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The Faber Operator Acting on BMOA,BMO-Teichmüller Space and Chord-arc Curves

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Acta Mathematica Sinica,English Series 2024年第10期40卷 2359-2387页

作者： Tai liang liu Yu liang SHEN Department of Mathematics Soochow UniversitySuzhou 215006P.R.China

After reviewing Grunsky operator and Faber operator acting on Dirichlet space,we discuss the boundedness of Faber operator on BMOA,a new subject which turns out to be closely related to the BMO theory of the universal Teichmüller *** particular,we show that the Faber operator acts as a bounded operator on BMOA if the symbol conformal map stays nearly to the base point in the BMO-Teichmüller ***,we obtain several results on quasiconformal mappings,BMOTeichm¨uller space and chord-arc curves as *** by-products,this provides a complex analysis approach to the boundedness of the Cauchy integral acting on BMO functions on a chord-arc curve near to the unit circle in the BMO-Teichmüller space.

关键词： Faber operator quasiconformal mapping quasicircle BMO-Teichmüller space chord-arc curve Grunsky operator BMO BMOA Carleson measure Cauchy integral

On Discreteness of the Hopf Equation

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Acta Mathematicae Applicatae Sinica 2008年第3期24卷 423-440页

作者： Hai-liang liu Iowa State University USA

The principle aim of this essay is to illustrate how different phenomena is captured by different discretizations of the Hopf equation and general hyperbolic conservation laws. This includes dispersive schemes, shock capturing schemes as well as schemes for computing multi-valued solutions of the underlying equation. We introduce some model equations which describe the behavior of the discrete equation more accurate than the original equation. These model equations can either be conveniently discretized for producing novel numerical schemes or further analyzed to enrich the theory of nonlinear partial differential equations.

关键词： Hopf equation dispersive scheme shock capturing schemes multi-valued solutions level set equation

Steel-Making and Continuous/Ingot Casting Scheduling of Mixed Charging Plan Based on Batch Splitting Policy

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Journal of Iron and Steel Research International 2012年第4期19卷 17-21页

作者： liu Wei SUN liang-liang State Key Laboratory of Synthetical Automation for Process Industries Northeastern UniversityShenyang 110004 Liaoning China

For steel-making and continuous/ingot casting are the key processes of modern iron and steel enterprises, this paper proposes a batch splitting schedule policy to solve continuous and ingot casting schedule of mixed whole/ half charging plan for steel making. First establish the model of continuous and ingot casting schedule of mixed whole/half charging plan according to the complex constraints. Then solve this model by heuristic algorithm. Finally use actual data to prove the proposed algorithmrs validity and analyze the application result in steel plant.

关键词： continuous/ingot casiing whole/half charging batch splitting policy scheduling

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An Effective Description of Electron Correlation in the Green Function Approach

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Chinese Physics Letters 2013年第4期30卷 161-165页

作者： liu Yu-liang Department of Physics Renmin University of ChinaBeijing 100872

Beyond the usual many body perturbation theory,with the eigenfunctional theory,we directly calculate the correlation function produced by the Coulomb interaction of electrons in the equation of one-electron Green function,and give the general expression of the non-local effective interaction potential in a Hartree-type potential,which is absent in all previous many body perturbation *** effective interaction potential originates from the quantum many body effect of the system,and it cannot be obtained directly by the usual perturbation expression ***,using theoretical models,we demonstrate that this effective interaction potential can be used to characterize the electron correlation strength of the system.

关键词： perturbation interaction potential

A sequence pulse counting method for shape measurement in dual-beam speckle interferometry

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Science China(Physics,Mechanics & Astronomy) 2011年第4期54卷 640-646页

作者： liu liang LI XiDe Department of Engineering Mechanics Key Laboratory of Applied Mechanics Tsinghua University Beijing 100084 China

A temporal approach to fast shape measurement is *** principle,the rotational object method is used in combination with the sequence pulse counting method (SPCM) to determine the height of the object through calculating the related *** specimens are tested to demonstrate the validity of the *** is an object covered by a Chinese character (tea) with a height variety of 0.3 mm,and the other is an object surface with a relatively large fluctuation of 3.5 *** experimental results are compared with mechanical *** axis shifting method is also proposed to determine shapes with relatively large *** of such parameters on the height measurement as incident angle of the dual light beams,tilting angle of the object,and azimuth angle of the measured point are discussed as well.

关键词： shape measurement profilometry temporal speckle pattern interferometry phase measurement

Organocopper(Ⅲ)Compounds with Well-defined Structures Undergo Reductive Elimination to Form C-C or C-Heteroatom Bonds

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Chinese Journal of Chemistry 2018年第12期36卷 1213-1221页

作者： liang liu Zhenfeng Xi Beijing National Laboratory for Molecular Sciences (BNLMS) Key Laboratory of Bioorganic Chemistry and Molecular Engineering of Ministry of Education/College of ChemistryPeking UniversityBeijing 100871China

Reductive elimination around Cu(III) atom arises an increasing attention, since this organometallic pathway has been often proposed in a range of Cu‐based reactions. However, due to limited organocopper(III) compounds with well‐defined structures, this elementary reaction still remains an extremely challenging issue. In this review, structurally well‐defined organocopper(III) compounds are mainly divided into three classes based on their ligands: perfluoromethyl Cu(III) compounds, macrocyclic ligand‐based aryl‐Cu(III) compounds, and spiro organocopper(III) compounds chelated by bidentate ligands. The majority of organocopper(III) compounds display the typical square planar geometry. There also exist a few penta‐coordinated organocopper(III) complexes, which share a weak apical Cu‐L bond. In order to form a cis Cu(III)–C and Cu(III)–Nu bonding geometry required for reductive elimination, the re‐arrangement of coordination modes around tetra‐coordinated Cu(III) atoms is necessary. For the aryl‐Cu(III) cationic complexes with one Cu(III)–C bond, the re‐arrangement is triggered by the coordination of the fifth ligand (solvent or nucleophiles), while for the tetra‐carbon‐coordinated organocuprate(III) compounds, the process might be realized via the cleavage of one Cu(III)–C bond by attack of electrophiles. Stoichiometric and catalytic reactions involving well‐defined organocopper(III) compounds to form C—C or C–heteroatom bonds are discussed to support their intermediacy.

关键词： structure elucidation copper reactive intermediate organocopper(III) organocuprate(III) reductive elimination

On Double Degenerate Quasilinear Parabolic Variational Inequalities

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Acta Mathematicae Applicatae Sinica 2013年第4期29卷 861-868页

作者： Gui-fang liu Yi-liang liu Department of Mathematics Hunan City University College of Sciences Guangxi University for Nationalities

We deal with the existence of weak solutions of double degenerate quasilinear parabolic inequalities with a Signorini-Dirichlet-Neumann type mixed boundary condition, which may degenerate in certain subset of the boundary or on a segment in the interior of the domain and in time. The main tools in our study are the maximM monotone property of the derivative operator with zero-initial valued conditions and the theory of pseudomonotone perturbations of maximal monotone mappings.

关键词： double degeneration quasilinear parabolic variational inequalities existence results

Modal parameter determination and chatter prediction for blade whirling: a comparative study based on symmetric and asymmetric FRF

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Advances in Manufacturing 2021年第1期9卷 145-159页

作者： Lu-Yi Han Ri-liang liu Xin-Feng liu School of Mechanical Engineering Shandong UniversityJinan 250061People's Republic of China Key Laboratory of High Efficiency and Clean Mechanical Manufacture Shandong UniversityJinan 250061People's Republic of China National Demonstration Center for Experimental Mechanical Engineering Education Shandong UniversityJinan 250061People's Republic of China

Whirling has been adopted for the cost-effective machining of blade-shape components in addition to traditional end milling and flank milling *** satisfy the requirements of rotary forming in the blade whirling process,the workpiece must be clamped at both ends in suspension and rotated slowly during machining,which complicates the *** study aims to identify the dynamic characteristics within the blade whirling operation and present strategies for stability *** this study,the dynamic characteristics of a whirling system are modeled by assuming symmetric and asymmetric *** prediction frequency response function(FRF)results are compared with experimental ***,semi-discretization stability lobe diagrams(SLDs)obtained using the dynamic parameters of these models are investigated *** results show that the asymmetric model is more suitable for describing the whirling system,whereas the symmetric model presents limitations associated with the frequency range and location of measuring ***,a set of airfoil propeller blade whirling operations is conducted to verify the prediction accuracy.

关键词： Whirling Asymmetric frequency response function(FRF) Stability lobe diagrams(SLD) Semi-discretization method

Role of platelet-derived extracellular vesicles in traumatic brain injury-induced coagulopathy and inflammation

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Neural Regeneration Research 2022年第10期17卷 2102-2107页

作者： liang liu Quan-Jun Deng Department of Neurosurgery Tianjin Institute of NeurologyTianjin Medical University General HospitalTianjinChina

Extracellular vesicles are composed of fragments of exfoliated plasma membrane,organelles or nuclei and are released after cell activation,apoptosis or ***-derived extracellular vesicles are the most abundant type of extracellular vesicle in the blood of patients with traumatic brain *** laboratory and clinical evidence shows that platelet-derived extracellular vesicles play an important role in coagulopathy and inflammation after traumatic brain *** review discusses the recent progress of research on platelet-derived extracellular vesicles in coagulopathy and inflammation and the potential of platelet-derived extracellular vesicles as therapeutic targets for traumatic brain injury.

关键词： angiogenesis clotting factors coagulopathy delivery inflammation platelet-derived extracellular vesicles review target traumatic brain injury