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Two algorithms for two-phase Stefan type problems

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Applied Mathematics(A Journal of Chinese Universities) 2009年第3期24卷 298-308页

作者： LIAN xiao-peng CHENG xiao-liang HAN Wei-min Dept. of Math. Zhejiang Univ. Hangzhou 310027 China Dept. of Math. University of Iowa Iowa City IA 52242 USA

In this paper,the relaxation algorithm and two Uzawa type algorithms for solving discretized variational inequalities arising from the two-phase Stefan type problem are *** analysis of their convergence is presented and the upper bounds of the convergence rates are *** numerical experiments are shown to demonstrate that for the second Uzawa algorithm which is an improved version of the first Uzawa algorithm,the convergence rate is uniformly bounded away from 1 if τh^-2 is kept bounded,where τ is the time step size and h the space mesh size.

关键词： relaxation method Uzawa algorithm variational inequality two-phase Stefan type problem

Numerical estimation of the piecewise constant Robin coefficient by identifying its discontinuous points

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Applied Mathematics(A Journal of Chinese Universities) 2015年第1期30卷 1-16页

作者： CHENG xiao-liang YU Yuan-jie Department of Mathematics Zhejiang University

We propose a new numerical method for estimating the piecewise constant Robin coefficient in two-dimensional elliptic equation from boundary measurements. The Robin in- verse problem is recast into a minimization of an output least-square formulation. A technique based on determining the discontinuous points of the unknown coefficient is suggested, and we investigate the differentiability of the solution and the objective functional with respect to the discontinuous points. Then we apply the Gauss-Newton method for reconstructing the shape of the unknown Robin coefficient. Numerical examples illustrate its efficiency and stability.

关键词： Inverse problem Robin coefficient differentiability the Gauss-Newton method.

The quantum cocktail party problem

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Science China(Physics,Mechanics & Astronomy) 2020年第5期63卷 2-5页

作者： xiao liang YaDong Wu Hui Zhai Institute for Advanced Study Tsinghua UniversityBeijing 100084China Laboratory of Quantum Information University of Science and Technology of ChinoHefei 230026China

The cocktail party problem refers to the phenomenon that the brain of a listener can focus on a single voice while filtering out a range of other voices in a multi-talker situation,say,in a cocktail party[1].This selective attention problem was firstly defined as the"cocktail party problem"(CPP)by Cherry[2]in *** recent years,machine-learning based approaches to solve the CPP were essential for many industrial applications such as automated speech *** independent component analysis(ICA)is such an algorithm particularly suitable for the *** CPP also has applications in physical science such as astrophysics data analysis[3,4].

关键词： quantum problem filtering

Reinforcement Learning-Based Sensitive Semantic Location Privacy Protection for VANETs

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China Communications 2021年第6期18卷 244-260页

作者： Minghui Min Weihang Wang liang xiao Yilin xiao Zhu Han Department of Information and Communication Engineering Xiamen UniversityXiamen 361005China School of Information and Control Engineering ChinaUniversity of Mining and TechnologyXuzhou 221116China The Affiliated Hospital of China University of Mining and Technology Xuzhou 221116China Department of Electrical and Computer Engineering University of HoustonHouston TX 77004USA Beijing Key Laboratory of Mobile Computing and Pervasive Device No.6 Kexueyuan South RoadBeijing 100190China

Location-based services(LBS)in vehicular ad hoc networks(VANETs)must protect users’privacy and address the threat of the exposure of sensitive locations during LBS *** release not only their geographical but also semantic information of the visited places(e.g.,hospital).This sensitive information enables the inference attacker to exploit the users’preferences and life *** this paper we propose a reinforcement learning(RL)based sensitive semantic location privacy protection *** scheme uses the idea of differential privacy to randomize the released vehicle locations and adaptively selects the perturbation policy based on the sensitivity of the semantic location and the attack *** scheme enables a vehicle to optimize the perturbation policy in terms of the privacy and the quality of service(QoS)loss without being aware of the current inference attack model in a dynamic privacy protection *** solve the location protection problem with high-dimensional and continuous-valued perturbation policy variables,a deep deterministic policy gradientbased semantic location perturbation scheme(DSLP)is *** actor part is used to generate continuous privacy budget and perturbation angle,and the critic part is used to estimate the performance of the *** demonstrate the DSLP-based scheme outperforms the benchmark schemes,which increases the privacy,reduces the QoS loss,and increases the utility of the vehicle.

关键词： semantic location sensitivity locationbased services VANET differential privacy reinforcement learning

Effects of Hirudin on High Glucose-Induced Oxidative Stress and Inflammatory Pathway in Rat Dorsal Root Ganglion Neurons

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Chinese Journal of Integrative Medicine 2020年第3期26卷 197-204页

作者： LIU Wei liang xiao-chun SHI Yue Department of Traditional Chinese Medicine Peking Union Medical College Hospital Peking Union Medical College Chinese Academy of Medical Sciences

Objective:To investigate protective effects of hirudin on oxidative stress and apoptosis of spinal dorsal root ganglion cells in high-glucose rats at the cellular and molecular ***:Dorsal root ganglion neurons(DRGn)were harvested from embryonic day in 15 SD rats,purified and identificated after primary *** were divided into the normal control group,high-glucose(HG)group,positive control(alpha-lipoic acid,ALA)group,low-dose hirudin group(H1),medium-dose hirudin group(H2)and high-dose hirudin group(H3).The control group was cultured by neuron specific culture medium,while the HG group was cultured by neuron specific culture medium and 20 mmol/L glucose(HG medium).The hirudin groups were cultured by HG medium+0.25 IU/mL hirudin(H1),HG medium+0.5 IU/mL hirudin(H2)and HG medium+1 IU/mL hirudin(H3).The ALA group was cultured by HG medium +100μmol/L ALA.3-(4,5-dimethylthiazol-2-yl)-2,5-diphenylt etrazolium bromide(MTT)assay was used to explore the optimum concentration and intervention *** cytometry assay was used to detect the level of reactive oxygen series(ROS).Western blot and quantificational realtime polymerase chain reaction(qRT-PCR)were used to detect the expression of protein and mRNA of nuclear factor erythroid 2-related factor 2(Nrf-2),hemeoxygence-1(HO-1),nuclear factor-κB(NF-κB)and *** assay was used to test the apoptosis rate of different ***:After 24 h of culture,the cell activity of hirudin and ALA groups were higher than that of HG group,and there was a statistical difference between the H1 group and HG group(P<0.05).In hirudin groups,the apoptosis rate of cells,the expression of activated Caspase-3 protein and Caspase-3 mRNA were lower than those of HG group(P<0.01),higher than those of ALA group(P<0.01 or P<0.05).The ROS level of hirudin groups was higher than that of ALA group(P<0.01),lower than that of HG group(P<0.01 or P<0.05).The expression of NF-κB(P65)protein in H3 group were lower than those of HG g

关键词： hirudin diabetic peripheral neuropathy oxidative stress apoptosis dorsal root ganglion neuron

Texture Repairing by Unified Low Rank Optimization

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Journal of Computer Science & Technology 2016年第3期31卷 525-546页

作者： xiao liang Xiang Ren Zhengdong Zhang Yi Ma Institute for Advanced Study Tsinghua University Beijing 100086 China Department of Computer Science University of Illinois at Urbana-Champaign Urbana IL 61801 U.S.A. Department of Electrical Engineering and Computer Science Massachusetts Institute of Technology Cambridge MA 02139 U.S.A. School of Information Science and Technology ShanghaiTech University Shanghai 200031 China

In this paper, we show how to harness both low-rank and sparse structures in regular or near-regular textures for image completion. Our method is based on a unified formulation for both random and contiguous corruption. In addition to the low rank property of texture, the algorithm also uses the sparse assumption of the natural image： because the natural image is pieeewise smooth, it is sparse in certain transformed domain （such as Fourier or wavelet transform）. We combine low-rank and sparsity properties of the texture image together in the proposed algorithm. Our algorithm based on convex optimization can automatically and correctly repair the global structure of a corrupted texture, even without precise information about the regions to be completed. This algorithm integrates texture rectification and repairing into one optimization problem. Through extensive simulations, we show our method can complete and repair textures corrupted by errors with both random and contiguous supports better than existing low-rank matrix recovery methods. Our method demonstrates significant advantage over local patch based texture synthesis techniques in dealing with large corruption, non-uniform texture, and large perspective deformation.

关键词： low-rank texture convex optimization sparse error correction image repairing

AN EFFECTIVE CONTINUOUS ALGORITHM FOR APPROXIMATE SOLUTIONS OF LARGE SCALE MAX-CUT PROBLEMS

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Journal of Computational Mathematics 2006年第6期24卷 749-760页

作者： Cheng-xian Xu xiao-liang Feng-min Xu Department of Mathematics Xi 'an Jiaotong University Xi ' an 710049 China

An effective continuous algorithm is proposed to find approximate solutions of NP-hard max-cut problems. The algorithm relaxes the max-cut problem into a continuous nonlinear programming problem by replacing n discrete constraints in the original problem with one single continuous constraint. A feasible direction method is designed to solve the resulting nonlinear programming problem. The method employs only the gradient evaluations of the objective function, and no any matrix calculations and no line searches are required. This greatly reduces the calculation cost of the method, and is suitable for the solution of large size max-cut problems. The convergence properties of the proposed method to KKT points of the nonlinear programming are analyzed. If the solution obtained by the proposed method is a global solution of the nonlinear programming problem, the solution will provide an upper bound on the max-cut value. Then an approximate solution to the max-cut problem is generated from the solution of the nonlinear programming and provides a lower bound on the max-cut value. Numerical experiments and comparisons on some max-cut test problems （small and large size） show that the proposed algorithm is efficient to get the exact solutions for all small test problems andwell satisfied solutions for most of the large size test problems with less calculation costs.

关键词： Max-cut problems Algorithm Feasible direction method Laplacian matrix,Eigenvectors.

One-step green method to prepare progressive burning gun propellant through gradient denitration strategy

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Defence Technology（防务技术） 2023年第4期22卷 135-143页

作者： Shi-ying Li Yu Li Ya-jun Ding Hao liang Zhong-liang xiao School of Chemical Engineering Nanjing University of Science and TechnologyNanjing210094China Key Laboratory of Special Energy Materials(Nanjing University of Science and Technology) Ministry of EducationNanjing210094China

Gradiently denitrated gun propellant(GDGP)prepared by a“gradient denitration”strategy is obviously superior in progressive burning performance to the traditional deterred gun ***,the preparation of GDGP employed a tedious two-step method involving organic solvents,which hinders the large-scale preparation of *** this paper,GDGP was successfully prepared via a novelty and environmentally friendly one-step *** obtained samples were characterized by FT-IR,Raman,SEM and *** results showed that the content of nitrate groups gradiently increased from the surface to the core in the surface layer of GDGP and the surface layer of GDGP exhibited a higher compaction than that of raw gun propellant,with a well-preserved nitrocellulose *** denitration process enabled the propellant surface with regressive energy density and good progressive burning performance,as confirmed by oxygen bomb and closed bomb *** the same time,the effects of different solvents on the component loss of propellant were *** result showed that water caused the least component ***,the stability of GDGP was confirmed by methyl-violet *** work not only provided environmentally friendly,simple and economic preparation of GDGP,but also confirmed the stability of GDGP prepared by this method.

关键词： Gradiently denitrated gun propellant One-step green method Denitration Progressive burning Stability

Stochastic averaging technique for SDOF strongly nonlinear systems with delayed feedback fractional-order PD controller

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Science China(Technological Sciences) 2019年第2期62卷 287-297页

作者： CHEN LinCong liang xiao ZHU WeiQiu ZHAO YaoBing College of Civil Engineering Huaqiao University Departments of Mechanics State Key Laboratory of Fluid Power Transmission and Control Zhejiang University

A stochastic averaging technique is proposed to study the randomly excited single-degree-of-freedom(SDOF) strongly nonlinear systems with delayed feedback fractional-order proportional-derivative(PD) controller. The delayed feedback fractional-order PD control force is approximated by an equivalent non-delay feedback control force combining with a quasi-linear elastic force and a quasi-linear damping force. The averaged It? stochastic differential equation for amplitude of the equivalent nonlinear system is derived by the generalized harmonic functions. The analytical stationary probability density function(PDF) is obtained with solving the reduced Fokker-Planck-Kolmogorov(FPK) equation. Two examples of van der Pol oscillator and RayleighDuffing oscillator are studied to illustrate the application and effectiveness of the proposed method. Numerical results display that the proposed method can yield to the high precision, and the time delay could ruin the control effectiveness, but also even amplifies the response of the system more than that of uncontrolled system. Furthermore, the study finds that the parameters of fractional-order α and time delay may cause the stochastic P-bifurcation. It is indicated that the delayed feedback fractional-order PD controller can offer a potentially effective tool for anti-control of stochastic bifurcation

关键词： αstochastic averaging strongly nonlinear system time delay fractional-order PD^a controller