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1.
<正>In this work we consider the problem of shape reconstruction from an unorganized data set which has many important applications in medical imaging,scientific computing,reverse engineering and geometric modelling.The reconstructed surface is obtained by continuously deforming an initial surface following the Partial Differential Equation(PDE)-based diffusion model derived by a minimal volume-like variational formulation.The evolution is driven both by the distance from the data set and by the curvature analytically computed by it.The distance function is computed by implicit local interpolants defined in terms of radial basis functions.Space discretization of the PDE model is obtained by finite co-volume schemes and semi-implicit approach is used in time/scale.The use of a level set method for the numerical computation of the surface reconstruction allows us to handle complex geometry and even changing topology, without the need of user-interaction.Numerical examples demonstrate the ability of the proposed method to produce high quality reconstructions.Moreover,we show the effectiveness of the new approach to solve hole filling problems and Boolean operations between different data sets.  相似文献   

2.
<正>This paper presents alternating direction finite volume element methods for three-dimensional parabolic partial differential equations and gives four computational schemes,one is analogous to Douglas finite difference scheme with second-order splitting error,the other two schemes have third-order splitting error,and the last one is an extended LOD scheme.The L~2 norm and H~1 semi-norm error estimates are obtained for the first scheme and second one,respectively.Finally,two numerical examples are provided to illustrate the efficiency and accuracy of the methods.  相似文献   

3.
Generalizing wavelets by adding desired redundancy and flexibility,framelets(i.e.,wavelet frames)are of interest and importance in many applications such as image processing and numerical algorithms.Several key properties of framelets are high vanishing moments for sparse multiscale representation,fast framelet transforms for numerical efficiency,and redundancy for robustness.However,it is a challenging problem to study and construct multivariate nonseparable framelets,mainly due to their intrinsic connections to factorization and syzygy modules of multivariate polynomial matrices.Moreover,all the known multivariate tight framelets derived from spline refinable scalar functions have only one vanishing moment,and framelets derived from refinable vector functions are barely studied yet in the literature.In this paper,we circumvent the above difficulties through the approach of quasi-tight framelets,which behave almost identically to tight framelets.Employing the popular oblique extension principle(OEP),from an arbitrary compactly supported M-refinable vector functionφwith multiplicity greater than one,we prove that we can always derive fromφa compactly supported multivariate quasi-tight framelet such that:(i)all the framelet generators have the highest possible order of vanishing moments;(ii)its associated fast framelet transform has the highest balancing order and is compact.For a refinable scalar functionφ(i.e.,its multiplicity is one),the above item(ii)often cannot be achieved intrinsically but we show that we can always construct a compactly supported OEP-based multivariate quasi-tight framelet derived fromφsatisfying item(i).We point out that constructing OEP-based quasi-tight framelets is closely related to the generalized spectral factorization of Hermitian trigonometric polynomial matrices.Our proof is critically built on a newly developed result on the normal form of a matrix-valued filter,which is of interest and importance in itself for greatly facilitating the study of refinable vector functions and multiwavelets/multiframelets.This paper provides a comprehensive investigation on OEP-based multivariate quasi-tight multiframelets and their associated framelet transforms with high balancing orders.This deepens our theoretical understanding of multivariate quasi-tight multiframelets and their associated fast multiframelet transforms.  相似文献   

4.
We introduce a class of singular integral operators on product domains along twisted surfaces.We prove that the operators are bounded on Lp provided that the kernels satisfy weak conditions.  相似文献   

5.
<正>Image restoration is often solved by minimizing an energy function consisting of a data-fidelity term and a regularization term.A regularized convex term can usually preserve the image edges well in the restored image.In this paper,we consider a class of convex and edge-preserving regularization functions,i.e.,multiplicative half-quadratic regularizations,and we use the Newton method to solve the correspondingly reduced systems of nonlinear equations.At each Newton iterate,the preconditioned conjugate gradient method,incorporated with a constraint preconditioner,is employed to solve the structured Newton equation that has a symmetric positive definite coefficient matrix. The eigenvalue bounds of the preconditioned matrix are deliberately derived,which can be used to estimate the convergence speed of the preconditioned conjugate gradient method.We use experimental results to demonstrate that this new approach is efficient, and the effect of image restoration is reasonably well.  相似文献   

6.
本文主要讨论组合地图列举问题.刘的一部专著中提出了一个判定两个地图是否同构的算法.该算法的时间复杂度为O(m2),其中m为下图的规模.在此基础上,本文给出一个用于地图列举以及进而计算任意连通下图的地图亏格分布的通用算法.本文所得结果比之前文献中所给结果更优.  相似文献   

7.
<正>The gas-kinetic theory based flux splitting method has been successfully proposed for solving one-and two-dimensional ideal magnetohydrodynamics by Xu et al. [J.Comput.Phys.,1999;2000],respectively.This paper extends the kinetic method to solve three-dimensional ideal magnetohydrodynamics equations,where an adaptive parameter 17 is used to control the numerical dissipation in the flux splitting method. Several numerical examples are given to demonstrate that the proposed method can achieve high numerical accuracy and resolve strong discontinuous waves in three dimensional ideal MHD problems.  相似文献   

8.
In this paper,we use a unified framework to study Poisson stable(including stationary,periodic,quasi-periodic,almost periodic,almost automorphic,Birkhoff recurrent,almost recurrent in the sense of Bebutov,Levitan almost periodic,pseudo-periodic,pseudo-recurrent and Poisson stable)solutions for semilinear stochastic differential equations driven by infinite dimensional L′evy noise with large jumps.Under suitable conditions on drift,diffusion and jump coefficients,we prove that there exist solutions which inherit the Poisson stability of coefficients.Further we show that these solutions are globally asymptotically stable in square-mean sense.Finally,we illustrate our theoretical results by several examples.  相似文献   

9.
This paper is concerned with a singular second-order nonlinear boundary value problem with a time depending on derivative operator and posed on the positive half-line. The nonlinearity is derivative-dependent, which has singularities at t=0 and/or x=0, and may change sign. The method of the upper and lower solutions on unbounded domains combined with the topological degree theory are employed to prove the existence and multiplicity of solutions.  相似文献   

10.
<正>The formulation of optimal control problems governed by Fredholm integral equations of second kind and an efficient computational framework for solving these control problems is presented.Existence and uniqueness of optimal solutions is proved. A collective Gauss-Seidel scheme and a multigrid scheme are discussed.Optimal computational performance of these iterative schemes is proved by local Fourier analysis and demonstrated by results of numerical experiments.  相似文献   

11.
刘任河  熊晓龙 《经济数学》2005,22(2):123-126
本文首先对比分析了两类风险秩序:随机控制秩序与对偶随机控制秩序.得到并证明了下述命题:(1)效用自由秩序等价于随机控制秩序;(2)畸变自由秩序等价于对偶随机控制秩序;(3)第一、第二阶随机控制秩序等价于第一、第二阶的对偶随机控制秩序,但对高于三阶的情况由实例说明不一定成立.  相似文献   

12.
本文考虑n阶复矩阵可嵌入到n+1阶的正规矩阵的条件.证明了n>2阶的复矩阵不一定可嵌入到n+1阶的正规矩阵,而2阶复矩阵总可嵌入到3阶正规矩阵中.本文还证明了任意n阶复方阵可嵌入到2n阶正规矩阵中  相似文献   

13.
SOME COMPARISONS BETWEEN GENERALIZED ORDER STATISTICS   总被引:1,自引:0,他引:1  
Some stochastic comparisons of generalized order statistics under the right spread order,the location independent riskier order and the total time transform order are investigated in this paper.The underlying distributions and parameters on which generalized order statistics are based are also surveyed to obtain the conditions for increasing the expectations of spacings between the first two generalized order statistics and between the last two generalized order statistics.  相似文献   

14.
考虑两组相互独立的来自非齐次总体Gompertz分布的样本,给出了最小顺序统计量的反向失效率序、散度序以及凸变换序之间的比较和最大顺序统计量的普通随机序的比较.  相似文献   

15.
Convolutions of independent random variables often arise in a natural way in many applied areas. In this paper, we study various stochastic orderings of convolutions of heterogeneous gamma random variables in terms of the majorization order [p-larger order, reciprocal majorization order] of parameter vectors and the likelihood ratio order [dispersive order, hazard rate order, star order, right spread order, mean residual life order] between convolutions of two heterogeneous gamma sets of variables wherein they have both differing scale parameters and differing shape parameters. The results established in this paper strengthen and generalize those known in the literature.  相似文献   

16.
We consider two geometric formulations of Lagrangian formalism on fibred manifolds: Krupka's theory of finite order variational sequences, and Vinogradov's infinite order variational sequence associated with the -spectral sequence. On one hand, we show that the direct limit of Krupka's variational bicomplex is a new infinite order variational bicomplex which yields a new infinite order variational sequence. On the other hand, by means of Vinogradov's -spectral sequence, we provide a new finite order variational sequence whose direct limit turns out to be the Vinogradov's infinite order variational sequence. Finally, we provide an equivalence of the two finite order and infinite order variational sequences modulo the space of Euler-Lagrange morphisms.  相似文献   

17.
分别在有pre-order的无线性结构的集合和拓扑空间中,给出了有效点的存在性。作为应用,讨论了向量优化问题中解的存在性。最后给出了紧、弱紧、锥紧、锥半紧、上序紧、下序紧、上序半紧、准上序半紧和准下序半紧等之间的关系。  相似文献   

18.
In this paper, we obtain necessary and sufficient second order optimality conditions for multiobjective problems using second order directional derivatives. We propose the notion of second order KT-pseudoinvex problems and we prove that this class of problems has the following property: a problem is second order KT-pseudoinvex if and only if all its points that satisfy the second order necessary optimality condition are weakly efficient. Also we obtain second order sufficient conditions for efficiency.  相似文献   

19.
Extrapolation with a parallel splitting method is discussed. The parallel splitting method reduces a multidimensional problem into independent one-dimensional problems and can improve the convergence order of space variables to an order as high as the regularity of the solution permits. Therefore, in order to match the convergence order of the space variables, a high order method should also be used for the time integration. Second and third order extrapolation methods are used to improve the time convergence and it was found that the higher order extrapolation method can produce a more accurate solution than the lower order extrapolation method, but the convergence order of high order extrapolation may be less than the actual order of the extrapolation. We also try to show a fact that has not been studied in the literature, i.e. when the extrapolation is used, it may decrease the convergence of the space variables. The higher the order of the extrapolation method, the more it decreases the convergence of the space variables. The global extrapolation method also improves the parallel degree of the parallel splitting method. Numerical tests in the paper are done in a domain of a unit circle and a unit square.Supported by the Academy of Finland.  相似文献   

20.
In this paper,we use the L(o)wner partial order and the star partial order to introduce a new partial order (denoted by "L*") on the set of group matrices,and get some characteristics and properties of the new partial order.In particular,we prove that the L* partial order is a special kind of the core par-tial order and it is equivalent to the star partial order under some conditions.We also illustrate its difference from other partial orders with examples and find out under what conditions it is equivalent to other partial orders.  相似文献   

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