Abstract:
Protein disulfide isomerase (PDI) is a chaperone protein involved in oxidative protein folding by acting as a catalyst and assisting folding in the endoplasmic reticulum (ER). A genome database search showed that rice contains 19 PDI-like genes. However, their functions are not clearly identified. This paper shows possible functions of rice PDI-like protein 1-1 (PDIL1-1) during seed development. Seeds of the T-DNA insertion PDIL1-1 mutant, PDIL1-1Δ, identified by genomic DNA PCR and western blot analysis, display a chalky phenotype and a thick aleurone layer. Protein content per seed was significantly lower and free sugar content higher in PDIL1-1Δ mutant seeds than in the wild type. Proteomic analysis of PDIL1-1Δ mutant seeds showed that PDIL1-1 is post-translationally regulated, and its loss causes accumulation of many types of seed proteins including glucose/starch metabolism- and ROS (reactive oxygen species) scavenging-related proteins. In addition, PDIL1-1 strongly interacts with the cysteine protease OsCP1. Our data indicate that the opaque phenotype of PDIL1-1Δ mutant seeds results from production of irregular starch granules and protein body through loss of regulatory activity for various proteins involved in the synthesis of seed components.

Abstract:
Plant mitochondria possess alternative respiratory pathwaysmediated by the type II NAD(P)H dehydrogenases and alternativeoxidases. Here, E3 SUMO ligase was shown to regulatealternative respiratory pathways and to participate in the maintenanceof carbon and nitrogen balance in Arabidopsis. Thetranscript abundance of the type II NAD(P)H dehydrogenasesNDA2 and NDB2 and alternative oxidases AOX1a and AOX1dgenes was low in siz1-2 mutants compared to that in wild-type.The addition of nitrate or ammonium resulted in a decrease oran increase in the expression of the same gene families, respectively,in both wild-type and siz1-2 mutants. The amountof free sugar (glucose, fructose and sucrose) was lower in siz1-2mutants than that in wild-type. These results indicate that lownitrate reductase activity due to the AtSIZ1 mutation is correlatedwith an overall decrease in alternative respiration andwith a low carbohydrate content to maintain the carbon to nitrogenratio in siz1-2 mutants.

Abstract:
A rate of complete convergence for weighted sums of arrays of rowwise independent random variables was obtained by Sung and Volodin (2011). In this paper, we extend this result to negatively associated and negatively dependent random variables. Similar results for sequences of -mixing and ？-mixing random variables are also obtained. Our results improve and generalize the results of Baek et al. (2008), Kuczmaszewska (2009), and Wang et al. (2010).

Abstract:
We obtain the complete convergence for weighted sums of -mixing random variables. Our result extends the result of Peligrad and Gut (1999) on unweighted average to a weighted average under a mild condition of weights. Our result also generalizes and sharpens the result of An and Yuan (2008). 1. Introduction In many stochastic models, the assumption that random variables are independent is not plausible. So it is of interest to extend the concept of independence to dependence cases. One of these dependence structures is -mixing. Let be a sequence of random variables defined on a probability space and let denote the -algebra generated by the random variables For any define Given two -algebras in put where Define the -mixing coefficients by Obviously, The sequence is called -mixing (or -mixing) if there exists such that Note that if is a sequence of independent random variables, then for all A number of limit results for -mixing sequences of random variables have been established by many authors. We refer to Bradley [1] for the central limit theorem, Bryc and Smoleński [2], Peligrad and Gut [3], and Utev and Peligrad [4] for moment inequalities, Gan [5], Kuczmaszewska [6], and Wu and Jiang [7] for almost sure convergence, and An and Yuan [8], Cai [9], Gan [5], Kuczmaszewska [10], Peligrad and Gut [3], and Zhu [11] for complete convergence. The concept of complete convergence of a sequence of random variables was introduced by Hsu and Robbins [12]. A sequence of random variables converges completely to the constant if In view of the Borel-Cantelli lemma, this implies that almost surely. Therefore, the complete convergence is a very important tool in establishing almost sure convergence of summation of random variables as well as weighted sums of random variables. Hsu and Robbins [12] proved that the sequence of arithmetic means of independent and identically distributed random variables converges completely to the expected value if the variance of the summands is finite. Erd？s [13] proved the converse. The result of Hsu-Robbins-Erd？s is a fundamental theorem in probability theory and has been generalized and extended in several directions by many authors. One of the most important generalizations is Baum and Katz [14] strong law of large numbers. Theorem 1.1 (Baum and Katz [14]). Let and Let be a sequence of independent and identically distributed random variables with Then the following statements are equivalent: (i) (ii) for all Peligrad and Gut [3] extended the result of Baum and Katz [14] to -mixing random variables. Theorem 1.2 (Peligrad and Gut [3]).

Abstract:
Using exponential inequalities, Wu et al. (2009) and Wang et al. (2010) obtained asymptotic approximations of inverse moments for nonnegative independent random variables and nonnegative negatively orthant dependent random variables, respectively. In this paper, we improve and extend their results to nonnegative random variables satisfying a Rosenthal-type inequality.

Abstract:
A complete convergence result for an array of rowwise independent mean zero random variables was established by Kruglov et al. (2006). This result was partially extended to negatively associated and negatively dependent mean zero random variables by Chen et al. (2007) and Dehua et al. (2011), respectively. In this paper, we obtain complete extended versions of Kruglov et al. Mathematics Subject Classification 60F15

Abstract:
Let {Yi, 1≤i≤n} and {Zi, 1≤i≤n} be sequences of random variables. For any >0 and a>0, bounds for E(|∑i=1n(Yi+Zi)| a)+ and E(max 1≤k≤n|∑i=1k(Yi+Zi)| a)+ are obtained. From these results, we establish general methods for obtaining the complete moment convergence. The results of Chow (1988), Zhu (2007), and Wu and Zhu (2009) are generalized and extended from independent (or dependent) random variables to random variables satisfying some mild conditions. Some applications to dependent random variables are discussed.

Abstract:
An exponential inequality is established for identically distributed negatively associated random variables which have the finite Laplace transforms. The inequality improves the results of Kim and Kim (2007), Nooghabi and Azarnoosh (2009), and Xing et al. (2009). We also obtain the convergence rate O(1)n1/2(log n) 1/2 for the strong law of large numbers, which improves the corresponding ones of Kim and Kim, Nooghabi and Azarnoosh, and Xing et al.

Abstract:
For a sequence {Xn,n ￠ ‰ ￥1} of dependent square integrable random variables and a sequence {bn,n ￠ ‰ ￥1} of positive numbers, we establish a maximal inequality for weighted sums of dependent random variables. Applying this inequality, we obtain the almost sure convergence of ￠ ‘i=1nXi/bi and ￠ ‘i=1nXi/bn.