On Complete Convergence for Arrays of Rowwise Strong Mixing Random Variables

In this paper, we present a general method to prove the complete conver- gence for arrays of rowwise strong mixing random variables, and give some results on complete convergence under some suitable conditions. Some Marcinkiewicz-Zygmund type strong laws of large numbers are also obtained.

Joint empirical likelihood confidence regions for a finite number of quantiles under strong mixing samples

In this paper, we obtain the joint empirical likelihood confidence regions for a finite number of quantiles under strong mixing samples. As an application of this result, the empirical likelihood confidence intervals for the difference of any two quantiles are also obtained.

Maximal Moment Inequality for Partial Sums of Strong Mixing Sequences and Application

Some maximal moment inequalities for partial sums of the strong mixing random variable sequence are established. These inequalities use moment sums as up-boundary and improve the corre- sponding ones obtained by Shao （1996）. To show the application of the inequalities, we apply them to discuss the asymptotic normality of the weight function estimate for the fixed design regression model.

Nonparametric estimation for stationary and strongly mixing processes on Riemannian manifolds

In this paper,nonparametric estimation for a stationary strongly mixing and manifoldvalued process(X_(j))is considered.In this non-Euclidean and not necessarily i.i.d setting,we propose kernel density estimators of the joint probability density function,of the conditional probability density functions and of the conditional expectations of functionals of X_(j)given the past behavior of the process.We prove the strong consistency of these estimators under sufficient conditions,and we illustrate their performance through simulation studies and real data analysis.

An oracle inequality for regularized risk minimizers with strongly mixing observations

We establish a general oracle inequality for regularized risk minimizers with strongly mixing observations, and apply this inequality to support vector machine （SVM） type algorithms. The obtained main results extend the previous known results for independent and identically distributed samples to the case of exponentially strongly mixing observations.

Two-electron and one-photon transitions in highly charged nickel-like ions

This paper calculates the transition wavelengths and probabilities of the two-electron and one-photon （TEOP） transition from the （3s1/2^-14dj）J=1,2 to （3P3/2^-14s1/2）J=1 and the （3P1/2^-14s1/2）J=1 to （3dj^-14dj＇）J=1,2 for highly charged Ni-like ions with atomic number Z in the range 47 〈 Z 〈 92. In the calculations, the multi-configuration Dirac-Fock method and corresponding program packages GRASP92 and REOS99 were used, and the relativistic effects, correlation effects and relaxation effects were considered systematically. It is found that the TEOP transitions are very sensitive to the correlation of electrons, and the probabilities will be enhanced sharply in some special Z regions along the isoelectronic sequence. The present TEOP transition wavelengths are compared with the available data from some previous publications, good agreement is obtained.

Bahadur Representation of Nonparametric M-Estimators for Spatial Processes

Under some mild conditions, we establish a strong Bahadur representation of a general class of nonparametric local linear M-estimators for mixing processes on a random field. If the socalled optimal bandwidth hn = O（｜n｜^-1/5）, n ∈ Z^d, is chosen, then the remainder rates in the Bahadur representation for the local M-estimators of the regression function and its derivative are of order O（｜n｜^-4/5 log ｜n｜）. Moreover, we derive some asymptotic properties for the nonparametric local linear M-estimators as applications of our result.

A Note on Quasi-weakly Almost Periodic Point

Recently, He et al. [On quasi-weakly almost periodic points. Sci. China Math., 56, 597- 606 （2013）] constructed two binary sub-shifts to solve an open problem posed by Zhou and Feng in [Twelve open problems on the exact value of the Hausdorff measure and on topological entropy： A brief survey of recent results. Nonlinearity, 17, 493-502 （2004）]. In this paper, we study more dynamical properties of those two binary sub-shifts. We show that the first one has zero topological entropy and is transitive but not weakly mixing, while the second one has positive topological entropy and is strongly mixing.