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We study the complete convergence and complete moment convergence for martingale difference sequence. Especially, we get the Baum-Katz-type Theorem and Hsu-Robbins-type Theorem for martingale difference sequence. As a result, the Marcinkiewicz-Zygmund strong law of large numbers for martingale difference sequence is obtained. Our results generalize the corresponding ones of Stoica (2007, 2011).

We investigate the complete moment convergence of double-indexed weighted sums of martingale differences. Then it is easy to obtain the Marcinkiewicz-Zygmund-type strong law of large numbers of double-indexed weighted sums of martingale differences. Moreover, the convergence of double-indexed weighted sums of martingale differences is presented in mean square. On the other hand, we give the application to study the convergence of the state observers of linear-time-invariant systems and present the convergence with probability one and in mean square. [ABSTRACT FROM AUTHOR]

Suspensions of graphene, prepared from graphite foil by sonochemical exfoliation, have been treated with new nonpolar pyrenebutyric amides. The assemblies, in suspension and after deposition on solid supports, were characterized by NMR, absorption, and fluorescence spectroscopy and by transmission electron microscopy, where the well-defined shape and size of an appended [60]fulleropyrrolidine unit facilitates TEM detection of the nonstationary molecules. The accumulated evidence, also including direct comparisons of carbon nanotubes treated with pyrene amides under the same conditions, proves the successful noncovalent functionalization of graphene suspended in non-polar solvent with non-polar pyrene derivatives. [ABSTRACT FROM AUTHOR]

We investigate the moving average process such that Xn = Σi=1∞ αiΓi+n n ≥ 1, where Σi=1#8734; |αi| < ∞ and {Γi, 1 ≤ i < ∞} is a sequence of asymptotically almost negatively associated (AANA) random variables. The complete convergence, complete moment convergence, and the existence of the moment of supermum of normed partial sums are presented for this moving average process. [ABSTRACT FROM AUTHOR]

We study the complete consistency for estimator of nonparametric regression model based on ...-mixing sequences by using the classical Rosenthal-type inequality and the truncated method. As an application, the complete consistency for the nearest neighbor estimator is obtained. [ABSTRACT FROM AUTHOR]

Let {Xni,i ≥ 1, n ≥ 1} be an array of rowwise asymptotically almost negatively associated (AANA, in short) random variables. The complete convergence for weighted sums of arrays of rowwise AANA random variables is studied, which complements and improves the corresponding result of Baek et al. (2008). As applications, the Baum and Katz type result for arrays of rowwise AANA random variables and the Marcinkiewicz-Zygmund type strong law of large numbers for sequences of AANA random variables are obtained. [ABSTRACT FROM AUTHOR]

Let {Xni,i ≥ 1,n ≥ 1} be an array of rowwise asymptotically almost negatively associated random variables. Some sufficient conditions for complete convergence for arrays of rowwise asymptotically almost negatively associated random variables are presented without assumptions of identical distribution. As an application, the Marcinkiewicz-Zygmund type strong law of large numbers for weighted sums of asymptotically almost negatively associated random variables is obtained. [ABSTRACT FROM AUTHOR]