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Rock discontinuity extraction from 3D point clouds using pointwise clustering algorithm 认领 引用 被引量：1
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作者 Xiaoyu Yi Wenxuan Wu +2 位作者 Wenkai Feng Yongjian Zhou Jiachen Zhao 《Journal of Rock Mechanics and Geotechnical Engineering》 SCIE CSCD 2025年第7期4429-4444,共16页
Recognizing discontinuities within rock masses is a critical aspect of rock engineering.The development of remote sensing technologies has significantly enhanced the quality and quantity of the point clouds collected ... Recognizing discontinuities within rock masses is a critical aspect of rock engineering.The development of remote sensing technologies has significantly enhanced the quality and quantity of the point clouds collected from rock outcrops.In response,we propose a workflow that balances accuracy and efficiency to extract discontinuities from massive point clouds.The proposed method employs voxel filtering to downsample point clouds,constructs a point cloud topology using K-d trees,utilizes principal component analysis to calculate the point cloud normals,and employs the pointwise clustering(PWC)algorithm to extract discontinuities from rock outcrop point clouds.This method provides information on the location and orientation(dip direction and dip angle)of the discontinuities,and the modified whale optimization algorithm(MWOA)is utilized to identify major discontinuity sets and their average orientations.Performance evaluations based on three real cases demonstrate that the proposed method significantly reduces computational time costs without sacrificing accuracy.In particular,the method yields more reasonable extraction results for discontinuities with certain undulations.The presented approach offers a novel tool for efficiently extracting discontinuities from large-scale point clouds. 展开更多
关键词 Rock mass discontinuity 3D point clouds Pointwise clustering(PWC)algorithm Modified whale optimization algorithm(MWOA)
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POINTWISE CONVERGENCE RATE OF VANISHING VISCOSITY APPROXIMATIONS FOR SCALAR CONSERVATION LAWS WITH BOUNDARY 认领 引用 被引量：3
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作者 刘红霞 潘涛 《Acta Mathematica Scientia》 SCIE 2009年第1期111-128,共18页
This article is concerned with the pointwise error estimates for vanishing vis- cosity approximations to scalar convex conservation laws with boundary.By the weighted error function and a bootstrap extrapolation techn... This article is concerned with the pointwise error estimates for vanishing vis- cosity approximations to scalar convex conservation laws with boundary.By the weighted error function and a bootstrap extrapolation technique introduced by Tadmor-Tang,an optimal pointwise convergence rate is derived for the vanishing viscosity approximations to the initial-boundary value problem for scalar convex conservation laws,whose weak entropy solution is piecewise C 2 -smooth with interaction of elementary waves and the ... 展开更多
关键词 Scalar conservation laws with boundary vanishing viscosity approximations error estimate pointwise convergence rate transport inequality
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POINTWISE CONVERGENCE FOR EXPANSIONS IN SPHERICAL MONOGENICS 认领 引用 被引量：2
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作者 费铭岗 钱涛 《Acta Mathematica Scientia》 SCIE 2009年第5期1241-1250,共10页
We offer a new approach to deal with the pointwise convergence of FourierLaplace series on the unit sphere of even-dimensional Euclidean spaces. By using spherical monogenics defined through the generalized Cauchy-Rie... We offer a new approach to deal with the pointwise convergence of FourierLaplace series on the unit sphere of even-dimensional Euclidean spaces. By using spherical monogenics defined through the generalized Cauchy-Riemann operator, we obtain the spherical monogenic expansions of square integrable functions on the unit sphere. Based on the generalization of Fueter＇s theorem inducing monogenic functions from holomorphic functions in the complex plane and the classical Carleson＇s theorem, a pointwise convergence theorem on the new expansion is proved. The result is a generalization of Carleson＇s theorem to the higher dimensional Euclidean spaces. The approach is simpler than those by using special functions, which may have the advantage to induce the singular integral approach for pointwise convergence problems on the spheres. 展开更多
关键词 spherical monogenics pointwise convergence of Fourier-Laplace series generalized Cauchy-Riemann operator unit sphere generalization of Fueter＇s theorem
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Pointwise characterization for combinations of Szász-Mirakjan operators 认领 引用 被引量：1
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作者 XIE Lin-sen SHI Zhong-rui 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE 2008年第2期202-212,共11页
The purpose of this paper is to characterize the pointwise rate of convergence for the combinations of Szász-Mirakjan operators using Ditzian-Totik modulus of smoothness.
关键词 Szász-Mirakjan operator combination pointwise approximation.
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POINTWISE MULTIPLIERS FOR LOCALIZED MORREY-CAMPANATO SPACES ON RD-SPACES 认领 引用 被引量：2
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作者 林海波 杨大春 《Acta Mathematica Scientia》 SCIE CSCD 2014年第6期1677-1694,共18页
In this article, the authors characterize pointwise multipliers for localized MorreyCampanato spaces, associated with some admissible functions on RD-spaces, which include localized BMO spaces as a special case. The r... In this article, the authors characterize pointwise multipliers for localized MorreyCampanato spaces, associated with some admissible functions on RD-spaces, which include localized BMO spaces as a special case. The results obtained are applied to Schrdinger operators and some Laguerre operators. 展开更多
关键词 RD-space pointwise multiplier localized Morrey-Campanato space BMO space
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ON THE POINTWISE ESTIMATIONS OF APPROXIMATION OF FUNCTIONS AND THEIR DERIVATIVES BY HERMITE INTERPOLATION 认领 引用 被引量：1
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作者 Tingfan Xie Ziyu Wang China Institute of Metrology, China Henan University, China 《Analysis in Theory and Applications》 1994年第3期45-55,共11页
The object of this paper is to establish the pointwise estimations of approximation of functions in C^1 and their derivatives by Hermite interpolation polynomials. The given orders have been proved to be exact in gen-... The object of this paper is to establish the pointwise estimations of approximation of functions in C^1 and their derivatives by Hermite interpolation polynomials. The given orders have been proved to be exact in gen- eral. 展开更多
关键词 Math ON THE POINTWISE ESTIMATIONS OF APPROXIMATION OF FUNCTIONS AND THEIR DERIVATIVES BY HERMITE INTERPOLATION 石瓦
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GREEN'S FUNCTION AND THE POINTWISE BEHAVIORS OF THE VLASOV-POISSON-FOKKER-PLANCK SYSTEM 认领 引用 被引量：1
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作者 钟明溁 《Acta Mathematica Scientia》 SCIE CSCD 2023年第1期205-236,共32页
The pointwise space-time behaviors of the Green’s function and the global solution to the Vlasov-Poisson-Fokker-Planck(VPFP)system in three dimensional space are studied in this paper.It is shown that the Green’s fu... The pointwise space-time behaviors of the Green’s function and the global solution to the Vlasov-Poisson-Fokker-Planck(VPFP)system in three dimensional space are studied in this paper.It is shown that the Green’s function consists of the diffusion waves decaying exponentially in time but algebraically in space,and the singular kinetic waves which become smooth for all(t,x,v)when t>0.Furthermore,we establish the pointwise space-time behaviors of the global solution to the nonlinear VPFP system when the initial data is not necessarily smooth in terms of the Green’s function. 展开更多
关键词 Vlasov-Poisson-Fokker-Planck system Green’s function pointwise behavior spectrum structure
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POINTWISE ESTIMATES OF SOLUTIONS FOR THE NONLINEAR VISCOUS WAVE EQUATION IN EVEN DIMENSIONS 认领 引用 被引量：1
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作者 Nianying LI 《Acta Mathematica Scientia》 SCIE CSCD 2020年第4期1001-1019,共19页
In this article,we study the pointwise estimates of solutions to the nonlinear viscous wave equation in even dimensions(n≥4).We use the Green’s function method.Our approach is on the basis of the detailed analysis o... In this article,we study the pointwise estimates of solutions to the nonlinear viscous wave equation in even dimensions(n≥4).We use the Green’s function method.Our approach is on the basis of the detailed analysis of the Green’s function of the linearized system.We show that the decay rates of the solution for the same problem are different in even dimensions and odd dimensions.It is shown that the solution exhibits a generalized Huygens principle. 展开更多
关键词 viscous wave equation pointwise estimate even dimensions
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Pointwise Estimate of Solutions to the Three-Dimensional Compressible Magnetohydrodynamic Equations 认领 引用 被引量：1
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作者 ZHOU Fang 《Wuhan University Journal of Natural Sciences》 CAS CSCD 2015年第3期185-192,共8页
This paper is devoted to the pointwise estimate of solutions for the initial value problem to the three-dimensional compressible magnetohydrodynamic equations, which models the dynamics of compressible quasi-neutrally... This paper is devoted to the pointwise estimate of solutions for the initial value problem to the three-dimensional compressible magnetohydrodynamic equations, which models the dynamics of compressible quasi-neutrally ionized fluids under the influence of electromagnetic fields. Based on the detailed analysis of the Green function of the linearized system, we obtain the pointwise estimates of smooth solutions when the initial data is sufficiently small with the algebraic decay to the constant equilibrium. As the by-product, we also show the corresponding pL-estimates of the smooth solutions. 展开更多
关键词 compressible MHD equations pointwise estimate Green function pL-estimates
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THE POINTWISE ESTIMATES TO SOLUTIONS FOR 1-DIMENSIONAL LINEAR THERMO-VISCO-ELASTIC SYSTEM 认领 引用
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作者 郝兴文 彭少玉 《Acta Mathematica Scientia》 SCIE CSCD 2011年第4期1259-1271,共13页
In this paper, we study the linear thermo-visco-elastic system in one-dimensional space variable. The mathematical model is a hyperbolic-parabolic partial differential system. The solutions of the system show some dec... In this paper, we study the linear thermo-visco-elastic system in one-dimensional space variable. The mathematical model is a hyperbolic-parabolic partial differential system. The solutions of the system show some decay property due to the parabolicity. Based on detailed analysis on the Green function of the system, the pointwise estimates of the solutions are obtained, from which the generalized Huygens’ principle is shown. 展开更多
关键词 thermo-visco-elastic system Fourier transform Green function pointwise estimate Huygens’ principle
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Pointwise Estimate of Cahn-Hilliard Equation with Inertial Term in R3 认领 引用
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作者 XU Hongmei ZHU Yue 《Wuhan University Journal of Natural Sciences》 CAS CSCD 2022年第5期361-366,共6页
Cauchy problem of Cahn-Hilliard equation with inertial term in three-dimensional space is considered.Using delicate analysis of its Green function and its convolution with nonlinear term,pointwise decay rate is obtained.
关键词 Cahn-Hilliard equation with inertial term Green function pointwise decay
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POINTWISE SIMULTANEOUS APPROXIMATION BY LEFT GAMMA QUASI-INTERPOLANTS 认领 引用
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作者 Hongbiao Jiang 《Analysis in Theory and Applications》 2008年第2期120-128,共9页
Recently some classical operator quasi-interpolants were introduced to obtain much faster convergence. We consider left Gamma quasi-interpolants and give a pointwise simultaneous approximation equivalence theorem with... Recently some classical operator quasi-interpolants were introduced to obtain much faster convergence. We consider left Gamma quasi-interpolants and give a pointwise simultaneous approximation equivalence theorem with ωφλ^2r（f,t）∞ by means of unified the classical modulus and Ditzian-Totick modulus. 展开更多
关键词 gamma operator quasi-interpolant pointwise simultaneous approximation,equivalent theorem
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POINTWISE CONVERGENCE OF FOURIER-JACOBI SERIES 认领 引用
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作者 Zhongkai Li 《Analysis in Theory and Applications》 1995年第4期58-77,共20页
The purpose of this paper is to study the pointwise and almost everywhere convergence of the Cesaro means (C,δ) of Fourier-Jacobi expansions, the main term of the Lebesgue constant of the (C ,8) means for - 1α+1/2 a... The purpose of this paper is to study the pointwise and almost everywhere convergence of the Cesaro means (C,δ) of Fourier-Jacobi expansions, the main term of the Lebesgue constant of the (C ,8) means for - 1α+1/2 and equiconvergence theorems for - 1<δ≤α+1/2 are proved. The analogues of the Lebesgue, Salem and Young theorems of the Cesaro means at the critical index δ = α+1/2 are established. 展开更多
关键词 POINTWISE CONVERGENCE OF FOURIER-JACOBI SERIES Math lim
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THE POINTWISE ESTIMATES OF SOLUTIONS FOR A NONLINEAR CONVECTION DIFFUSION REACTION EQUATION 认领 引用 被引量：1
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作者 刘国威 《Acta Mathematica Scientia》 SCIE CSCD 2017年第1期79-96,共18页
This paper studies the time asymptotic behavior of solutions for a nonlinear convection diffusion reaction equation in one dimension.First,the pointwise estimates of solutions are obtained,furthermore,we obtain the op... This paper studies the time asymptotic behavior of solutions for a nonlinear convection diffusion reaction equation in one dimension.First,the pointwise estimates of solutions are obtained,furthermore,we obtain the optimal Lp,1≤ p ≤ ＋∞,convergence rate of solutions for small initial data.Then we establish the local existence of solutions,the blow up criterion and the sufficient condition to ensure the nonnegativity of solutions for large initial data.Our approach is based on the detailed analysis of the Green function of the linearized equation and some energy estimates. 展开更多
关键词 convection diffusion reaction equation pointwise estimate Green function energy method
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ON THE RATE OF POINTWISE CONVERGENCE OF THE DURRMEYER-TYPE OPERATORS 认领 引用 被引量：1
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作者 G. Aniol P. Pych-Taberska 《Analysis in Theory and Applications》 1995年第2期94-105,共12页
For bounded or some locally bounded functions f measurable on an interval I there is estimated the rate of convergence of the Durrmeyer-type operators Lnf at those points x∈IntI at which the one-sided limits f(x±... For bounded or some locally bounded functions f measurable on an interval I there is estimated the rate of convergence of the Durrmeyer-type operators Lnf at those points x∈IntI at which the one-sided limits f(x± 0) exist. In the main theorems the Chanturiya's modulus of variation is used. 展开更多
关键词 ON THE RATE OF POINTWISE CONVERGENCE OF THE DURRMEYER-TYPE OPERATORS lim
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GLOBAL EXISTENCE AND POINTWISE ESTIMATES OF SOLUTIONS TO GENERALIZED KURAMOTO-SIVASHINSKY SYSTEM IN MULTI-DIMENSIONS 认领 引用
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作者 Yingshu ZHANG Lang LI Shaomei FANG 《Acta Mathematica Scientia》 SCIE CSCD 2019年第1期180-194,共15页
The Cauchy problem of the generalized Kuramoto-Sivashinsky equation in multidimensions(n ≥ 3) is considered. Based on Green's function method, some ingenious energy estimates are given. Then the global existence ... The Cauchy problem of the generalized Kuramoto-Sivashinsky equation in multidimensions(n ≥ 3) is considered. Based on Green's function method, some ingenious energy estimates are given. Then the global existence and pointwise convergence rates of the classical solutions are established. Furthermore, the L^p convergence rate of the solution is obtained. 展开更多
关键词 Kuramoto-Sivashinsky equation global existence pointwise estimates Green’s function method energy method
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POINTWISE ESTIMATE OF SOLUTIONS OF ISENTROPIC NMIER-STOKES EQUATIONS IN EVEN SPACE-DIMENSIONS 认领 引用 被引量：10
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作者 徐红梅 王维克 《Acta Mathematica Scientia》 SCIE 2001年第3期417-427,共11页
This paper is concerned with the dissipation of solutions of the isentropic Navier-Stokes equations in even and bigger than two multi-dimensions. Pointwise estimates of the time-asymptotic shape of the solutions are o... This paper is concerned with the dissipation of solutions of the isentropic Navier-Stokes equations in even and bigger than two multi-dimensions. Pointwise estimates of the time-asymptotic shape of the solutions are obtained and the generalized Huygan's principle is exhibited. The approch of the paper is based on the detailed analysis of the Green function of Iinearized system. This is used to study the coupling of nonlinear diffesion waves. 展开更多
关键词 Isentropic Navier-Stokes equation multi-dimensions Green's function pointwise estimate
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Deep convolutional adversarial graph autoencoder using positive pointwise mutual information for graph embedding 认领 引用
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作者 MA Xiuhui WANG Rong +3 位作者 CHEN Shudong DU Rong ZHU Danyang ZHAO Hua 《High Technology Letters》 EI CAS 2022年第1期98-106,共9页
Graph embedding aims to map the high-dimensional nodes to a low-dimensional space and learns the graph relationship from its latent representations.Most existing graph embedding methods focus on the topological struct... Graph embedding aims to map the high-dimensional nodes to a low-dimensional space and learns the graph relationship from its latent representations.Most existing graph embedding methods focus on the topological structure of graph data,but ignore the semantic information of graph data,which results in the unsatisfied performance in practical applications.To overcome the problem,this paper proposes a novel deep convolutional adversarial graph autoencoder(GAE)model.To embed the semantic information between nodes in the graph data,the random walk strategy is first used to construct the positive pointwise mutual information(PPMI)matrix,then,graph convolutional net-work(GCN)is employed to encode the PPMI matrix and node content into the latent representation.Finally,the learned latent representation is used to reconstruct the topological structure of the graph data by decoder.Furthermore,the deep convolutional adversarial training algorithm is introduced to make the learned latent representation conform to the prior distribution better.The state-of-the-art experimental results on the graph data validate the effectiveness of the proposed model in the link prediction,node clustering and graph visualization tasks for three standard datasets,Cora,Citeseer and Pubmed. 展开更多
关键词 graph autoencoder(GAE) positive pointwise mutual information(PPMI) deep convolutional generative adversarial network(DCGAN) graph convolutional network(GCN) se-mantic information
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Pointwise convergence of some conjugate convolution operators with applications to wavelets 认领 引用
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作者 HU Lan SHI Xian-liang 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2016年第3期320-330,共11页
In this paper, we discuss the pointwise convergence of conjugate convolution op- erators with some applications to wavelets. Some criteria of convergence at （C, 1） continuous points, Lebesgue points and almost every... In this paper, we discuss the pointwise convergence of conjugate convolution op- erators with some applications to wavelets. Some criteria of convergence at （C, 1） continuous points, Lebesgue points and almost everywhere are established. 展开更多
关键词 Hilbert transform pointwise convergence wavelet
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ON POINTWISE R-SUBWEAKLY COMMUTING MAPS AND BEST APPROXIMATIONS 认领 引用
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作者 F. Akbar N. Sultana 《Analysis in Theory and Applications》 2008年第1期40-49,共10页
The main purpose of this paper is to prove some common fixed point theorems for pointwise R-subweakly commuting maps on non-starshaped domains in p-normed spaces and locally convex topological vector spaces. As applic... The main purpose of this paper is to prove some common fixed point theorems for pointwise R-subweakly commuting maps on non-starshaped domains in p-normed spaces and locally convex topological vector spaces. As applications, invariant approximation results are established. This work provides extension as well as substantial improvement of several results in the existing literature. 展开更多
关键词 common fixed point contractive family of functions pointwise R-subweaklycommuting maps invariant approximation
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