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Differential equations and Lie group representations

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Frontiers of Mathematics in China 2022年第2期17卷 171-225页

作者： King Fai lai School of Mathematics and Statistics Henan UniversityKaifeng 475004China

We discuss the role of diflterential equations in Lie group representation *** use Kashiwara's pentagon as a reference frame for the real representation theory and then report on some work arising from its p-adic analogue by Emerton,Kisin,Patel,Huyghe,Schmidt,Strauch using Berthelofs theory of arithmetic D-modules and Schneider-Stuhler theory of sheaves on buildings.

关键词： Differential equations Lie groups representation theory arithmetic D-modules flag variety

An Improved Algorithm for Constructing Moving Quadrics from Moving Planes

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Journal of Systems Science & Complexity 2017年第6期30卷 1483-1506页

作者： lai Yisheng CHEN Falai Department of Mathematics Zhejiang Gongshang University Department of Mathematics University of Science and Technology of China

This paper proposes an improved algorithm to construct moving quadrics from moving planes that follow a tensor product surface with no base points, assuming that there are no moving planes of low degree following the surface. These moving quadrics provide an efficient method to implicitize the tensor product surface which outperforms a previous approach by the present authors.

关键词： Implicitization moving plane moving quadric rational surface

A novel ligand-free palladium catalytic system with SO_3H-functional ionic liquids as cocatalyst for amidocarbonylation reaction

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Chinese Chemical Letters 2008年第10期19卷 1175-1178页

作者： Qing Lu Zhao lai lai Wang State Key Laboratory for Oxo Synthesis ＆ Selective Oxidation Lanzhou Institute of Chemical Physics Chinese Academy of Sciences Lanzhou 730000 China Graduate University of Chinese Academy of Sciences Beijing 100039 China

Effects of Lewis acid BF3·OEt2, and BrCnsted acids TsOH, CF3COOH, H3PO4, and HCIO4 as cocatalyst respectively on the ligand-free palladium-catalyzed amidocarbonylation were investigated. SO3H-functional ionic liquids 1-methyl-3-（4-sulfonic acid）butylimidazolium hydrosulfate [MIm（CH2）4803H][HSO4] and 1-methyl-3-（4-sulfonic acid）butylimidazolium triflate [MIm（CH2）4SO3H][OTf] were firstly employed as cocatalysts instead of these Lewis acid and Brφnsted acids. By using a ligand-free and weak corrosive catalyst in situ prepared form PdBr2, LiBr.H2O, and [MIm（CH2）4SO3H][OTf], the arnidocarbo- nylation of benzaldehyde, acetamide, and CO could proceed smoothly and afford N-acetyl-α-phenylglycine with yield of 58% in [C6mim]PF6 medium.

关键词： Amidocarbonylation Palladium Ionic liquids Benzaldehyde N-Acyl-α-amino acid

Time stepping in discontinuous Galerkin method

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Journal of Hydrodynamics 2013年第3期25卷 321-329页

作者： lai Wencong KHAN Abdul A Glenn Department of Civil Engineering Clemson University Clemson S.C. USA

The time discretization in the Discontinuous Galerkin （DG） scheme has been traditionally based on the Total Variation Diminishing （TVD） second-order Runge-Kutta （RK2） scheme. Computational efficiency and accuracy with the Euler Forward （EF） and the TVD second-order RK2 time stepping schemes in the DG method are investigated in this work. Numerical tests are condu- cted with the scalar Burgers equation, 1-D and 2-D shallow water flow equations. The maximum Courant number or time step size required for stability for the EF scheme and RK2 scheme with different slope limiters are compared. Numerical results show that the slope limiters affect the stability requirement in the DG method. The RK2 scheme is generally more diffusive than the EF scheme, and the RK2 scheme allows larger time step sizes. The EF scheme is found to be more efficient and accurate than the RK2 scheme in the DG method in computation.

关键词： Discontinuous Galerkin (DG) method Euler Forward (EF) scheme second-order Runge-Kutta scheme

Transparent soft PDMS eggshell

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Science China(Technological Sciences) 2015年第2期58卷 273-283页

作者： lai YiYu LIU Jing Department of Biomedical Engineering School of Medicine Tsinghua University Beijing Key Laboratory of Cryo Biomedical Engineering and Key Laboratory of Cryogenics Technical Institute of Physics and ChemistryChinese Academy of Sciences

In vivo 3D fluorescent image remains a technological barrier for biologists and clinical scientists although green fluorescent protein(GFP)imaging has long been performed rather well at cellular ***,robust enough portable devices are also challenging lab-on-a-chip advocators who wish their designs to be nurtured by the end *** work is dedicated to propose a conceptually innovated transparent soft PDMS avian eggshell to directly tackle the above two ***,an"egg-on-a-chip"scheme is originally developed and demonstrated by a newly developed PDMS"soft"process *** its ancestor–the conventional"lab-on-a-chip"(LOC)which is basically chemically based,the current"egg-on-a-chip",intrinsically inherited with biological natures,opens a way to integrate biological parts or whole system in a miniature sized *** biomimics system contains much condensed environmental evolutional tensor inside than those of the existing LOC compacted with artificial components which however are quite difficult to incorporate various life factors *** unique advantages,a series of transparent PDMS whole"eggshells"have been fabricated and applied to culture avian embryos up to 17.5 days and chimeric eggshells were engineered on normal *** addition,X-stage embryos were successfully initiated in such system and pre-chorioallantoic membrane was ***,limitation of the present process was interpreted and potential approach to improve it was *** both high optical transparency and engineering subtlety fully integrated together,the present method not only provides an ideal transparent imaging platform for studying functional embryo development including life mystery,but also promises a future strategy for"lab-on-an-egg"technology which may be important in a wide variety of either fundamental or practical areas.

关键词： soft PDMS process method biological mould egg-on-a-chip portable device pre-chorioallantoic membrane biomimics

Oxygen-penetration-induced large hardness enhancement in nanoscale Nb/Ti multilayers

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Acta Metallurgica Sinica(English Letters) 2012年第2期25卷 141-152页

作者： Yuxin ZHAO Wensheng lai Advanced Material Laboratory Department of Materials Science&EngineeringTsinghua UniversityBeijing 100084China

Nb/Ti multilayers with different modulation periods were prepared by magnetron sputtering deposition. Microstructure and mechanical properties were investigated by XRD, SEM and Nanoindentation. It turns out that hardness of samples increases with decreasing modulation wavelength （A） and then dropped at small A. Through scrutinizing other results in literature, we found that the coherent stress rather than modulus mismatch played more important role for hardness enhancement with de- creasing A of the bcc-hcp multilayers. Annealing of samples in low （or high） vacuum at 400 ~C for 30 min led to large （or medium） enhancement of hardness, while the modulated structure was still maintained. It was found that annealing in low vac- uum resulted in oxygen penetration into the multilayers as revealed by auger electron spectroscopy, but hardly changed metallic sheet resistivity. XRD results suggested that some niobium oxides were formed in Nb layers and oxygen distributed intersti- tially in Ti layers. The large hardness enhancement after annealing is mainly due to the strengthening effect from dispersive distribution of nano-scale niobium oxides and interstitial oxygen in the multilayers. In addition, interfaces between adjacent layers were more distinct after annealing which indicated good thermal stability of laminated structure.

关键词： Nb/Ti multilayer Hardness Microstructure Annealing Nanoindentation

Numerical Investigation on the Self-Induced Unsteadiness in Tip Leakage Flow of a Micro-Axial Fan Rotor

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Journal of Thermal Science 2015年第4期24卷 334-343页

作者： CHEN Jinxin lai Huanxin School of Mechanical and Power Engineering East China University of Science and Technology

The self-induced unsteadiness in tip leakage flow(TLF)of a micro-axial fan rotor is numerically studied by solving Reynolds-averaged Navier-Stokes *** micro-axial fan,which is widely used in cooling systems of electronic devices,has a tip clearance of 6%of the axial chord length of the *** the design rotation speed,four cases near the peak efficiency point(PEP)with self-induced unsteadiness and four steady cases which have much weaker pressure fluctuations are *** the"interface"separating the incoming main flow and the TLF defined by Duet al.[1],an explanation based on the propagation of the low energy spot and its multi-passing through the high gradient zone of the relative total pressure,is proposed to clarify the originating mechanism of the *** the operating points near the PEP,the main flow is weaker than the TLF and the interface moves *** low energy spot which propagates along in the close behind of the interface has opportunity to circulate in the circumferential direction and passes through the sensitive interfaces several times,a slight perturbation therefore may be magnified significantly and develops into the self-induced *** explanation is demonstrated by numerical results.

关键词： micro-axial fan tip leakage flow (TLF) self-induced unsteadiness secondary flow mechanism.

Computation model and improved ACO algorithm for p//T

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Journal of Systems Engineering and Electronics 2009年第6期20卷 1336-1343页

作者： Yi Yang lai Jieling School of Information Science & Technology Sun Yat-sen Univ. Guangzhou 510275 P. R. China

Scheduling jobs on parallel machines to minimize the total tardiness（p//T） is proved to be NP hard.A new ant colony algorithm to deal with p//T（p//T ACO） is addressed, and the computing model of mapping p//T to the ant colony optimization environment is ***, based on the academic researches on p//T, some new properties used in the evolutionary computation are analyzed and *** theoretical analysis and comparative experiments demonstrate that p//T ACO has much better performance and can be used to solve practical large scale problems efficiently.

关键词： scheduling evolutionary computation ant colony optimization.

Analytical solutions for elastic binary nanotubes of arbitrary chirality

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Acta Mechanica Sinica 2016年第6期32卷 1046-1057页

作者： lai Jiang Wanlin Guo State Key Laboratory of Mechanics and Control for Mechanical Structures and Key Laboratory for Intelligent Nano Materials and Devices (MOE) Nanjing University of Aeronautics and Astronautics

Analytical solutions for the elastic properties of a variety of binary nanotubes with arbitrary chirality are obtained through the study of systematic molecular mechanics. This molecular mechanics model is first extended to chiral binary nanotubes by introducing an additional out-of-plane inversion term into the so-called stick-spiral model, which results from the polar bonds and the buckling of binary graphitic crystals. The closed-form expressions for the longitudinal and circumferential Young's modulus and Poisson's ratio of chiral binary nanotubes are derived as functions of the tube diameter. The obtained inversion force constants are negative for all types of binary nanotubes, and the predicted tube stiffness is lower than that by the former stick-spiral model without consideration of the inversion term, reflecting the softening effect of the buckling on the elastic properties of binary nanotubes. The obtained properties are shown to be comparable to available density functional theory calculated results and to be chirality and size sensitive. The developed model and explicit solutions provide a systematic understanding of the mechanical performance of binary nanotubes consisting of III-V and II-VI group elements.

关键词： Binary nanotubes Elastic properties Molecular mechanics Chirality Analytical solutions