Accurate trajectory tracking serves as a core technology for quadrotor unmanned aerial vehicles to perform inspection, mapping, monitoring and low-altitude autonomous flight missions. Affected by underactuated, nonlinear and strongly coupled dynamics, the horizontal motion of quadrotors is realized by adjusting attitudes to change the direction of thrust, while attitude responses are jointly restricted by rotational coupling, inertia parameters and external disturbances. This study adopts three typical trajectory tracking methods, namely proportional-integral-derivative control, sliding mode control and integral backstepping sliding mode control, and constructs a performance evaluation framework from the perspectives of trajectory response, position error, attitude variation and comprehensive error indicators. The results indicate that the three-dimensional root mean square error and maximum three-dimensional error of PID control under periodic trajectories are 0.5836 m and 0.8560 m respectively, which proves that the basic feedback structure presents noticeable deviations in curve tracking. Sliding mode control reduces the maximum three-dimensional error to 0.0509 m, showing excellent capability in limiting error bounds. For integral backstepping sliding mode control, its three-dimensional root mean square error and terminal three-dimensional error are 0.0419 m and 0.0050 m separately. It demonstrates that integral compensation and backstepping sliding mode structure help enhance overall precision and terminal convergence performance. The findings clarify the differences among the three control structures in error suppression, attitude regulation and terminal accuracy, and can provide references for the selection of trajectory tracking controllers for quadrotor unmanned aerial vehicles.

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The Epoch of Reionization was a major change in cosmic history because it altered the ionization state of the gas between galaxies. Before this transition, much of the universe contained neutral hydrogen. That hydrogen did not block every light frequency equally, but for radiation connected to hydrogen transitions, it was a significant obstacle. As the first stars and galaxies formed, their ultraviolet radiation gradually ionized surrounding hydrogen. Over time, the universe moved from a mostly neutral state toward a more ionized and transparent one. The broad sequence is known, but the detailed history is still uncertain: when reionization began, how quickly it advanced, how uneven it was, and which galaxies supplied most of the ionizing radiation remained unanswered. This paper examines Lyman alpha emitters as one way to study that history. Lyman alpha emission is useful because neutral hydrogen in the intergalactic medium affects whether Lyman alpha photons reach observers; changes in Lyman alpha visibility, rest-frame equivalent width, escape fraction, velocity offset, and emitter fraction can help infer how the neutral hydrogen fraction changed over time. Recent James Webb Space Telescope (JWST) Near-Infrared Spectrograph observations from the JWST Advanced Deep Extragalactic Survey (JADES) provide a stronger observational base, while simulations such as THESAN help interpret the final signal after photons pass through galaxies, circumgalactic gas, intergalactic gas, dust, scattering, and cosmic expansion. Lyman alpha emitters are powerful probes of reionization, but not direct measuring sticks. They are most useful when spectroscopy, completeness corrections, model comparisons, and simulations are used together.

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Full-waveform inversion (FWI) adopts the dynamic and kinematic information contained in pre-stack seismic wavefields and fits actual observed seismic data using the wave equation. It can realize high-resolution quantitative imaging of physical property parameters of underground media, with a theoretical imaging accuracy reaching half of the seismic wavelength. Since Tarantola and Lailly established the core theoretical framework in the 1980s, FWI has gradually evolved from two-dimensional acoustic approximate algorithms to a three-dimensional elastic and viscoelastic multi-parameter inversion system, and its application scope has expanded from simple geological structures to complex stratigraphic regions. In recent years, the iteration and upgrading of high-performance computing hardware, the application of deep learning algorithms in geosciences, and the popularization of multi-component and wide-azimuth seismic acquisition equipment have jointly driven FWI into a brand-new development stage. This paper systematically sorts out the theoretical system and classical research methods of FWI, and summarizes the development context of core technologies including multi-scale inversion, objective function construction, initial model establishment and computational efficiency optimization. Meanwhile, it concludes the latest achievements of research hotspots such as elastic and viscoelastic multi-parameter inversion, deep learning integrated FWI, uncertainty quantification, 4D time-lapse monitoring and cross-scale imaging. Finally, combined with the industrial development trend, this paper prospects future research directions including deep integration of physics and artificial intelligence, large-scale high-efficiency inversion, multi-physical field coupled imaging, and standardization of result interpretability. It aims to provide a systematic literature review and research reference for researchers engaged in seismic inversion and oil and gas exploration.

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The stock price sequence has a low signal-to-noise ratio, strong nonlinearity and statistical characteristics drift over time. Once it is necessary to continuously predict multiple moments in the future, the error will continue to accumulate along the step length, making the difficulty of prediction significantly increased. In response to this problem, this paper embeds the attention mechanism into the long-term and short-term memory network to construct an LSTM-Attention hybrid model for multi-step prediction: first, LSTM encodes the timing dependence of historical sequences, and then assigns learningable weights to the hidden state of each time step through the attention layer, so as to highlight the key points that are more distinguishable for future trends. Finally, the full connection layer gives the price of several future moments at once. The experiment selects the daily frequency data of the Shanghai-Shenzhen 300 Index from 2015 to 2024 and compares it horizontally with models such as ARIMA, LSTM, GRU, CNN-LSTM and Transformer. The results show that the proposed model leads the overall accuracy of RMSE, MAE, MAPE and direction, and the root mean square error decreases by about 20% compared with the single LSTM; and with the predicted step length increases, the attention mechanism can significantly inhibit the accumulation of error. The average absolute percentage error of 10-step prediction is about 31% lower than that of LSTM, indicating that the hybrid structure has a good effect in multi-step prediction tasks.

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