Periodic solutions for a porous medium equation

In this paper, we study with a periodic porous medium equation with nonlinear convection terms and weakly nonlinear sources under Dirichlet boundary conditions. Based on the theory of Leray-Shauder fixed point theorem, we establish the existence of periodic solutions

Coherence-Assisted Superradiant Laser with Hz Linewidth and 10−1010^{-10}W Power

The superradiant laser, based on the clock transition between the electric ground state $^1$S$_0$ and the metastable state $^3$P$_0$ of fermionic alkaline-earth(-like) atoms, has been proposed to be a new promising light source with linewidth being the order of millihertz. However, due to the small $^1$S$_0$-to-$^3$P$_0$ transition strength, the steady-state power in that system is relatively low ($\sim 10^{-12}$W). In this work, we propose an alternative superradiant laser scheme based on a Raman-transition-induced coupling between the $^3$P$_0$ and $^3$P$_1$ states in bosonic alkaline-earth(-like) atoms, and achieve a laser with linewidth $\lesssim 2\pi\times1$Hz and power $\gtrsim 10^{-10}$W ($\sim 10^{3}$ photons in steady state) at a small pumping cost. The Raman beams play two significant roles in our scheme. First, the coherence between the dark and bright states induced by the Raman beams produce a new local minimum in the pumping-linewidth curve with pumping rate lower than $2\pi \times 10$kHz, which is beneficial for continuous output. Second, the Raman beams mix the long-lived $^3$P$_0$ state into the lasing state and thus reduce the linewidth. Our work greatly improves the output performance of the superradiant laser system with coherence induced by Raman transitions and may offer a firm foundation for its practical use in future

Image Denoising via Nonlinear Hybrid Diffusion

A nonlinear anisotropic hybrid diffusion equation is discussed for image denoising, which is a combination of mean curvature smoothing and Gaussian heat diffusion. First, we propose a new edge detection indicator, that is, the diffusivity function. Based on this diffusivity function, the new diffusion is nonlinear anisotropic and forward-backward. Unlike the Perona-Malik (PM) diffusion, the new forward-backward diffusion is adjustable and under control. Then, the existence, uniqueness, and long-time behavior of the new regularization equation of the model are established. Finally, using the explicit difference scheme (PM scheme) and implicit difference scheme (AOS scheme), we do numerical experiments for different images, respectively. Experimental results illustrate the effectiveness of the new model with respect to other known models

SaaFormer: Spectral-spatial Axial Aggregation Transformer for Hyperspectral Image Classification

Hyperspectral images (HSI) captured from earth observing satellites and aircraft is becoming increasingly important for applications in agriculture, environmental monitoring, mining, etc. Due to the limited available hyperspectral datasets, the pixel-wise random sampling is the most commonly used training-test dataset partition approach, which has significant overlap between samples in training and test datasets. Furthermore, our experimental observations indicates that regions with larger overlap often exhibit higher classification accuracy. Consequently, the pixel-wise random sampling approach poses a risk of data leakage. Thus, we propose a block-wise sampling method to minimize the potential for data leakage. Our experimental findings also confirm the presence of data leakage in models such as 2DCNN. Further, We propose a spectral-spatial axial aggregation transformer model, namely SaaFormer, to address the challenges associated with hyperspectral image classifier that considers HSI as long sequential three-dimensional images. The model comprises two primary components: axial aggregation attention and multi-level spectral-spatial extraction. The axial aggregation attention mechanism effectively exploits the continuity and correlation among spectral bands at each pixel position in hyperspectral images, while aggregating spatial dimension features. This enables SaaFormer to maintain high precision even under block-wise sampling. The multi-level spectral-spatial extraction structure is designed to capture the sensitivity of different material components to specific spectral bands, allowing the model to focus on a broader range of spectral details. The results on six publicly available datasets demonstrate that our model exhibits comparable performance when using random sampling, while significantly outperforming other methods when employing block-wise sampling partition.Comment: arXiv admin note: text overlap with arXiv:2107.02988 by other author

The Position and Function of Macroscopic Analysis in the Failure Analysis of Railway Fasteners

Macroscopic analysis plays an important role in failure analysis, which cannot be replaced by other analyzing methods. In recent years, with the development of characterization techniques, more and more engineers and technicians rely on the advanced analytical testing methods in the process of failure analysis, ignoring the methods and means of macroscopic analysis. This can easily lead to some wrong judgments. Therefore, this chapter will combine with the cases to explain the position and role of macroanalysis in the failure analysis of rail fastening clips and to offer references for engineers and technicians in relevant fields