574 research outputs found
Rawnsley's -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 -function
of
,
where is a K\"ahler metric associated with the K\"ahler potential
on the generalized Cartan-Hartogs domain
and obtain
necessary and sufficient conditions for to
become a polynomial in . Secondly, we study the Berezin
quantization on
with the metric .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
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