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The Time Asymptotic Expansion of the Bipolar Hydrodynamic Model for Semiconductors

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Acta Mathematicae Applicatae Sinica 2023年第1期39卷 95-108页

作者： xiao-chun WU School of Mathematics and Statistics&HNP-LAMA Central South UniversityChangsha 410083China

In 2003, Gasser-Hsiao-Li [JDE(2003)] showed that the solution to the bipolar hydrodynamic model for semiconductors(HD model) without doping function time-asymptotically converges to the diffusion wave of the porous media equation(PME) for the switch-off case. Motivated by the work of Huang-Wu[arXiv:2210.13157], we will confirm that the time-asymptotic expansion proposed by Geng-Huang-Jin-Wu [arXiv:2202.13385] around the diffusion wave is a better asymptotic profile for the HD model in this paper, where we mainly adopt the approximate Green function method and the energy method.

关键词： time asymptotic expansion bipolar hydrodynamic model for semiconductors switch-off approximate Green function

AF-Embedding of Crossed Products of Certain Graph C＊-algebras by Quasi-free Actions （II）

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Acta Mathematica Sinica,English Series 2011年第8期27卷 1581-1590页

作者： xiao chun FANG Department of Mathematics Tongji University Shanghai 200092 P. R. China

Let E be a row-finite directed graph, let G be a locally compact abelian group with dual group G = F, let w be a labeling map from E＊ to F, and let （C＊（E）, G,a^w） be the C＊-dynamical system defined by w. Some mappings concerning the AF-embedding construction of C＊（E） X（aw） G are studied in more detail. Several necessary conditions of AF-embedding and some properties of almost proper labeling map are obtained. Moreover it is proved that if E is constructed by attaching some l-loops to a directed graph T consisting of some rooted directed trees and G is compact, then oJ is k almost proper, that is a sufficient condition for AF-embedding, if and only if ∑j^Kk=1^wγ j ≠fi 1r for any loop γi, γ2 …γk attached to one path in T

关键词： AF-embedding crossed products graph C*-algebras

Effect of stress-relief annealing on thermal fatigue cracks for die-casting die steels

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Journal of Iron and Steel Research International 2024年第5期31卷 1164-1176页

作者： Zhi-xiong Bai xiao-chun Wu School of Materials Science and Engineering Shanghai UniversityShanghai200444China

The effect of stress-relief annealing at different stages of thermal fatigue tests on crack growth was investigated using a self-built thermal cycle *** results showed that annealing could limit crack expansion *** reduced dislocation density and released the accumulation of residual *** addition,the strain accumulation in carbides was reduced by this *** was also found that double annealing was even more effective at inhibiting crack expansion compared to single stress-relief *** 1000 cycles,the maximum crack length was reduced by 31.1%and 45.2%for the samples after using the optimal single and double annealing processes,*** single stress-relief annealing,earlier annealing provides more benefit in delaying crack ***,effective double stress-relief annealing requires a suitable time interval between the annealing ***,after 800 cycles,surface hardness decreased significantly accompanied by an increase in the size and number of carbides,and cracks expanded predominantly along grain boundaries.

关键词： Thermal fatigue Steel Carbide Stress-relief annealing Dislocation Residual stress

On Principal Invariant Subspaces

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Acta Mathematica Sinica,English Series 2015年第10期31卷 1621-1628页

作者： xiao Ming XU xiao chun FANG School of Science Shanghai Institute of Technology Department of Mathematics Tongji University

Let F and G be closed subspaces of the complex Hilbert spaceH, and U and V be closed subspaces of F- and G, respectively. In this paper, using the technique of operator block, we present the necessary and sufficient conditions under which （U, V） is a pair of （strictly, non-degenerate） principal invariant subspaces for （F, G）.

关键词： Hilbert space operator matrix invariant subspace principal invariant subspace

Multi-scale analysis of subgrid stress and energy dissipation in turbulent channel flow

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Acta Mechanica Sinica 2010年第1期26卷 81-90页

作者： chun-xiao Xu School of Aerospace Tsinghua University 100084 Beijing China

In present study, the subgrid scale （SGS） stress and dissipation for multiscale formulation of large eddy simulation are analyzed using the data of turbulent channel flow at Ret = 180 obtained by direct numerical simulation. It is found that the small scale SGS stress is much smaller than the large scale SGS stress for all the stress components. The dominant contributor to large scale SGS stress is the cross stress between small scale and subgrid scale motions, while the cross stress between large scale and subgrid scale motions make major contributions to small scale SGS stress. The energy transfer from resolved large scales to subgrid scales is mainly caused by SGS Reynolds stress, while that between resolved small scales and subgrid scales are mainly due to the cross stress. The multiscale formulation of SGS models are evaluated a priori, and it is found that the small- small model is superior to other variants in terms of SGS dissipation.

关键词： SGS stress SGS dissipation - Multi-scale energy transfer Multi-scale SGS model - Turbulent channel flow

Fractal Dimension of Random Attractors for Non-autonomous Fractional Stochastic Ginzburg–Landau Equations

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Acta Mathematica Sinica,English Series 2020年第3期36卷 318-336页

作者： chun xiao GUO Ji SHU xiao Hu WANG Department of Mathematics China University of Mining and Technology BeijingBeijing 100083P.R.China School of Mathematical Science and V.C.&V.R.Key Lab Sichuan Normal UniversityChengdu 610068P.R.China Department of Mathematics Sichuan UniversityChengdu 610064P.R.China

This paper considers the dynamical behavior of solutions for non-autonomous stochastic fractional Ginzburg–Landau equations driven by additive noise with α∈(0, 1). First, we give some conditions for bounding the fractal dimension of a random invariant set of non-autonomous random dynamical system. Second, we derive uniform estimates of solutions and establish the existence and uniqueness of tempered pullback random attractors for the equation in H. At last, we prove the finiteness of fractal dimension of random attractors.

关键词： Non-autonomous stochastic fractional Ginzburg–Landau equation random dynamical system random attractor additive noise fractal dimension

Strategies and Research Progress of Chinese Medicine in Prevention and Treatment of Diabetic Peripheral Neuropathy

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Chinese Journal of Integrative Medicine 2018年第10期24卷 794-800页

作者： YANG Dan LIANG xiao-chun Department of Traditional Chinese Medicine Peking Union Medical College Hospital Peking Union Medical CollegeTranslational Medicine Center Chinese Academy of Medical Sciences

Diabetic peripheral neuropathy （DPN） seriously affects the quality of life in patients with type 2 diabetes mellitus. This paper reviews the role of Chinese medicine in the main treatment goal of DPN, including protecting pancreatic β-cells, in the use of antioxidation therapy to delay disease progression, and in the endpoint of neural repair and regeneration. We propose that protecting the body from injury caused by high glucose and oxidative stress, and promoting repair and regeneration of nerves should be the research direction for the prevention and treatment of DPN.

关键词： diabetic peripheral neuropathy pancreatic β-cell anti-oxidative stress neural repair and regeneration Chinese medicine

A Remark on the Beale-Kato-Majda Criterion for the 3D MHD Equations with Zero Kinematic Viscosity

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Acta Mathematicae Applicatae Sinica 2012年第2期28卷 209-214页

作者： Sadek GALA xiao-chun CHEN Department of Mathematics University of Mostaganem Box 227 Mostaganem 27000 Algeria Department of Mathematics Chonqing Three Gorges University Wanzhou 404000 China

In this paper, we study the blow-up criterion of smooth solutions to the 3D magneto-hydrodynamic system in B^0∞,∞. We show that a smooth solution of the 3D MHD equations with zero kinematic viscosity in the whole sp... 详细信息

关键词： Magneto-hydrodynamic equations with zero viscosity B^0∞,∞ space blow-up criterion

Common Properties of the Operator Products in Local Spectral Theory

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Acta Mathematica Sinica,English Series 2015年第11期31卷 1715-1724页

作者： Kai YAN xiao chun FANG Department of Mathematics Tongji University

Let X,Y be Banach spaces, A,D ： X - Y and B,C ： Y - X be the bounded linear operators satisfying operator equation set ACD=DBD DBA=ACAIn this paper, we show that AC and BD share some basic operator properties such as the injectivity and the invertibility. Moreover, we show that AG＇ and BD share many common local spectral properties including SVEP, Bishop property （β） and Dunford property （C）.

关键词： Jacobson's lemma operator equation set common property local spectral theory