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1.
研究欧几里得格 Zd 内离散分形指标的线性不变性质 ,即证明了上、下离散质量维数的线性不变性质 ,离散 Hausdorff维数的线性不变性质以及离散填充维数的线性不变性质 .  相似文献   

2.
孙青杰  苏维宜 《数学学报》2001,44(6):1003-101
Dupain Y,France M.M.和 Tricot C.[1]利用积分几何中的经典的Steinhaus定理,引入 Steinhaus维数,并研究了螺线的 Steinhaus维数与盒维数的关系.本文深入这一研究,对Steinhaus维数的值域,单调性等基本性质作了进一步的考察.  相似文献   

3.
文章通过对空间变量的有限差分方法离散了具有周期边值的Burgers Ginzburg Landau方程组.研究了这个离散方程组初值问题解的适定性.证明了当差分网格足够大时离散方程组存在吸引子,并得到了吸引子的Hausdorff维数和分形维数的上界估计.这个上界不会随着网格的加细而无限增大,因此数值分析离散的有限维系统的吸引子可以近似探讨原无限维系统的吸引子.  相似文献   

4.
余旌胡 《数学杂志》1998,18(1):103-106
设(Ω,F,μ)为概率空间,v为(Ω,F)上的有限测度的密度定理,并研究了v的维数及维数分布的若干性质。  相似文献   

5.
R~n上分形集的多重维数   总被引:5,自引:0,他引:5  
本文推广Hausdorff测度和维数的概念,引入了被称作为多重维测度和多重维数的概念.文中证明了关于多重维测度的Frostman定理,构造了一个例子说明存在一类点集,其Hausdorff测度是零或十∞,但其多重维测度是一个正数,并说明了多重维数除第一个分量是正数外,其它分量可以取到任何实数.  相似文献   

6.
直线上的Cookie-Cutter集是一个扩张动力系统的不变集,并且是一个Fractal集合.本文得到Cookie-Cutter集的多重Fractal分解的Packing维数,从而证明其是Taylor意义下的Fractal集合  相似文献   

7.
稳定随机游动重点集的离散豪斯道夫维数   总被引:1,自引:0,他引:1  
设是d维格子点上的严格α-稳定的随机游动,称为的P重点集(P1),本文讨论了的离散豪斯道夫维数,并对,(a<d),证明了P重点集的维数都等于a,即  相似文献   

8.
带五次项的NLS方程及其谱逼近的整体吸引子的维数估计   总被引:1,自引:0,他引:1  
通过给出一般发展方程和其近似方程解的整体吸引子的Hausdorff维数上界间的关系,继[1,2]的讨论,本文进一步得到了带五次项的NLS方程和半离散Fourier谱近似解的整体吸引子的Hausdorff维数的上界估计。  相似文献   

9.
探讨了Z^d中离散填充指标的一些性质,给出了Z^d中离散填充维数的一个等价定义.  相似文献   

10.
Barnsley-Elton-Hardin的一个定理的修正   总被引:1,自引:0,他引:1  
Barnsley等在关联矩阵不可约的条件下,得到了递归FIF的分形维数公式。本文首先指出该九公式是错误的,然后给出新的维数公式,并且新维数公式没有关联矩阵为不可约的限制条件。  相似文献   

11.
In this note we show the convergence of semi-discrete finite element (Galerkin) methods for computing the time evolution of an elastic thermo-plastic system. Finally we indicate how the problem may be discretized in the time dimension.  相似文献   

12.
建立了一维和二维分数阶Burgers方程的有限元格式.时间分数阶导数使用L1方法离散,空间方向使用有限元方法离散.通过选择合适的基函数,将离散后的方程转化成一个非线性代数方程组,并应用牛顿迭代方法求解.数值实验显示出了方法的有效性.  相似文献   

13.
Summary Backward differentiation methods up to orderk=5 are applied to solve linear ordinary and partial (parabolic) differential equations where in the second case the space variables are discretized by Galerkin procedures. Using a mean square norm over all considered time levels a-priori error estimates are derived. The emphasis of the results lies on the fact that the obtained error bounds do not depend on a Lipschitz constant and the dimension of the basic system of ordinary differential equations even though this system is allowed to have time-varying coefficients. It is therefore possible to use the bounds to estimate the error of systems with arbitrary varying dimension as they arise in the finite element regression of parabolic problems.  相似文献   

14.
ABSTRACT

This article is devoted to prove the existence of a non-negative solution for a degenerate parabolic strongly coupled system which arises from seawater intrusion model in confined aquifers. An approximate linear discretized in time scheme is then set up yielding to the existence result with no restriction on the space dimension. The availability of an entropy estimate turns out to be a central tool to obtain the existence result.  相似文献   

15.
Numerical results for suboptimal boundary control of an integro partial differential algebraic equation system of dimension 28 are presented. The application is a molten carbonate fuel cell power plant. The technically and economically important fast tracking of the new stationary cell voltage during a load change is optimized. The nonstandard optimal control problem s.t. degenerated PDE is discretized by the method of lines yielding a very large DAE constrained standard optimal control problem. An index analysis is performed to identify consistent initial conditions.  相似文献   

16.
We obtain a simple tensor representation of the kernel of the discrete d-dimensional gradient operator defined on tensor semi-staggered grids. We show that the dimension of the nullspace grows as O(nd-2), where d is the dimension of the problem, and n is one-dimensional grid size. The tensor structure allows fast orthogonalization to the kernel. The usefulness of such procedure is demonstrated on three-dimensional Stokes problem, discretized by finite differences on semi-staggered grids, and it is shown by numerical experiments that the new method outperforms usually used stabilization approach.  相似文献   

17.
Many processes in the sciences and in engineering are modelled by dynamical systems and—in discretized version—by nonlinear maps. To understand the often complicated dynamical behaviour it is a well established tool to use the concept of invariant manifolds of the system. In this way it is often possible to reduce the dimension of the system considerably. In this paper we propose a new method to calculate numerically invariant manifolds near fixed points of maps. We prove convergence of our procedure and provide an error estimation. Finally, the application of the method is illustrated by examples.  相似文献   

18.
A recent work (Acary et al. 2010) introduces a formulation as a nonsmooth fixed-point problem of a basic problem in numerical mechanics (namely the dynamical Coulomb friction problem in finite dimension with discretized time). Using this new formulation, the existence of a solution to the problem and its numerical resolution are then guaranteed under a strong assumption on the data of this problem. In this paper, we show that the fixed point problem admits solution under a natural, weaker assumption. This existence proof uses a perturbation argument combined with continuity properties of a set-valued mapping associated with the constraints of the problem.  相似文献   

19.
We describe an algorithm for the construction of discretized Voronoi diagrams on a CPU within the context of a large scale numerical fluid simulation. The Discrete Voronoi Chain (DVC) algorithm is fast, flexible and robust. The algorithm stores the Voronoi diagram on a grid or lattice that may be structured or unstructured. The Voronoi diagram is computed by alternatively updating two lists of grid cells per particle to propagate a growth boundary of cells from the particle locations. Distance tests only occur when growth boundaries from different particles collide with each other, hence the number of distance tests is effectively minimized. We give some empirical results for two and three dimensions. The method generalizes to any dimension in a straight forward manner. The distance tests can be based any metric.  相似文献   

20.
A fully discrete method is presented for computing inertial manifolds of dissipative partial differential equations. In particular, only an approximate spectral decomposition of the dominant differential operator needs to be known. The first few of the smallest eigenvalues and eigenvectors of the discretized operator are approximated using the Lanczos algorithm. Numerical experiments are performed for an equation in one space dimension by discretizing the space variable on a sufficiently fine grid. The basic ideas and techniques are exemplified for selected bifurcation diagrams of an integrated form of the Kuramoto-Sivashinsky equation.This research was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) grant OGP0036901, NSERC and Schweizerischer Nationalfonds zur Förderung der Wissenschaften BEF 0150297, and Forschungsinstitut für Mathematik, ETH Zürich.  相似文献   

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