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1.
In this paper an anisotropic interpolation theorem is presentedthat can be easily used to check the anisotropy of an element.A kind of quasi-Wilson element is considered for second-orderproblems on narrow quadrilateral meshes for which the usualregularity condition K/hK c0 > 0 is not satisfied, wherehK is the diameter of the element K and K is the radius of thelargest inscribed circle in K. Anisotropic error estimates ofthe interpolation error and the consistency error in the energynorm and the L2-norm are given. Furthermore, we give a Poincaréinequality on a trapezoid which improves a result of eniek.  相似文献
2.
Uniform perfectness of self-affine sets   总被引:2,自引:0,他引:2  
Let be affine maps of Euclidean space with each nonsingular and each contractive. We prove that the self-affine set of is uniformly perfect if it is not a singleton.

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3.
On the tail index of a heavy tailed distribution   总被引:1,自引:0,他引:1  
This paper proposes some new estimators for the tail index of a heavy tailed distribution when only a few largest values are observed within blocks. These estimators are proved to be asymptotically normal under suitable conditions, and their Edgeworth expansions are obtained. Empirical likelihood method is also employed to construct confidence intervals for the tail index. The comparison for the confidence intervals based on the normal approximation and the empirical likelihood method is made in terms of coverage probability and length of the confidence intervals. The simulation study shows that the empirical likelihood method outperforms the normal approximation method.  相似文献
4.
Smoothed jackknife empirical likelihood method for ROC curve   总被引:1,自引:0,他引:1  
In this paper we propose a smoothed jackknife empirical likelihood method to construct confidence intervals for the receiver operating characteristic (ROC) curve. By applying the standard empirical likelihood method for a mean to the jackknife sample, the empirical likelihood ratio statistic can be calculated by simply solving a single equation. Therefore, this procedure is easy to implement. Wilks’ theorem for the empirical likelihood ratio statistic is proved and a simulation study is conducted to compare the performance of the proposed method with other methods.  相似文献
5.
Computability of measurable sets via effective topologies   总被引:1,自引:0,他引:1  
We investigate in the frame of TTE the computability of functions of the measurable sets from an infinite computable measure space such as the measure and the four kinds of set operations. We first present a series of undecidability and incomputability results about measurable sets. Then we construct several examples of computable topological spaces from the abstract infinite computable measure space, and analyze the computability of the considered functions via respectively each of the standard representations of the computable topological spaces constructed. The authors are supported by grants of NSFC and DFG.  相似文献
6.
Uniform perfectness of the attractor of bi-Lipschitz IFS   总被引:1,自引:0,他引:1  
In this paper, we prove that the attractor of C1,a bi-Lipschitz IFS in R is uniformly perfect if it is not a singleton. Then we construct an example to show that this does not hold for C1 bi-Lipschitz IFS in Rn.  相似文献
7.
The topology of Julia sets for polynomials   总被引:1,自引:0,他引:1  
We prove that wandering components of the Julia set of a polynomial are singletons provided each critical point in a wandering Julia component is non-recurrent. This means a conjecture of Branner-Hubbard is true for this kind of polynomials  相似文献
8.
GEOMETRY AND DIMENSION OF SELF—SIMILAR SET   总被引:1,自引:0,他引:1       下载免费PDF全文
The authors show that the self-similar set for a finite family of contractive similitudes (similarities, i.e., |fi(x) - fi(y)| = αi|x - y|, x,y ∈ RN, where 0 < αi < 1) is uniformly perfect except the case that it is a singleton. As a corollary, it is proved that this self-similar set has positive Hausdorff dimension provided that it is not a singleton. And a lower bound of the upper box dimension of the uniformly perfect sets is given. Meanwhile the uniformly perfect set with Hausdorff measure zero in its Hausdorff dimension is given.  相似文献
9.
For any polynomialp(z)=a 0 z n +a|z n–1++a n , a00, n2,F is the Julia set and * is the equilibrium distribution onF. Hans Brolin[1] proved that (F)>0, andS * =F. Up to now, we know nothing about rational functions. The aim of this paper is to discuss the case of rational functions.Project supported by the Science Fund of the Chinese Academy of Sciences.  相似文献
10.
Empirical likelihood for general estimating equations is a method for testing hypothesis or constructing confidence regions on parameters of interest. If the number of parameters of interest is smaller than that of estimating equations, a profile empirical likelihood has to be employed. In case of dependent data, a profile blockwise empirical likelihood method can be used. However, if too many nuisance parameters are involved, a computational difficulty in optimizing the profile empirical likelihood arises. Recently, Li et al. (2011) [9] proposed a jackknife empirical likelihood method to reduce the computation in the profile empirical likelihood methods for independent data. In this paper, we propose a jackknife-blockwise empirical likelihood method to overcome the computational burden in the profile blockwise empirical likelihood method for weakly dependent data.  相似文献
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