c)$

$c=c_+/c_-$

$\{ (\xi, c)\,:\, \xi \in \mathbb{R}, \ c\gt 0, \ \xi =y/t\}$

$u(y,t)$

$\mathcal{O}(t^{-2})$

$\mathcal{O}(t^{-1})$

Rhopalosiphum padi is an important grain pest, causing severe losses during crop production. As a systemic insecticide, flonicamid can control piercing-sucking pests efficiently. In our study, the lethal effects of flonicamid on the biological traits of R. padi were investigated via a life table approach. Flonicamid is highly efficiently toxic to R. padi, with an LC50 of 9.068 mg L−1. The adult longevity and fecundity of the R. padi F0 generation were markedly reduced under the LC25 and LC50 concentrations of flonicamid exposure. In addition, negative transgenerational effects on R. padi were observed under exposure to lethal concentrations of flonicamid, with noticeable decreases in the reproductive period, adult longevity, total longevity, and total fecundity of the F1 generation under the LC25 concentration of flonicamid. Furthermore, the third nymph stage (N3), preadult stage, duration of the adult pre-reproductive period, duration of the total pre-reproductive period, reproductive period, adult longevity, total longevity, and total fecundity of the F1 generation were significantly lower under treatment with the LC50 concentration of flonicamid. The life table parameters were subsequently analysed, revealing that the intrinsic rate of increase (rm) and the net reproductive rate (R0) were significantly lower but that the finite rate of increase (λ) and the mean generation time (T) were not significantly different under the LC25 and LC50 concentrations of flonicamid. These data are beneficial for grain aphid control and are critical for exploring the role of flonicamid in the integrated management of this key pest.

Traditional bulky and complex control devices such as remote control and ground station cannot meet the requirement of fast and flexible control of unmanned aerial vehicles (UAVs) in complex environments. Therefore, a data glove based on multi-sensor fusion is designed in this paper. In order to achieve the goal of gesture control of UAVs, the method can accurately recognize various gestures and convert them into corresponding UAV control commands. First, the wireless data glove fuses flexible fiber optic sensors and inertial sensors to construct a gesture dataset. Then, the trained neural network model is deployed to the STM32 microcontroller-based data glove for real-time gesture recognition, in which the convolutional neural network-Attention mechanism (CNN-Attention) network is used for static gesture recognition, and the convolutional neural network-bidirectional long and short-term memory (CNN-Bi-LSTM) network is used for dynamic gesture recognition. Finally, the gestures are converted into control commands and sent to the vehicle terminal to control the UAV. Through the UAV simulation test on the simulation platform, the average recognition accuracy of 32 static gestures reaches 99.7%, and the average recognition accuracy of 13 dynamic gestures reaches 99.9%, which indicates that the system’s gesture recognition effect is perfect. The task test in the scene constructed in the real environment shows that the UAV can respond to the gestures quickly, and the method proposed in this paper can realize the real-time stable control of the UAV on the terminal side.

The model-implied instrumental variable (MIIV) estimator is an equation-by-equation estimator of structural equation models that is more robust to structural misspecifications than full information estimators. Previous studies have concentrated on endogenous variables that are all continuous (MIIV-2SLS) or all ordinal. We develop a unified MIIV approach that applies to a mixture of binary, ordinal, censored, or continuous endogenous observed variables. We include estimates of factor loadings, regression coefficients, variances, and covariances along with their asymptotic standard errors. In addition, we create new goodness of fit tests of the model and overidentification tests of single equations. Our simulation study shows that the proposed MIIV approach is more robust to structural misspecifications than diagonally weighted least squares (DWLS) and that both the goodness of fit model tests and the overidentification equations tests can detect structural misspecifications. We also find that the bias in asymptotic standard errors for the MIIV estimators of factor loadings and regression coefficients are often lower than the DWLS ones, though the differences are small in large samples. Our analysis shows that scaling indicators with low reliability can adversely affect the MIIV estimators. Also, using a small subset of MIIVs reduces small sample bias of coefficient estimates, but can lower the power of overidentification tests of equations.

The problem of penalized maximum likelihood (PML) for an exploratory factor analysis (EFA) model is studied in this paper. An EFA model is typically estimated using maximum likelihood and then the estimated loading matrix is rotated to obtain a sparse representation. Penalized maximum likelihood simultaneously fits the EFA model and produces a sparse loading matrix. To overcome some of the computational drawbacks of PML, an approximation to PML is proposed in this paper. It is further applied to an empirical dataset for illustration. A simulation study shows that the approximation naturally produces a sparse loading matrix and more accurately estimates the factor loadings and the covariance matrix, in the sense of having a lower mean squared error than factor rotations, under various conditions.

Asymptotic robustness against misspecification of the underlying distribution for the polychoric correlation estimation is studied. The asymptotic normality of the pseudo-maximum likelihood estimator is derived using the two-step estimation procedure. The t distribution assumption and the skew-normal distribution assumption are used as alternatives to the normal distribution assumption in a numerical study. The numerical results show that the underlying normal distribution can be substantially biased, even though skewness and kurtosis are not large. The skew-normal assumption generally produces a lower bias than the normal assumption. Thus, it is worth using a non-normal distributional assumption if the normal assumption is dubious.

Fiber Bragg grating-based Raman oscillators are capable of achieving targeted frequency conversion and brightness enhancement through the provision of gain via stimulated Raman scattering across a broad gain spectrum. This capability renders them an exemplary solution for the acquisition of high-brightness, specialized-wavelength lasers. Nonetheless, the output power of all-fiber Raman oscillators is typically limited to several hundred watts, primarily due to limitations in injectable pump power and the influence of higher-order Raman effects, which is inadequate for certain application demands. In this study, we introduce an innovative approach by employing a graded-index fiber with a core diameter of up to 150 μm as the Raman gain medium. This strategy not only enhances the injectable pump power but also mitigates higher-order Raman effects. Consequently, we have successfully attained an output power of 1780 W for the all-fiber Raman laser at 1130 nm, representing the highest output power in Raman fiber oscillators with any configuration reported to date.