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
In this paper,we give improved error estimates for linearized and nonlinear CrankNicolson type finite difference schemes of Ginzburg-Landau equation in two dimensions.For linearized Crank-Nicolson scheme,we use mathem...In this paper,we give improved error estimates for linearized and nonlinear CrankNicolson type finite difference schemes of Ginzburg-Landau equation in two dimensions.For linearized Crank-Nicolson scheme,we use mathematical induction to get unconditional error estimates in discrete L^(2)and H^(1)norm.However,it is not applicable for the nonlinear scheme.Thus,based on a‘cut-off’function and energy analysis method,we get unconditional L^(2)and H^(1)error estimates for the nonlinear scheme,as well as boundedness of numerical solutions.In addition,if the assumption for exact solutions is improved compared to before,unconditional and optimal pointwise error estimates can be obtained by energy analysis method and several Sobolev inequalities.Finally,some numerical examples are given to verify our theoretical analysis.展开更多
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
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
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
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
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
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
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.
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
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 Schrdinger operators and some Laguerre operators.展开更多
In this paper, we characterize the pointwise rate of convergence for the combinations of the Baskakov operators using the Ditzian-Totik modulus of smoothness.
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
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
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
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
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
This paper research on the pointwise behavior of perturbations from a viscous shock solution to a scalar viscous conservation law by introducing an approximate Green’s function. The authors obtain not only the pointw...This paper research on the pointwise behavior of perturbations from a viscous shock solution to a scalar viscous conservation law by introducing an approximate Green’s function. The authors obtain not only the pointwise decay of the perturbation and but also the high derivative of it. Stability in anyL(p≥1) norm is a direct consequence.展开更多
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.
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
基金supported by the National Natural Science Foundation of China(Grant No.42407232)the Sichuan Science and Technology Program(Grant No.2024NSFSC0826).
文摘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.
基金Supported by the National Natural Science Foundation of China(Grant No.11571181)the Research Start-Up Foundation of Nantong University(Grant No.135423602051).
文摘In this paper,we give improved error estimates for linearized and nonlinear CrankNicolson type finite difference schemes of Ginzburg-Landau equation in two dimensions.For linearized Crank-Nicolson scheme,we use mathematical induction to get unconditional error estimates in discrete L^(2)and H^(1)norm.However,it is not applicable for the nonlinear scheme.Thus,based on a‘cut-off’function and energy analysis method,we get unconditional L^(2)and H^(1)error estimates for the nonlinear scheme,as well as boundedness of numerical solutions.In addition,if the assumption for exact solutions is improved compared to before,unconditional and optimal pointwise error estimates can be obtained by energy analysis method and several Sobolev inequalities.Finally,some numerical examples are given to verify our theoretical analysis.
基金Supported in part by National Natural Science Foundationof China (19871065) Hua-Cheng Grant
文摘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.
基金supported by the NSF China#10571075NSF-Guangdong China#04010473+1 种基金The research of the second author was supported by Jinan University Foundation#51204033the Scientific Research Foundation for the Returned Overseas Chinese Scholars,State education Ministry#2005-383
文摘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 ...
文摘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.
基金supported by National Natural Science Foundation of China(11671100 and 12171104)the National Science Fund for Excellent Young Scholars(11922107)Guangxi Natural Science Foundation(2018GXNSFAA138210 and 2019JJG110010)。
文摘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.
基金Sponsored by Research Grant of the University of Macao No. RG024/03-04S/QT/FST
文摘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.
文摘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.
文摘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.
文摘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.
基金supported by the National Natural Science Foundation of China(11301534)the National Natural Science Foundation of China(11171027 and 11361020)+3 种基金Da Bei Nong Education Fund(1101-2413002)Chinese Universities Scientific Fund(2013QJ003)the Specialized Research Fund for the Doctoral Program of Higher Education of China(20120003110003)the Fundamental Research Funds for Central Universities of China(2012LYB26 and 2012CXQT09)
文摘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 Schrdinger operators and some Laguerre operators.
基金This research is supported by Zhejiang Provincial Natural Science Foundation of China.
文摘In this paper, we characterize the pointwise rate of convergence for the combinations of the Baskakov operators using the Ditzian-Totik modulus of smoothness.
文摘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.
基金Supported by Research Grant of Department of Education of Hubei Province(Q20142803)
文摘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.
基金supported by the National Natural Science Foundation of China(11271141)Chongqing Science&Technology Commission(cstc2018jcyjAX0787)
文摘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.
基金Xingwen Hao's research was supported in part by National Natural Science Foundation of China (10571120 and 10971135)Shanghai Shuguang Project (06SG11)+1 种基金the Program for New Century Excellent Talents of Chinese Ministry of Education (NCET-07-0546) Doctorial Foundation of Weifang University (2011BS11)
文摘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.
文摘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.
基金the National Natural Science Foundation of China(10131050)
文摘This paper research on the pointwise behavior of perturbations from a viscous shock solution to a scalar viscous conservation law by introducing an approximate Green’s function. The authors obtain not only the pointwise decay of the perturbation and but also the high derivative of it. Stability in anyL(p≥1) norm is a direct consequence.
基金Supported by the National Natural Science Foundation of China(11801137)。
文摘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.
文摘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.
