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Existence and Uniqueness of Solutions of Surface Reconstruction Problem

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Acta Mathematicae Applicatae Sinica 2011年第2期27卷 263-276页

作者： Zhu-cui Jing guo-liang xu LSEC Institute of Computational Mathematics Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 China

Surface reconstruction from scattered data is an important problem in such areas as reverse engineering and computer aided design. In solving partial differential equations derived from surface reconstruction problems, level-set method has been successfully used. We present in this paper a theoretical analysis on the existence and uniqueness of the solution of a partial differential equation derived from a model of surface recon- struction using the level-set approach. We give the uniqueness analysis of the classical solution. Results on the existence and uniqueness of the viscosity solution are also established.

关键词： existence and uniqueness viscosity solution surface reconstruction

TETRAHEDRAL C^m INTERPOLATION BY RATIONAL FUNCTIONS

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Journal of Computational Mathematics 2001年第2期19卷 131-138页

作者： guo-liang xu Chuan I Chu Wei-min xue State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering ComputingAcademy of Mathematics an d Systems SciencesChinese Academy of SciencesBeijing 100080China Department of Mathematics Hong Kong Baptist UniversityKowloonHong Kong

A general local C-m(m greater than or equal to 0) tetrahedral interpolation scheme by polynomials of degree 4m + 1 plus low order rational functions from the given data is proposed. The scheme can have either 4m + 1 order algebraic precision if C-2m data at vertices and C-m data on faces are given or k + E[k/3] + 1 order algebraic precision if C-k (k less than or equal to 2m) data are given at vertices. The resulted interpolant and its partial derivatives of up to order m are polynomials on the boundaries of the tetrahedra.

关键词： C-m interpolation rational functions tetrahedra

A Geometric Flow Approach for Region-based Image Segmentation-theoretical Analysis

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Acta Mathematicae Applicatae Sinica 2018年第1期34卷 65-76页

作者： Zhu-cui JING Juntao YE guo-liang xu School of Economics and Management Beijing Jim)tong University Beijing 100044 China Institute of Automation Chinese Academy of Sciences Beijing 100190 China Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 China

In this paper, we analyze the well-posedness of an image segmentation model. The main idea of that segmentation model is to minimize one energy functional by evolving a given piecewise constant image towards the image to be segmented. The evolution is controlled by a serial of mappings, which can be represented by B-spline basis functions. The evolution terminates when the energy is below a given threshold. We prove that the correspondence between two images in the segmentation model is an injective and surjective mapping under appropriate conditions. We further prove that the solution of the segmentation model exists using the direct method in the calculus of variations. These results provide the theoretical support for that segmentation model.

关键词： L^2-gradient flow Bi-cubic B-spline direct method image segmentation

Geohazards and risk assessment along highway in Sichuan Province, China

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Journal of Mountain Science 2023年第6期20卷 1695-1711页

作者： YANG Hong-zhi DONG Jia-yu guo xu-liang School of Highway Chang’an UniversityXi'an 710064China

Geohazards along highways are the main natural hazards that could affect the safety and operation of highway *** the risks faced by highways in areas affected by geohazards is an urgent problem to be *** study used historical geohazard events from Sichuan Province and highway network data to propose a geohazard risk index that reflects the risk geohazards along ***,this work applied the entropy method and expert scoring to calculate the weight of the *** spatial distributions of landslides,debris flows,collapses,and unstable slopes along the highways were analysed based on ArcGIS spatial statistics,and the highway geohazard intensity index were *** relationships between slope,rainfall,vegetation coverage,rock type,land use,and incision depth with geohazards were analysed,and the highway geohazard susceptibility index was calculated by the weighted information *** on the intensity and susceptibility index,we obtained a geohazard risk index which can better evaluate the risk of highways,and made a highway geohazard risk map to aid the prevention and mitigation of geohazards along highways and assist with highway network planning.

关键词： Geohazards Highway network Geohazard risk index Intensity index Susceptibility

Dielectric properties of spark plasma sintered AlN/SiC composite ceramics

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International Journal of Minerals,Metallurgy and Materials 2014年第6期21卷 589-594页

作者： Peng Gao Cheng-chang Jia Wen-bin Cao Cong-cong Wang Dong liang guo-liang xu School of Materials Science and Engineering University of Science and Technology Beijing

In this study, we have investigated how the dielectric loss tangent and permittivity of AlN ceramics are affected by factors such as powder mixing methods, milling time, sintering temperature, and the addition of a second conductive phase. All ceramic samples were pre-pared by spark plasma sintering （SPS） under a pressure of 30 MPa. AlN composite ceramics sintered with 30wt%-40wt%SiC at 1600℃ for 5 min exhibited the best dielectric loss tangent, which is greater than 0.3. In addition to AlN and β-SiC, the samples also contained 2H-SiC and Fe5Si3, as detected by X-ray difraction （XRD）. The relative densities of the sintered ceramics were higher than 93%. Experimental results indicate that nano-SiC has a strong capability of absorbing electromagnetic waves. The dielectric constant and dielectric loss of AlN-SiC ce-ramics with the same content of SiC decreased as the frequency of electromagnetic waves increased from 1 kHz to 1 MHz.

关键词： ceramic materials composite materials aluminum nitride silicon carbide spark plasma sintering dielectric losses

Dielectric properties of AlN/Mo composite ceramics prepared by spark plasma sintering method at different processing conditions

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Rare Metals 2022年第4期41卷 1369-1374页

作者： Peng Gao Cheng-Chang Jia Wen-Bin Cao Cong-Cong Wang guo-liang xu Dong liang Zhao-Wen Cui School of Materials Science and Engineering University of Science and Technology BeijingBeijing 100083China

In this study,the effects of powder mixed method,sintering temperature,and the additive amount of the conductive phase on the dielectric loss tangent and permittivity constant of AlN/Mo composite ceramics were *** the ceramic samples were prepared by spark plasma sintering(SPS).AlN composite ceramics with additional 10 vol%Mo sintered at 1400℃holding for 5 min exhibit the best dielectric loss tangent,which is greater than ***/Mo ceramics with additional 20 vol%Mo become conductive,with the resistivity of 0.05–0.06Ω·***-energy ball milling is better than magnetic stirring powder mixing *** addition,the additive Mo and lower sintering temperature lead to a better property with the increase in the electromagnetic wave frequency range of 1×10^(3)–1×10^(6)Hz.

关键词： Aluminum nitride Molybdenum Dielectric loss Spark plasma sintering

In-situ deposited anti-aging TiN capping layer for Nb superconducting quantum circuits

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Chinese Physics B 2024年第9期33卷 133-137页

作者： Hao-Ran Tao Lei Du liang-liang guo Yong Chen Hai-Feng Zhang Xiao-Yan Yang guo-liang xu Chi Zhang Zhi-Long Jia Peng Duan guo-Ping guo CAS Key Laboratory of Quantum Information University of Science and Technology of ChinaHefei 230026China CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics University of Science and Technology of ChinaHefei 230026China Origin Quantum Computing Company Limited Hefei 230088China

The performance of Nb superconducting quantum devices is predominantly limited by dielectric loss at the metal–air interface,where Nb2O5 is considered the main loss ***,we suppress the formation of native oxides by in-situ deposition of a TiN capping layer on the Nb *** TiN capping layers,no Nb2O5 forms on the surface of the Nb *** quality factor Qi of the Nb resonator increases from 5.6×10^(5) to 7.9×10^(5) at low input power and from 6.8×10^(6) to 1.1×10^(7)at high input ***,the TiN capping layer also shows good aging resistance in Nb resonator devices,with no significant performance fluctuations after one month of *** findings highlight the effectiveness of TiN capping layers in enhancing the performance and longevity of Nb superconducting quantum devices.

关键词： anti-aging oxidation dielectric loss Nb superconducting quantum circuits

Effects of hydrostatic pressure and temperature on the nonlinear optical properties of semiparabolic plus semi-inverse squared quantum wells

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Communications in Theoretical Physics 2021年第8期73卷 139-145页

作者： guo-liang xu Zi Zhen Yi-Sheng Shi Kang-Xian guo E Feddi Jian-Hui Yuan Zhi-Hai Zhang School of Physics and Electronics Yancheng Teachers UniversityYancheng 224002China Department of Physics College of Physics and Electronic EngineeringGuangzhou UniversityGuangzhou 510006China Laboratoire de la matiere condensee et Sciences Interdisciplinaires(LAMCScI) Group of Optoelectronic of Semiconductors and NanomaterialsENSETMohammed V University in RabatMorocco Laboratory of Biomedical Photonics and Engineering Guangxi Medical UniversityNanning 530021China

In this study,the effects of hydrostatic pressure and temperature on nonlinear optical rectification(OR),second-harmonic generation(SHG),third-harmonic generation(THG)and the linear,nonlinear,and total optical absorption coefficients(OACs)of a semiparabolic plus semi-inverse squared quantum well(QW)are theoretically *** results show that hydrostatic pressure and temperature have significant effects on the optical properties of semiparabolic plus semi-inverse squared QWs,and that the energy levels and magnitudes of the resonant peaks of OR,SHG,THG,and the total OACs vary according to the shape of the limiting potential,the hydrostatic pressure,and the *** is easily seen that the peak positions of the resonant peaks of OR,SHG,THG,and the total OACs in the semiparabolic plus semi-inverse squared QW show a red shift with increasing hydrostatic pressure,but a blue shift with increasing ***,the magnitude and position of the resonant peaks of OR,SHG,THG,and the total OACs can be adjusted by changing the hydrostatic pressure and the temperature,which promise a new degree of freedom in the tunability of various electro-optical devices.

关键词： Quantum well Optical properties Hydrostatic pressure Temperature

SOME NONLINEAR APPROXIMATIONS FOR MATRIX-VALUED FUNCTIONS

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Journal of Computational Mathematics 2003年第6期21卷 801-814页

作者： guo-liang xu(Academy of Mathematics and System Sciences, Chinese Academy of Sciences,Beijing 100080, China) Academy of Mathematics and System Sciences Chinese Academy of Sciences 北京 100080

Some nonlinear approximants, i.e., exponential-sum interpolation with equal distance or at origin, (0,1)-type, (0,2)-type and (1,2)-type fraction-sum approximations, for matrix-valued functions are introduced. All these approximation problems lead to a same form system of nonlinear equations. Solving methods for the nonlinear system are discussed. Conclusions on uniqueness and convergence of the approximants for certain class of functions are given.

关键词： Matrix-valued function Nonlinear approximation Interpolation.