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Communications in Theoretical Physics 2007年第3X期48卷 487-490页

作者： QIAN Xian-Min hon-wah tam Department of Physics Shaoxing College of Arts and Sciences Shaoxing 312000 China Department of Physics Shanghai Jiao Tong University Shanghai 200030 China Department of Computer Science Hong Kong Baptist University Hong Kong China

In this paper, we obtain a 1＋1 dimensional integrable differential-difference model for the sine-Gordon equation by Hirota＇s discretization method. A bilinear Backlund transformation and the associated Lax pair are ... 详细信息

关键词： sine-Gordon equation Hirota's discretization method Backlund transformation Lax pair

Generation of Nonlinear Evolution Equations by Reductions of the Self-Dual Yang–Mills Equations

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Communications in Theoretical Physics 2014年第2期61卷 203-206页

作者：张玉峰 hon-wah tam College of Sciences China University of Mining and Technology Department of Computer Science Hong Kong Baptist University

With the help of some reductions of the self-dual Yang Mills(briefly written as sdYM) equations, we introduce a Lax pair whose compatibility condition leads to a set of(2 + 1)-dimensional equations. Its first reduction gives rise to a generalized variable-coefficient Burgers equation with a forced term. Furthermore, the Burgers equation again reduces to a forced Burgers equation with constant coefficients, the standard Burgers equation, the heat equation,the Fisher equation, and the Huxley equation, respectively. The second reduction generates a few new(2 + 1)-dimensional nonlinear integrable systems, in particular, obtains a kind of(2 + 1)-dimensional integrable couplings of a new(2 + 1)-dimensional integrable nonlinear equation.

关键词： self-dual Yang-Mills equation Lax pair (2+ 1)-dimensional integrable system integrable coupling

One variant of a （2 ＋ 1）-dimensional Volterra system and its （1 ＋ 1）-dimensional reduction

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Frontiers of Mathematics in China 2013年第5期8卷 1085-1097页

作者： Yingnan ZHANG Yi HE hon-wah tam LSEC Institute of Computational Mathematics and Scientific Engineering ComputingAcademy of Mathematics and System Sciences Chinese Academy of SciencesBeijing 100190 China University of Chinese Academy of Sciences Beijing 100049 China Wuhan Institute of Physics and Mathematics Chinese Academy of Sciences Wuhan 430071 China Department of Computer Science Hong Kong Baptist University Hong Kong China

A new system is generated from a multi-linear form of a （2＋1）- dimensional Volterra system. Though the system is only partially integrable and needs additional conditions to possess two-soliton solutions, its （1＋1）- dimensional reduction gives an integrable equation which has been studied via reduction skills. Here, we give this （1＋1）-dimensional reduction a simple bilinear form, from which a Backlund transformation is derived and the corresponding nonlinear superposition formula is built.

关键词： Integrability soliton solution Bgcklund transformation (BT),nonlinear superposition formula

A Bilinear Bcklund Transformation and Lax Pair for a(1+1)-Dimensional Differential-Difference sine-Gordon Equation

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Communications in Theoretical Physics 2007年第9期 487-490页

作者： hon-wah tam Department of Computer Science Hong Kong Baptist UniversityHong KongChina

In this paper,we obtain a 1+1 dimensional integrable differential-difference model for the sine-Gordonequation by Hirota’s discretization method.A bilinear Bklund transformation and the associated Lax pair are alsopr... 详细信息

关键词： sine-Gordon equation Hirota’s discretization method Bcklund transformation Lax pair

Coupled modified Kd V equations, skew orthogonal polynomials, convergence acceleration algorithms and Laurent property

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Science China Mathematics 2018年第6期61卷 1063-1078页

作者： Xiangke Chang Yi He Xingbiao Hu Shihao Li hon-wah tam Yingnan Zhang LSEC ICMSEC Academy of Mathematics and Systems ScienceChinese Academy of Sciences School of Mathematical Sciences University of Chinese Academy of Sciences Wuhan Institute of Physics and Mathematics Chinese Academy of Sciences Department of Computer Science Hong Kong Baptist University School of Mathematical Sciences Nanjing Normal University

In this paper, we show that the coupled modified Kd V equations possess rich mathematical structures and some remarkable properties. The connections between the system and skew orthogonal polynomials,convergence accel... 详细信息

关键词： integrable system skew orthogonal polynomial convergence acceleration algorithm Laurent prop-erty

Nucleoside modified mRNA-lipid nanoparticles as a new delivery platform for the repair of the injured spinal cord

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Neural Regeneration Research 2025年第8期20卷 2311-2312页

作者： Krisztián Pajer tamás Bellák Antal Nógrádi Department of Anatomy Histology and EmbryologyAlbert Szent-Györgyi Medical SchoolUniversity of SzegedSzegedHungary

Spinal cord injury and treatment opportunities:The adult mammalian spinal cord has a very limited capacity for spontaneous regeneration due to various intrinsic molecular and cellular *** the spinal cord neurons have the capacity to regenerate their axons,the expression of growth inhibitory factors,lack or suppression of proper guidance cues,and profound inflammatory responses do not permit successful regeneration(Khyeam et al.,2021).

关键词： injured capacity modified

Integrable discretization of soliton equations via bilinear method and Backlund transformation

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Science China Mathematics 2015年第2期58卷 279-296页

作者： ZHANG Ying Nan CHANG Xiang Ke HU Juan HU Xing Biao tam hon-wah Institute of Computational Mathematics and Scientific Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences School of Mathematical Sciences University of Chinese Academy of Sciences Department of Applied Mathematics Zhejiang University of Technology Department of Computer Science Hong Kong Baptist University

We present a systematic procedure to derive discrete analogues of integrable PDEs via Hirota’s bilinear *** approach is mainly based on the compatibility between an integrable system and its B¨acklund *** apply this procedure to several equations,including the extended Korteweg-deVries(Kd V)equation,the extended Kadomtsev-Petviashvili(KP)equation,the extended Boussinesq equation,the extended Sawada-Kotera(SK)equation and the extended Ito equation,and obtain their associated semidiscrete *** the continuum limit,these differential-difference systems converge to their corresponding smooth *** these new integrable systems,their B¨acklund transformations and Lax pairs are derived.

关键词： integrable discretization bilinear method Backlund transformation

Flat-end tool orientation based on rotation-minimizing frame

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Advances in Manufacturing 2019年第3期7卷 257-269页

作者： Xiang Zou hon-Yuen tam Hai-Yin Xu Ke Shi School of Computer Science and Technology Huazhong University of Science and TechnologyWuhan 430074People's Republic of China College of Science and Engineering Department of Mechanical EngineeringCity University of Hong KongHong KongPeople's Republic of China

Well-designed tool orientation is crucial for the quality execution of five-axis machining with flat-end *** orientation can be specified in terms of tool inclination and tool tilt *** a given surface path,these aspects need to be specified for each cutter contact point along the path,because poor tool orientation choice can cause large axial acceleration of the machine tool,leading to inferior quality of the machined *** rotation-minimizing frame aims to reduce unnecessary frame rotation during *** concept has been adopted to develop tool orientation methods that allow variation in the inclination angle,the tilt angle,and both the inclination and tilt *** intention is to reduce unnecessary rotation of the tool frame as the tool follows a specified *** was conducted in the context of five-axis flat-end tool *** on these methods,tool orientation was planned along surface paths of a torus,sphere,and *** in tool orientation were always *** the perspective of reducing tool orientation changes and axial acceleration,it was demonstrated that simultaneous variation of the inclination and tilt angles based on rotation minimization provided the best results.

关键词： Five-axis machining Tool orientation Rotation-minimizing frame Numerical control

Tool Orientation Optimization Based on Spatial Tractrix Method for Five-Axis CNC Machining with Ball End Cutters

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Communications in Mathematics and Statistics 2022年第4期10卷 705-737页

作者： Xiang Zou Ke Shi Hai-Yin Xu hon-yuen tam School of Computer Science and Technology Huazhong University of Science and TechnologyWuhanPeople’s Republic of China Department of Mechanical Engineering College of Science and EngineeringCity University of Hong KongKowloonHong KongPeople’s Republic of China

When milling part surfaces with a ball-end tool in 5-axis CNC machining,maintaining a constant cutting speed by keeping a fixed inclination angle between the tool axis and surface normal is crucial to ensure safe operation and achieve high quality of the machined *** this constraint,the variation of tool orientation is expected to be“smoothest possible”to reduce the angular speed of the rotary axes for the efficient and robust *** address this issue,the spatial tractrix which is the extension of classic tractrix is presented to establish the geometry model of the tool orientation kinematics in the part coordinate *** proposed model describes the relations between the tilt angle and the variation of ball-end tool *** spatial tractrix-based methods,synchronizing tractrix-based method and equilibrating tractrix-based method,are developed to minimize the variation of tool orientation by controlling the variation of tilt *** methods are used to plan the tool orientation on a part surface modeled by a bicubic spline *** performance evaluation carried by intense simulations demonstrates the equilibrating tractrix-based method provide the best results in most cases compared with the existing differential geometry-based methods such as the tractrix-based method and parallel transport *** synchronizing tractrix-based method works well in some special cases.

关键词： Five-axis machining Ball-end tool orientation Spatial tractrix Tool orientation optimization

Edge effect of optical surfacing process with different data extension algorithms

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Frontiers of Optoelectronics 2014年第1期7卷 77-83页

作者： Yang LIU Haobo CHENG Zhichao DONG hon-Yuen tam School of Optoelectronics Beijing Institute of Technology Beijing 100081 China Department of Mechanical and Biomedical Engineering City University of Hong Kong Hong Kong China

This study presents a strategy which integrates extra polishing path （EPP） and error map extension to weaken the edge effect in the ultraprecise optical surfacing process. Different data extension algorithms were pre- sented and analyzed. The neighbor-hood average can be selected as the frequently-used method, as it has not bad precision and time-saving performance for most surface forms through the simulation results and practical experi- ment. The final error map was obtained, its peak-to-valley （PV） was 0.2732 and root mean square （RMS） was 0.0282 （2 = 632.8nm）. The edge effect was weakened and suppressed well through the experiment.

关键词： edge effect convergence rate extensionalgorithms