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The Variable-Step L1 Scheme Preserving a Compatible Energy Law for Time-Fractional Allen-Cahn Equation

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Numerical Mathematics(Theory,Methods and Applications) 2022年第4期15卷 1128-1146页

作者： hong-lin liao Xiaohan Zhu Jindi Wang MIIT Key Laboratory of Mathematical Modelling and High Performance Computing of Air Vehicles Nanjing 211106P.R.China School of Mathematics Nanjing University of Aeronautics and Astronautics211106P.R.China School of Mathematics and Computational Science Xiangtan UniversityXiangtan 411105P.R.China

In this work,we revisit the adaptive L1 time-stepping scheme for solving the time-fractional Allen-Cahn equation in the Caputo’s *** L1 implicit scheme is shown to preserve a variational energy dissipation law on arbitrary nonuniform time meshes by using the recent discrete analysis tools,i.e.,the discrete orthogonal convolution kernels and discrete complementary convolution *** the discrete embedding techniques and the fractional Gronwall inequality are applied to establish an L^(2)norm error estimate on nonuniform time *** adaptive time-stepping strategy according to the dynamical feature of the system is presented to capture the multi-scale behaviors and to improve the computational performance.

关键词： Time-fractional Allen-Cahn equation adaptive L1 scheme variational energy dissipation law orthogonal convolution kernels complementary convolution kernels

Positive definiteness of real quadratic forms resulting from the variable-step L1-type approximations of convolution operators

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Science China Mathematics 2024年第2期67卷 237-252页

作者： hong-lin liao Tao Tang Tao Zhou School of Mathematics Nanjing University of Aeronautics and AstronauticsNanjing 211106China Division of Science and Technology BNU-HKBU United International CollegeZhuhai 519087China SUSTech International Center for Mathematics Shenzhen 518055China NCMIS&LSEC Institute of Computational Mathematics and Scientific/Engineering ComputingAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China

The positive definiteness of real quadratic forms with convolution structures plays an important rolein stability analysis for time-stepping schemes for nonlocal operators. In this work, we present a novel analysistool to handle discrete convolution kernels resulting from variable-step approximations for convolution *** precisely, for a class of discrete convolution kernels relevant to variable-step L1-type time discretizations, weshow that the associated quadratic form is positive definite under some easy-to-check algebraic conditions. Ourproof is based on an elementary constructing strategy by using the properties of discrete orthogonal convolutionkernels and discrete complementary convolution kernels. To our knowledge, this is the first general result onsimple algebraic conditions for the positive definiteness of variable-step discrete convolution kernels. Using theunified theory, we obtain the stability for some simple nonuniform time-stepping schemes straightforwardly.

关键词： discrete convolution kernels positive definiteness variable time-stepping orthogonal convolution kernels complementary convolution kernels

An Energy Stable Filtered Backward Euler Scheme for the MBE Equation with Slope Selection

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Numerical Mathematics(Theory,Methods and Applications) 2023年第1期16卷 165-181页

作者： Jiexin Wang hong-lin liao Ying Zhao School of Mathematics Nanjing University of Aeronautics and AstronauticsNanjing 211106China Key Laboratory of Mathematical Modelling and High Performance Computing of Air Vehicles(NUAA) MIITNanjing 211106China

As a promising strategy to adjust the order in the variable-order BDF algorithm,a time filtered backward Euler scheme is investigated for the molecular beam epitaxial equation with slope *** temporal second-order convergence in the L^(2)norm is established under a convergence-solvability-stability(CSS)-consistent time-step *** CSS-consistent condition means that the maximum stepsize limit required for convergence is of the same order to that for solvability and stability(in certain norms)as the small interface parameterε→0^(+).Similar to the backward Euler scheme,the time filtered backward Euler scheme preserves some physical properties of the original problem at the discrete levels,including the volume conservation,the energy dissipation law and L^(2)norm *** tests are included to support the theoretical results.

关键词： MBE model time filter energy dissipation law error estimate

Analysis of the second-order BDF scheme with variable steps for the molecular beam epitaxial model without slope selection

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Science China Mathematics 2021年第5期64卷 887-902页

作者： hong-lin liao Xuehua Song Tao Tang Tao Zhou Department of Mathematics Nanjing University of Aeronautics and AstronauticsNanjing 211101China Department of Mathematics and International Center for Mathematics Southern University of Science and TechnologyShenzhen 518055China Division of Science and Technology BNU-HKBU United International CollegeZhuhai 519087China NCMIS&LSEC Institute of Computational Mathematics and Scientific Engineering ComputingAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China

In this work,we are concerned with the stability and convergence analysis of the second-order backward difference formula(BDF2)with variable steps for the molecular beam epitaxial model without slope *** first show that the variable-step BDF2 scheme is convex and uniquely solvable under a weak time-step *** we show that it preserves an energy dissipation law if the adjacent time-step ratios satisfy r_(k):=τ_(k)/τ_(k-1)<***,with a novel discrete orthogonal convolution kernels argument and some new estimates on the corresponding positive definite quadratic forms,the L^(2)norm stability and rigorous error estimates are established,under the same step-ratio constraint that ensures the energy stability,i.e.,0

关键词： molecular beam epitaxial growth variable-step BDF2 scheme discrete orthogonal convolution kernels energy stability convergence analysis

Analysis of L1-Galerkin FEMs for Time-Fractional Nonlinear Parabolic Problems

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Communications in Computational Physics 2018年第6期24卷 86-103页

作者： Dongfang Li hong-lin liao Weiwei Sun Jilu Wang Jiwei Zhang School of Mathematics and Statistics Huazhong University of Science and TechnologyWuhan430074China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and TechnologyWuhan 430074China Department of Mathematics City University of Hong KongKowloonHong Kong Department of Mathematics Nanjing University of Aeronautics and AstronauticsNanjing211106China Department of Scientific Computing Florida StateUniversityTallahasseeFL 32306USA Beijing Computational Science Research Center Beijing 100094China.

This paper is concerned with numerical solutions of time-fractional nonlinear parabolic problems by a class of L1-Galerkin finite element *** analysis of L1 methods for time-fractional nonlinear problems is limited mainly due to the lack of a fundamental Gronwall type *** this paper,we establish such a fundamental inequality for the L1 approximation to the Caputo fractional *** terms of the Gronwall type inequality,we provide optimal error estimates of several fully discrete linearized Galerkin finite element methods for nonlinear *** theoretical results are illustrated by applying our proposed methods to the time fractional nonlinear Huxley equation and time fractional Fisher equation.

关键词： Time-fractional nonlinear parabolic problems L1-Galerkin FEMs Error estimates discrete fractional Gronwall type inequality linearized schemes

Near-infrared brain functional characteristics of mild cognitive impairment with sleep disorders

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World Journal of Psychiatry 2025年第1期15卷 106-116页

作者： Heng liao Sha liao Yu-Jiao Gao Xi Wang Li-hong Guo Su Zheng Wu Yang Yi-Nan Dai Sleep Psychosomatic Medicine Center Taihe Hospital of Shiyan CityAffiliated Hospital of Hubei University of MedicineShiyan 442000Hubei ProvinceChina Department of Integrated Chinese and Western Medicine Taihe Hospital of Shiyan CityAffiliated Hospital of Hubei University of MedicineShiyan 442000Hubei ProvinceChina Department of Orthopaedics Taihe Hospital of Shiyan CityAffiliated Hospital of Hubei University of MedicineShiyan 442000Hubei ProvinceChina Department of Rehabilitation Taihe Hospital of Shiyan CityAffiliated Hospital of Hubei University of MedicineShiyan 442000Hubei ProvinceChina

BACKGROUND Mild cognitive impairment(MCI)has a high risk of progression to Alzheimer’s *** disease is often accompanied by sleep disorders,and whether sleep disorders have an effect on brain function in patients with MCI is *** To explore the near-infrared brain function characteristics of MCI with sleep *** A total of 120 patients with MCI(MCI group)and 50 healthy subjects(control group)were *** subjects underwent the functional near-infrared spec-troscopy *** baseline data,Mini-Mental State Examination,Montreal Cognitive Assessment scale,fatigue severity scale(FSS)score,sleep parameter,and oxyhemoglobin(Oxy-Hb)concentration and peak time of functional near-infrared spectroscopy test during the task *** relationship between Oxy-RESULTS Compared with the control group,the FSS score of the MCI group was higher(t=11.310),and the scores of Pittsburgh sleep quality index,sleep time,sleep efficiency,nocturnal sleep disturbance,and daytime dysfunction were higher(Z=-10.518,-10.368,-9.035,-10.661,-10.088).Subjective sleep quality and total sleep time scores were lower(Z=-11.592,-9.924).The sleep efficiency of the MCI group was lower,and the awakening frequency,rem sleep latency period,total sleep time,and oxygen desaturation index were higher(t=5.969,5.829,2.887,3.003,5.937).The Oxy-Hb concentration at T0,T1,and T2 in the MCI group was lower(t=14.940,11.280,5.721),and the peak time was higher(t=18.800,13.350,9.827).In MCI patients,the concentration of Oxy-Hb during T0 was negatively correlated with the scores of Pittsburgh sleep quality index,sleep time,total sleep time,and sleep efficiency(r=-0.611,-0.388,-0.563,-0.356).It was positively correlated with sleep efficiency and total sleep time(r=0.754,0.650),and negatively correlated with oxygen desaturation index(r=-0.561)and FSS score(r=-0.526).All comparisons were P<*** Patients with MCI and sleep disorders have lower near-infrared brain function than norm

关键词： Mild Cognitive impairment Sleep disorders Near-infrared Brain functional Characteristics

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聚丙烯酸钠制备吸水膨胀天然橡胶的研究

弹性体 2010年第1期20卷 53-56页

作者：林鸿基廖双泉佘晓东廖建和海南大学材料与化工学院海南儋州571737

采用氧化还原引发体系,引发丙烯酸钠聚合并接枝到天然橡胶分子链上,并采用硫磺硫化体系进行硫化,制备高性能吸水橡胶。通过考察单体用量和多种配合剂对吸水橡胶的吸水和力学性能的影响,得出单体用量的增加引起吸水橡胶的物理机械性能的... 详细信息

采用氧化还原引发体系,引发丙烯酸钠聚合并接枝到天然橡胶分子链上,并采用硫磺硫化体系进行硫化,制备高性能吸水橡胶。通过考察单体用量和多种配合剂对吸水橡胶的吸水和力学性能的影响,得出单体用量的增加引起吸水橡胶的物理机械性能的降低,但吸水性能得到了提高。FTIR分析可知,产物是天然橡胶和聚丙烯酸钠的接枝共聚物。TG分析表明天然橡胶和聚丙烯酸钠的接枝共聚物的热力学稳定性得到很大程度的提高。

关键词：吸水膨胀天然橡胶聚丙烯酸钠接枝

The Involvement of Caveolae/caveolin-1 on Activation of ERK1/2 Induced by AngiotensinⅡin Vascular Smooth Muscle Cells

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The Involvement of Caveolae/caveolin-1 on Activation of ERK1...

Smoother and Bayesian filter based semi-codeless tracking of dual-frequency GPS signals

第十五届国际药理学大会

作者： Qin Li. WANG Qian - lei. ZHU Bing - yang. HUANG hong - lin. liao Du-an - fang . Division of Pharmacoproteomics. Institute of Pharmacy and Pharmacology. Nanhua University. Hengyang 421001. China

＜正＞ AIM To investigate the effects of caveolae/ caveolin - 1 on late - phage activation of ERK1/2 stimulated by angiotensin Ⅱ （AngⅡ ） in cultured vascular smooth muscle cells （VSMCs）. METHODS Cultured rat aortic VSMCs were challenged to Ang Ⅱ100 nmol/L for 2, 5. 10, 30, 60, 120, 240, 360, and 480 min. Western blot was used to analyze the expression of caveolin - 1 and p - ERK1/2. RESULTS Western blot showed that Ang stimulated ERK1/2 activation with two peaks at 5 min （early - phage） and 4 hr （late - phage） respectively. The late -phage activation of ERK1/2 was accompanied by a significant decrease of caveolin- 1 expression. Transfection of Antisense caveolin- 1 oligonucleotides enhanced Ang n - induced late - phage activation of ERK1/2. Furthermore, when caveolae structure was disrupted by Nystatin, Ang II - stimulated ERK1/2 activity was obviously attenuated. PD98059, an inhibitor of MEK - 1, decreased ERK1/2 activity without effect on caveolin- 1 expression. CONCLUSION Cave-olae/caveolin - 1 was involved in regulation of late - phage ERK1/2 activation induced by Ang @@@ in VSMC.

关键词： AngiotensinⅡ. ERK1/2. Caveolm-1 VSMC.

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Science in China(Series F) 2006年第4期49卷 533-544页

作者： liao Bingyu YUAN hong lin Baojun Academy of Opto-Electronics Chinese Academy of Sciences Beijing 100080 China

To precisely determine the integrated orbit of the Chinese manned spacecraft mission, a smoother and Bayesian filter based technique for optimum semi-codeless tracking of the P（Y） code on dual-frequency GPS signals has been advanced. This signal processing technique has been proven effective and robust for affording access to dual-frequency GPS signals. This paper introduces the signal dynamics and measurement models, describes the W o D bit estimation method, and corrects the mistakes of direct estimation of W bit in current semi-codeless tracking. Median filter is chosen as a smoother to find the best measurements at the current time among the history and current information. The Bayesian filter is used to track the L2 P（Y） code phase and L2 carrier phase recursively.

关键词： GPS P(Y) code W code A/S technology adapted median filter Bayesian filter.