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Blow-up of critical norms for the 3-D Navier-Stokes equations

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Science China Mathematics 2017年第4期60卷 637-650页

作者： wang wendong ZHANG ZhiFei School of Mathematical Sciences Dalian University of Technology School of Mathematical Sciences Peking University

Let u = （Uh,U3） be a smooth solution of the 3-D Navier-Stokes equations in R3 × [0, T）. It was proved that if u3 ∈ L^∞（0,T;Bp,q-1＋3/p（R3）） for 3 〈 p,q 〈 oe and uh ∈ L^∞（0, T;BMO-1（R3）） with uh（T） ∈ VMO-1（R3）, then u can be extended beyond T. This result generalizes the recent result proved by Gallagher et al. （2016）, which requires u ∈ L^∞（O,T;Bp,^-11＋3/P（R3））. Our proof is based on a new interior regularity criterion in terms of one velocity component, which is independent of interest.

关键词： Navier-Stokes equations interior regularity criterion BMO space Besov space

An Attempt at Axiomatization of Extending Mechanism of Solutions to the Fluid Dynamical Systems

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Chinese Annals of Mathematics,Series B 2024年第6期45卷 957-970页

作者： Jinkai LI Meng wang wendong wang South China Research Center for Applied Mathematics and Interdisciplinary Studies School of Mathematical Sciences South China Normal University Department of Mathematics Zhejiang University School of Mathematical Sciences Dalian University of Technology

Note that some classic fluid dynamical systems such as the Navier-Stokes equations, Magnetohydrodynamics (MHD for short), Boussinesq equations and etc., are observably different from each other but obey some energy inequalities of the similar *** this paper, the authors attempt to axiomatize the extending mechanism of solutions to these systems, merely starting from several basic axiomatized conditions such as the local existence, joint property of solutions and some energy inequalities. The results established have nothing to do with the concrete forms of the systems and, thus, give the extending mechanisms in a unified way to all systems obeying the axiomatized conditions. The key tools are several new multiplicative interpolation inequalities of Besov type, which have their own interests.

关键词： 35Q30 76D03 Blow-up criteria Interpolation inequalities of Besov type Navier-Stokes equations

The C~α regularity of a class of non-homogeneous ultraparabolic equations

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Science China Mathematics 2009年第8期52卷 1589-1606页

作者： wang wendong ZHANG LiQun Institute of Mathematics Academy of Mathematics and Systems ScienceHua Loo-Keng Key Laboratory of MathematicsChinese Academy of SciencesBeijing 100190China

We obtain the Cα regularity for weak solutions of a class of non-homogeneous ultra- parabolic equation, with measurable coefficients. The result generalizes our recent Cα regularity results of homogeneous ultraparab... 详细信息

关键词： non-homogeneous ultraparabolic equations C α regularity Kruzhkov’s approaches 35K70 35D10 35B65

ENHANCED BLOCK-SPARSE SIGNAL RECOVERY PERFORMANCE VIA TRUNCATED l2\l1-2 MINIMIZATION

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Journal of Computational Mathematics 2020年第3期38卷 437-451页

作者： Weichao Kong Jianjun wang wendong wang Feng Zhang School of Mathematics and Statistics Southwest UniversityChongqing 400715China Research Center for Artificial Intelligence Education Big Data Southwest UniversityChongqing 400715China

In this paper,we investigate truncated l2\l1-2 minimization and its associated alternating direction method of multipliers(ADMM)algorithm for recovering the block sparse *** on the block restricted isometry property(Block-RIP),a theoretical analysis is presen ted to guarantee the validity of proposed *** theore tical resul ts not only show a less error upper bound,but also promote the former recovery condition of truncated l1-2 method for sparse signal ***,the algorithm has been compared with some state-of-the-art algorithms and numerical experiments have shown excellent performances on recovering the block sparse signals.

关键词： Compressed sensing Block-sparse Trunca ted l2\l1-2 minimization met hod ADMM

A Novel Packet Marking Algorithm in Context-aware Autonomic QoS Framework

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China Communications 2009年第4期6卷 98-107页

作者： Gong Xiangyang wang wendong Li Yan State Key Laboratory of Networking and Switching Technology Beijing University of Posts and Telecommunications 100876 Beijing P.R. China

Autonomic networking is one of the hot research topics in the research area of future network *** this paper, we introduce context-aware and autonomic attributes into DiffServ QoS framework, and propose a novel autonomic packet marking(APM) *** the proposed autonomic QoS framework, APM is capable of collecting various QoS related contexts, and adaptively adjusting its behavior to provide better QoS guarantee according to users' requirements and network *** results show that APM provides better performance than traditional packet marker, and significantly improves user's quality of experience.

关键词： autonomic QoS framework DiffServ context-aware packet marking

Studying on equilibriums between price and QoS in multi-provider overlay access networks

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High Technology Letters 2006年第2期12卷 129-135页

作者：王玉峰 wang wendong College of Telecommunications and Information Engineering Nanjing University of Posts and Telecommunications Nanjing 210003 P.R. China State Key Laboratory of Networking and Switching Technology Beijing University of Posts and Telecommunications Beijing 100876 P.R. China

From the viewpoint of game theory, this paper proposes a model that combines QoS index with price factor in overlay access networks, and uses the multinomial logit （MNL） to model the choice behaviour of users. Each service class is considered an independent and competitive entity offered by each provider, which aims at maximizing its own utility. Based on noncooperative game, we prove the existence and uniqueness of equilibriums between QoS levels and prices among various service classes, and demonstrate the properties of equilibriums. Finally, these results are verified via ntunerieal analysis.

关键词： Overlay access network noncooperative game multinomial logit model Nash equilibrium

Spiking-free HGO-based DSC for flexible joint manipulator

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Chinese Journal of Aeronautics 2022年第3期35卷 419-431页

作者： Dezhi KONG wendong wang Yang wang Junbo ZHANG Yikai SHI Lingyun KONG School of Mechanical Engineering Northwestern Polytechnical University Xi'an 710072China Shaanxi Engineering Research Center of Controllable Neutron Source School of ScienceXijing UniversityXi'an 710123China

The tracking control problem for Flexible Joint Manipulator Control System(FJMCS)with unmeasurable states is addressed in this ***,a High-Gain Observer(HGO)is constructed to estimate the unmeasurable states and the ***,a Dynamic Surface Control(DSC)scheme is developed by using the estimation of *** newly proposed controller has two advantages over the existing methods:(A)a novel Spike Suppression Function(SSF)is developed to avoid the estimation spike problem in the existing HGO-based controllers.(B)Unlike the existing observer-based partial feedback control scheme that can only estimate the unmeasurable states,the proposed HGO can estimate both the unmeasurable states and *** closed-loop system stability is proved by the Lyapunov *** results demonstrate the effectiveness of the proposed controller.

关键词： Dynamic surface control Flexible joint manipulator High-gain observer Mismatched uncertainties Partial states feedback Spike suppression

Phosphate adsorption performance of a novel filter substrate made from drinking water treatment residuals

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Journal of Environmental Sciences 2016年第7期28卷 191-199页

作者： wendong wang Cui Ma Yinting Zhang Shengjiong Yang Yue Shao Xiaochang wang Department of Environmental and Municipal Engineering Xi'an University of Architecture and TechnologyXi'an 710055China Zhejiang Provincial Key Laboratory of Water Science and Technology Zhejiang 314006China Department of Chemical and Biomolecular Engineering Rice UniversityHouston 7Z005USA

Phosphate is one of the most predominant pollutants in natural waters. Laboratory experiments were conducted to investigate the phosphate adsorption performance of a（NFS） made from drinking water treatment residuals. The adsorption of phosphate on the NFS fitted well with the Freundlich isotherm and pseudo second-order kinetic models. At p H 7.0, the maximum adsorption capacity of 1.03 mg/g was achieved at 15°C corresponding to the wastewater temperature in cold months, and increased notably to 1.31 mg/g at 35°*** both acidic conditions（part of the adsorption sites was consumed） and basic conditions（negative charges formed on the surface of NFS, which led to a static repulsion of PO43-and HPO42-）, the adsorption of phosphate was slightly inhibited. Further study showed that part of the adsorption sites could be recovered by 0.25 mol/L Na OH. The activation energy was calculated to be above 8.0 k J/mol, indicating that the adsorption of phosphate on NFS was probably a chemical process. Considering the strong phosphate adsorption capacity and recoverability, NFS showed great promise on enhancing phosphate removal from the secondary treated wastewater in the filtration process.

关键词： Adsorption Drinking water treatment residuals Domestic wastewater Filter substrate Phosphate

On the feasibility and efficacy of control traffic protection in software-defined networks

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Science China(Information Sciences) 2015年第12期58卷 44-62页

作者： HU YanNan wang wendong GONG XiangYang QUE XiRong CHENG ShiDuan State Key Laboratory of Networking and Switching Technology Beijing University of Posts and Telecommunications

Software Defined Networking(SDN) is an emerging networking paradigm that assumes a logically centralized control plane separated from the data plane. Despite all its advantages, separating the control and data planes introduces new challenges regarding resilient communications between the two. That is, disconnections between switches and their controllers could result in substantial packet loss and performance *** paper addresses this challenge by studying the issue of control traffic protection in SDNs with arbitrary numbers of controllers. Specifically, we propose a control traffic protection scheme that combines both local rerouting and constrained reverse path forwarding protections, through which switches can locally react to failures and redirect the control traffic using standby backup forwarding options. Our goal is then to find a set of primary routes for control traffic, called protected control network, where as many switches as possible can benefit from the proposed protection scheme. We formulate the protected control network problem, prove its NP-hardness, and develop an algorithm that reconciles protectability and performance(e.g., switch-to-control latency). Through extensive simulations based on real topologies, we show that our approach significantly improves protectability of control traffic. The results should help further the process of deploying SDN in real-world networks.

关键词： software-defined network protection control traffic resilience optimization