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For a semilinear parabolic partial differential equation, we consider an asymptotic solution that converges to a traveling wave at large times . The velocity of such a wave is time dependent, and we construct the asymptotics as . We find that the asymptotics contains logarithms and cannot be constructed in the form of a power series.

We discuss estimation of treatment effects when the timing of treatment is the outcome of a stochastic process. We show that the duration framework in discrete time provides a fertile ground for effect evaluations. We suggest easy-to-use nonparametric survival function matching estimators that can be used to estimate the time profile of the treatment.We study the small-sample properties of the proposed estimators and apply one of them to evaluate the effects of an employment subsidy program. We find that the longerrun program effects are positive. The estimated time profile suggests locking-in effects while participating in the program and a significant upward jump in the employment hazard on program completion.

Agricultural scale operations and industrialization promote the transfer of the rural labor force to the industry sector, and the non-farm employment of farmers plays a great role in increasing their income and reducing poverty. It is of great significance to explore the non-farm employment of farmers for the governance of relative poverty and the achievement of common prosperity. The propensity score matching (PSM) and generalized propensity score matching (GPSM) were used to analyze the impact of rural land transfer on farm households’ non-farm employment. According to the PSM estimation, compared to the farmers’ land not transferred, the rural land transfer significantly increased the proportion of non-farm employment personnel in farm households and the months of per year non-farm employment per person. The total land transfer, paddy land transfer and dry land transfer could significantly increase the proportion of non-farm employment personnel in farm households by 0.074, 0.029 and 0.085 units, respectively, and could significantly increase the months of per year non-farm employment per person by 0.604, 0.394 and 0.617 units, respectively. According to the GPSM estimation, different types of rural land transfer areas have significant positive effects on the proportion of non-farm workers and the months of per year non-farm employment per person, and show an obvious increasing trend of returns to scale, that is, the proportion of non-farm workers and the months of per year non-farm employment per person of farmers are higher than the increase in rural land transfer area. Additionally, the return to scale effect of dry land transfer area is more obvious. In order to raise the income of farm households and narrow the gap between urban and rural areas, the land transfer system can be further improved, urbanization with the county town as an important carrier can be vigorously promoted, the participation of farm households in non-farm employment in the local area can be promoted and the support policy system for non-farm employment of rural labor force can be improved.

AbstractThe results obtained by Il’in and his school concerning the asymptotic behavior of solutions to the Cauchy problem for the quasi-linear parabolic equation with a small parameter multiplying the higher order derivative in the vicinity of singular points are presented. The equation under examination is of interest because it provides a model of the propagation of nonlinear waves in dissipative continuous media, and the importance of studying solutions in the vicinity of singular points is explained, in particular, by the fact that even though the singular events take a short time, they in many respects determine the subsequent evolution of the solutions. In this paper, we examine five types of singular points the emergence of which is caused by different initial data.

The method of evaluating the resonant frequencies of multilayered resonator containing uniaxial anisotropic dielectrics is presented. The detailed solution of Maxwell's equations for such a structure by means of the radial modes matching method for TE0mn modes is given. The results of calculations using developed and launched computer program are given. Results of calculations are compared with those obtained by other method using CST simulator. These results are in close agreement, which proves the correctness of the method. The developed solution, and the software program can be used to measure the tensor permittivity of dielectrics.

The method of evaluating the resonant frequencies of multilayered resonator containing demagnetized ferrites is presented. The detailed solution of Maxwell's equations for such a structure by means of the radial modes matching method for TE0mn modes is given. The results of calculations using developed and launched computer program are given. Results of calculations are compared with those obtained by other method using CST simulator. These results are in close agreement, which proves the correctness of the method. The developed solution, and the software program can be used to measure the initial permeability of ferrites.

The potential of augmented reality (AR) technology to assist minimally invasive surgery (MIS) lies in its computational performance and accuracy in dealing with challenging MIS scenes. Even with the latest hardware and software technologies, achieving both real-time and accurate augmented information overlay in MIS is still a formidable task. In this Letter, the authors present a novel real-time AR framework for MIS that achieves interactive geometric aware AR in endoscopic surgery with stereo views. The authors’ framework tracks the movement of the endoscopic camera and simultaneously reconstructs a dense geometric mesh of the MIS scene. The movement of the camera is predicted by minimising the re-projection error to achieve a fast tracking performance, while the three-dimensional mesh is incrementally built by a dense zero mean normalised cross-correlation stereo-matching method to improve the accuracy of the surface reconstruction. The proposed system does not require any prior template or pre-operative scan and can infer the geometric information intra-operatively in real time. With the geometric information available, the proposed AR framework is able to interactively add annotations, localisation of tumours and vessels, and measurement labelling with greater precision and accuracy compared with the state-of-the-art approaches.

Examining covariate balance is the prescribed method for determining the degree to which propensity score methods should be successful at reducing bias. This study assessed the performance of various balance measures, including a proposed balance measure based on the prognostic score (similar to a disease risk score), to determine which balance measures best correlate with bias in the treatment effect estimate. The correlations of multiple common balance measures with bias in the treatment effect estimate produced by weighting by the odds, subclassification on the propensity score, and full matching on the propensity score were calculated. Simulated data were used, based on realistic data settings. Settings included both continuous and binary covariates and continuous covariates only. The absolute standardized mean difference (ASMD) in prognostic scores, the mean ASMD (in covariates), and the mean t-statistic all had high correlations with bias in the effect estimate. Overall, prognostic scores displayed the highest correlations with bias of all the balance measures considered. Prognostic score measure performance was generally not affected by model misspecification, and the prognostic score measure performed well under a variety of scenarios. Researchers should consider using prognostic score–based balance measures for assessing the performance of propensity score methods for reducing bias in nonexperimental studies.

With the increasingly serious aging of our society, labor shortage will seriously hinder the development of social economy. Robots gradually integrate into human production and life, and gradually serve more and more people. In order to solve the problem of large path deviation of the transmission system in the food conveying path, an intelligent food conveying system based on machine vision is proposed. The hardware circuit of the whole system is composed of image acquisition module, power module, electric drive module, etc. in the software part, the vertical volume matching method is used to set the optimal path. Through practical investigation, the scheme is feasible, can rely on the actual intelligence of catering distribution, has good application and promotion value.