共查询到19条相似文献,搜索用时 109 毫秒
1.
The critical point set plays a central role in the theory of Tchebyshev approximation.Generally,in multivariate Tchebyshev approximation,it is not a trivial task to determine whether a set is critical or not.In this paper,we study the characterization of the critical point set of S 0 1(△) in geometry,where is restricted to some special triangulations(bitriangular,single road and star triangulations).Such geometrical characterization is convenient to use in the determination of a critical point set. 相似文献
2.
《数学研究及应用》2012,(1)
The critical point set plays a central role in the theory of Tchebyshev approximation.Generally,in multivariate Tchebyshev approximation,it is not a trivial task to determine whether a set is critical or not.In this paper,we study the characterization of the critical point set of S 0 1(△) in geometry,where is restricted to some special triangulations(bitriangular,single road and star triangulations).Such geometrical characterization is convenient to use in the determination of a critical point set. 相似文献
3.
The critical point set plays a central role in the theory of Tchebyshev approximation.Generally,in multivariate Tchebyshev approximation,it is not a trivial task to determine whether a set is critical ... 相似文献
4.
Yekini SHEHU 《数学物理学报(B辑英文版)》2014,(4):1081-1097
In this paper, we prove strong convergence theorems for approximation of a fixed point of a left Bregman strongly relatively nonexpansive mapping which is also a solution to a finite system of equilibrium problems in the framework of reflexive real Banach spaces. We also discuss the approximation of a common fixed point of a family of left Bregman strongly nonexpansive mappings which is also solution to a finite system of equilibrium problems in reflexive real Banach spaces. Our results complement many known recent results in the literature. 相似文献
5.
The core problem of dynamical systems is to study the asymptotic behaviors of orbits and their topological structures. It is well known that the orbits with certain recurrence and generating ergodic (or invariant) measures are important, such orbits form a full measure set for all invariant measures of the system, its closure is called the measure center of the system. To investigate this set, Zhou introduced the notions of weakly almost periodic point and quasi-weakly almost periodic point in 1990s, and presented some open problems on complexity of discrete dynamical systems in 2004. One of the open problems is as follows: for a quasi-weakly almost periodic point but not weakly almost periodic, is there an invariant measure generated by its orbit such that the support of this measure is equal to its minimal center of attraction (a closed invariant set which attracts its orbit statistically for every point and has no proper subset with this property)? Up to now, the problem remains open. In this paper, we construct two points in the one-sided shift system of two symbols, each of them generates a sub-shift system. One gives a positive answer to the question above, the other answers in the negative. Thus we solve the open problem completely. More important, the two examples show that a proper quasi-weakly almost periodic orbit behaves very differently with weakly almost periodic orbit. 相似文献
6.
《中国科学 数学(英文版)》2018,(12)
We study the quasisymmetric geometry of the Julia sets of McMullen maps f_λ(z) = z~m+ λ/z~?,where λ∈ C \ {0} and ? and m are positive integers satisfying 1/? + 1/m 1. If the free critical points of f_λ are escaped to the infinity, we prove that the Julia set J_λ of f_λ is quasisymmetrically equivalent to either a standard Cantor set, a standard Cantor set of circles or a round Sierpiński carpet(which is also standard in some sense).If the free critical points are not escaped, we give a sufficient condition on λ such that J_λ is a Sierpiński carpet and prove that most of them are quasisymmetrically equivalent to some round carpets. In particular, there exist infinitely renormalizable rational maps whose Julia sets are quasisymmetrically equivalent to the round carpets. 相似文献
7.
《分析论及其应用》1994,(2)
In this paper we study the approximation on set of full measure for functions in Sobolev spacesL_m~1 (R~n) (m∈N) by Bochner-Riesz means of conjugale Fourier integrals below the critical index. Atheorem concerning the precise approximation orders with relation to the number m of space L_m~1 (R~n) andthe index of Bochner-Riesz means is obtained. 相似文献
8.
渐近φ半压缩映象新的带误差的IshiKawa迭代逼近 总被引:4,自引:0,他引:4
杨理平 《高等学校计算数学学报》2004,26(1):47-52
Let E be a real Banach space and T be an asymptotically φ-hemicontractive mapping. By properties of a new analytical method, under general cases, the strong convergence of the set sequences {On} of the new Ishikawa iteration approximation with errors to the fixed point of mapping is proved. The paper generalizes and improves the corresponding results in {1},[3-8]. 相似文献
9.
<正> 1. INTRODUCTION. It is the purpose of this paper to presentsome results,on the problem of interpolation and approximation toa functiou f(z),analytic on a closed limited point set E in thecomplex z-plane whose complement K is connected and regular inthe sense that Green's fumction for K exists,by rational functionsf_n(z) of respective degrees n,n=1,2,…of the form 相似文献
10.
For a continuous domain D, some characterization that the convex powerdomain CD is a domain hull of Max(CD) is given in terms of compact subsets of D. And in this case, it is proved that the set of the maximal points Max(CD) of CD with the relative Scott topology is homeomorphic to the set of all Scott compact subsets of Max(.D) with the topology induced by the Hausdorff metric derived from a metric on Max(D) when Max(D) is metrizable. 相似文献
11.
Jeff Erickson 《Discrete and Computational Geometry》2005,33(1):83-115
The spread of a finite set of points is the ratio between the
longest and shortest pairwise distances. We prove that the Delaunay
triangulation of any set of $n$ points in~$\Real^3$ with spread
$\Delta$ has complexity $O(\Delta^3)$. This bound is tight in the
worst case for all $\Delta = O(\sqrt{n})$. In particular, the
Delaunay triangulation of any dense point set has linear complexity.
We also generalize this upper bound to regular triangulations of
$k$-ply systems of balls, unions of several dense point sets, and
uniform samples of smooth surfaces. On the other hand, for any $n$
and $\Delta = O(n)$, we construct a regular triangulation of
complexity $\Omega(n\Delta)$ whose $n$ vertices have spread $\Delta$. 相似文献
12.
This paper deals with the approximation of the unfolding of a smooth globally
developable surface (i.e. "isometric" to a domain of
) with a triangulation. We prove the following result: let Tn be a sequence of globally developable triangulations which tends to a globally developable smooth surface S in the Hausdorff
sense. If the normals of Tn tend to the normals of S, then the shape of the unfolding of Tn tends to the shape of the unfolding of S. We also provide several examples: first, we show globally developable triangulations
whose vertices are close to globally developable smooth surfaces; we also build sequences of globally developable triangulations
inscribed on a sphere, with a number of vertices and edges tending to infinity. Finally, we also give an example of a triangulation
with strictly
negative Gauss curvature at any interior point, inscribed in a smooth surface with a strictly positive Gauss curvature. The
Gauss curvature of these triangulations becomes positive (at each interior vertex) only by switching some of their edges. 相似文献
13.
We introduce series-triangular graph embeddings and show how to partition point sets with them. This result is then used to prove an upper bound on the number of Steiner points needed to obtain compatible triangulations of point sets. The problem is generalized to finding compatible triangulations for more than two point sets and we show that such triangulations can be constructed with only a linear number of Steiner points added to each point set. Moreover, the compatible triangulations constructed by these methods are regular triangulations. 相似文献
14.
Jean-Daniel Boissonnat Ramsay Dyer Arijit Ghosh 《Foundations of Computational Mathematics》2018,18(2):399-431
We present an algorithm for producing Delaunay triangulations of manifolds. The algorithm can accommodate abstract manifolds that are not presented as submanifolds of Euclidean space. Given a set of sample points and an atlas on a compact manifold, a manifold Delaunay complex is produced for a perturbed point set provided the transition functions are bi-Lipschitz with a constant close to 1, and the original sample points meet a local density requirement; no smoothness assumptions are required. If the transition functions are smooth, the output is a triangulation of the manifold. The output complex is naturally endowed with a piecewise-flat metric which, when the original manifold is Riemannian, is a close approximation of the original Riemannian metric. In this case the output complex is also a Delaunay triangulation of its vertices with respect to this piecewise-flat metric. 相似文献
15.
We call a point ??dynamically special?? if it has a dynamical property, which no other point has. We prove that, for continuous self maps of the real line, all dynamically special points are in the closure of the union of the full orbits of periodic points, critical points and limits at infinity. We completely describe the set of dynamically special points of real polynomial functions. The following characterization for the set of special points is also obtained: A subset of ${\mathbb{R}}$ is the set of dynamically special points for some continuous self map of ${\mathbb{R}}$ if and only if it is closed. 相似文献
16.
Yu. M. Burman 《Annals of Global Analysis and Geometry》1999,17(3):221-238
We consider triangulations of surfaces with boundary and marked points. These triangulations are classified with respect to flip equivalence. The results obtained are applied to the homotopy classification of functions without critical points on 2-manifolds. It is shown that the set of such functions satisfies the one-parametric h-principle. 相似文献
17.
We construct for each $n$ an Eulerian partially ordered set $T_n$ of
rank $n+1$ whose $ce$-index provides a non-commutative generalization of
the $n$th Tchebyshev polynomial. We show that the order complex of each $T_n$
is shellable, homeomorphic to a sphere, and that its face numbers minimize the
expression $\max_{|x|\leq 1} |\sum_{j=0}^n (f_{j-1}/f_{n-1})\cdot
2^{-j}\cdot (x-1)^j|$
among the $f$-vectors of all $(n-1)$-dimensional simplicial
complexes. The duals of the posets constructed have a recursive
structure similar to face lattices of simplices or cubes, offering the
study of a new special class of Eulerian partially ordered sets to test
the validity of Stanleys conjecture on the non-negativity of the
$cd$-index of all Gorenstein$^*$ posets. 相似文献
18.
19.
1.IntroductionConsideramodelellipticboundaryvalueproblemwhereflCRd,d=1,2,3,isaboundedpolyhedraldomainwithaLip8chitzboundaryfEL'(fl),aijareLipschitz-continuousfunctionsandthematrixA=(aij)issymmetricanduniformlypositivedefinitewithrespecttoxEn.Itisknownthatthefiniteelementmethodappliedto(1.1)mayproducesomesuperconvergencephenomenaeveniftheusedmeshesarenonuniform[5'8'9'1o'121.InarecentpaPer[61,aninteriorerrorestimatefortherecoveredgradientofGalerkinpiecewiselinearaPproximationshasbeenproposed… 相似文献