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pro vyhledávání: '"Li, Pengtao"'
The Grushin spaces, as one of the most important models in the Carnot-Carath\'eodory space, are a class of locally compact and geodesic metric spaces which admit a dilation. Function spaces on Grushin spaces and some related geometric problems are al
Externí odkaz:
http://arxiv.org/abs/2401.03409
In the study of the supremum of stochastic processes, Talagrand's chaining functionals and his generic chaining method are heavily related to the distribution of stochastic processes. In the present paper, we construct Talagrand's type functionals in
Externí odkaz:
http://arxiv.org/abs/2309.05498
Mechanical vibration signal denoising is a pivotal task in various industrial applications, including system health monitoring and failure prediction. This paper introduces a novel deep learning transformer-based architecture specifically tailored fo
Externí odkaz:
http://arxiv.org/abs/2308.02166
Autor:
Li, Pengtao, Wang, Hanchao
Catoni proposed a robust M-estimator and gave the deviation inequality for one fixed test function. The present paper is devoted to the uniform concentration inequality for a family of test functions. As an application, we consider empirical risk min
Externí odkaz:
http://arxiv.org/abs/2210.08211
This study introduces pre-orthogonal adaptive Fourier decomposition (POAFD) to obtain approximations and numerical solutions to the fractional Laplacian initial value problem and the extension problem of Caffarelli and Silvestre (generalized Poisson
Externí odkaz:
http://arxiv.org/abs/2207.10078
For $a \ge - {( \frac{{d}}{2}- 1)^2} $ and $2\sigma= {{d - 2}}-( {{{(d - 2)}^2} + 4a})^{1/2}$, let $$\begin{cases}\mathcal{H}_{a}= - \Delta + \frac{a} {{{{ | x |}^2}}},\\ \mathcal{\widetilde{H}}_{\sigma}= 2\big( { - \Delta + \frac{{{\sigma ^2}}} {{{{
Externí odkaz:
http://arxiv.org/abs/2203.16770
Let $u(\cdot,\cdot)$ be the Caffarelli-Silvestre extension of $f.$ The first goal of this article is to establish the fractional trace type inequalities involving the Caffarelli-Silvestre extension $u(\cdot,\cdot)$ of $f.$ In doing so, firstly, we es
Externí odkaz:
http://arxiv.org/abs/2201.00765
The purpose of this article is twofold. The first is to strengthen fractional Sobolev type inequalities in Besov spaces via the classical Lorentz space. In doing so, we show that the Sobolev inequality in Besov spaces is equivalent to the fractional
Externí odkaz:
http://arxiv.org/abs/2201.00753
Autor:
Zhao, Yongqing, Wang, Tao, Wan, Sumei, Tong, Yan, Wei, Yangyang, Li, Pengtao, Hu, Nan, Liu, Yuling, Chen, Hongqi, Pan, Xiaoping, Zhang, Baohong, Peng, Renhai, Hu, Shoulin
Publikováno v:
In Gene 30 August 2024 921
Publikováno v:
In Thermal Science and Engineering Progress August 2024 53