Rawnsley's ε\varepsilon-function on some Hartogs type domains over bounded symmetric domains and its applications

The purpose of this paper is twofold. Firstly, we will compute the explicit expression of the Rawnsley's $\varepsilon$-function $\varepsilon_{(\alpha,g(\mu;\nu))}$ of $\big(\big(\prod_{j=1}^k\Omega_j\big)^{{\mathbb{B}}^{d_0}}(\mu),g(\mu;\nu)\big)$, where $g(\mu;\nu)$ is a K\"ahler metric associated with the K\"ahler potential $-\sum_{j=1}^k\nu_j\ln N_{\Omega_j}(z_j,\overline{z_j})^{\mu_j}-\ln(\prod_{j=1}^kN_{\Omega_j}(z_j,\overline{z_j})^{\mu_j}-\|w\|^2)$ on the generalized Cartan-Hartogs domain $\big(\prod_{j=1}^k\Omega_j\big)^{{\mathbb{B}}^{d_0}}(\mu)$ and obtain necessary and sufficient conditions for $\varepsilon_{(\alpha,g(\mu;\nu))}$ to become a polynomial in $1-\|\widetilde{w}\|^2$. Secondly, we study the Berezin quantization on $\big(\prod_{j=1}^k\Omega_j\big)^{{\mathbb{B}}^{d_0}}(\mu)$ with the metric $g(\mu;\nu)$.Comment: 21 pages. arXiv admin note: text overlap with arXiv:1411.523

SRMAE: Masked Image Modeling for Scale-Invariant Deep Representations

Due to the prevalence of scale variance in nature images, we propose to use image scale as a self-supervised signal for Masked Image Modeling (MIM). Our method involves selecting random patches from the input image and downsampling them to a low-resolution format. Our framework utilizes the latest advances in super-resolution (SR) to design the prediction head, which reconstructs the input from low-resolution clues and other patches. After 400 epochs of pre-training, our Super Resolution Masked Autoencoders (SRMAE) get an accuracy of 82.1% on the ImageNet-1K task. Image scale signal also allows our SRMAE to capture scale invariance representation. For the very low resolution (VLR) recognition task, our model achieves the best performance, surpassing DeriveNet by 1.3%. Our method also achieves an accuracy of 74.84% on the task of recognizing low-resolution facial expressions, surpassing the current state-of-the-art FMD by 9.48%

Recent developments of SPH in modeling explosion and impact problems

Explosion and impact problems are generally characterized by the presence of shock waves, intense localized materials response and intensive loadings. Most of the wave propagation hydro-codes for such problems use traditional grid based methods such as finite difference methods (FDM) and finite element methods (FEM). Though many successful achievements have been made using these methods, some numerical difficulties still exist. These numerical difficulties generally arise from large deformations, large inhomogeneities, and moving interfaces, free or movable boundaries. Smoothed particle hydrodynamics (SPH) is a Lagrangian, meshfree particle method, and has been widely applied to different areas in engineering and science. SPH method has been intensively used for simulating high strain hydrodynamics with material strength, due to its special features of meshfree, Lagrangian and particle nature. In this paper, some recent developments of the SPH in modelling explosion and impact problems will be introduced. A modified scheme for approximating kernel gradient (kernel gradient correction, or KGC) has been used in the SPH simulation to achieve better accuracy and stability. The modified SPH method is used to simulate a number of problems including 1D TNT detonation, linear shaped charge and explosively driven welding. The effectiveness of the modified SPH method has been demonstrated by comparative studies of the SPH results with data from other resources.Peer ReviewedPostprint (published version