Hájek-Rényi-type Inequality for a Class of Random Variable Sequences and Its Applications

In this paper, we obtain the Hejek-Renyi-type inequality for a class of random variable sequences and give some applications for associated random variable sequences, strongly positive dependent stochastic sequences and martingale difference sequences which generalize and improve the results of Prakasa Rao and Soo published in Statist. Probab. Lett., 57（2002） and 78（2008）. Using this result, we get the integrability of supremum and the strong law of large numbers for a class of random variable sequences.

SOME LIMIT THEOREMS FOR SEQUENCES OF PAIRWISE NQD RANDOM VARIABLES

In this article, the authors study some limit properties for sequences of pairwise NQD random variables, which are not necessarily identically distributed. They obtain Baum and Katz complete convergence and the strong stability of Jamison＇s weighted sums for pairwise NQD random variables, which may have different distributions. Some wellknown results are improved and extended.

Strong Law of Large Numbers and Complete Convergence for Sequences of -Mixing Random Variables

We give some theorems of strong law of large numbers and complete convergence for sequences of φ-mixing random variables. In particular, Wittmann＇s strong law of large numbers and Teicher＇s strong law of large nnumbers for independent random variables are generalized to the case of φ -minxing random variables.

SOME LIMIT THEOREMS FOR WEIGHTED SUMS OF ARRAYS OF NOD RANDOM VARIABLES

In this paper the authors study the complete, weak and almost sure convergence for weighted sums of NOD random variables and obtain some new limit theorems for weighted sums of NOD random variables, which extend the corresponding theorems of Stout [1], Thrum [2] and Hu et al. [3].

On the Strong Law of Large Numbers for Non-Independent B-Valued Random Variables

This paper investigates some conditions which imply the strong laws of large numbers for Banach space valued random variable sequences. Some generalizations of the Marcinkiewicz-Zygmund theorem and the Hoffmann-J?rgensen and Pisier theorem are obtained. Key words strong law of large numbers - Banach space valued random variable sequence - p-smoothable Banach space CLC number O 211.4 - O 211.6 Foundation item: Supported by the National Natural Science Foundation of China (10071058)Biography: Gan Shi-xin (1939-), male, Professor, research direction: martingale theory, probability limiting theory and Banach space geometry theory.

The 20 April 2013 Lushan, Sichuan, mainshock, and its aftershock sequence: tectonic implications

Using the double-difference relocation algo- rithm, we relocated the 20 April 2013 Lushan, Sichuan, earthquake （Ms 7.0）, and its 4,567 aftershocks recorded during the period between 20 April and May 3, 2013. Our results showed that most aftershocks are relocated between 10 and 20 km depths, but some large aftershocks were relocated around 30 krn depth and small events extended upward near the surface. Vertical cross sections illustrate a shovel-shaped fault plane with a variable dip angle from the southwest to northeast along the fault. Furthermore, the dip angle of the fault plane is smaller around the mainshock than that in the surrounding areas along the fault. These results suggest that it may be easy to generate the strong earthquake in the place having a small dip angle of the fault, which is somewhat similar to the genesis of the 2008 Wenchuan earthquake. The Lushan mainshock is underlain by the seismically anomalous layers with low-Vp, low-Vs, and high-Poisson＇s ratio anomalies, possibly suggesting that the fluid-filled fractured rock matrices might signifi- cantly reduce the effective normal stress on the fault plane to bring the brittle failure. The seismic gap between Lushan and Wenchuan aftershocks is suspected to be vulnerable to future seismic risks at greater depths, if any.

Sequence variability of the 5, UTR in isolates of hepatitis C virus in China

Background: Hepatitis C virus infection is a great is- sue in China; however, there is very little informa- tion on genotyping investigations based on sequence variability in the 5' untranslated (5'UTR) reported. The present study was to define the sequence varia- bility based on the sequence divergences of the 5' UTR of the virus. Methods: Sequences of 91 isolates from patients with chronic hepatitis C from Yunnan, southwest China, were sequenced and genotypes were defined accord- ing to the sequence divergences of the 5' UTR of the virus. Results: Eighty-six isolates were classified into 3 clades (previously termed groups or major types) by the methods proposed by Chan et al in 1992 and phy- logenetic analysis based on nucleotide sequence diver- gences within the 5' UTR. Fifty-six percent of the i- solates were classified into clade 3, 35% into clade 1, and 34.9% into clade 2. New genotypes 1f, 2h, 3h and 3i were defined. In addition, 3 novel sequences were discovered, respectively with an 18-nt sequence deletion (corresponding to nucleotide position -173 to -156), a 28-nt sequence insertion, and a 40-nt se- quence insertion, between -56 and -55. Of these i- solates, 56% possessed a 'G' at position -66 in place of the 'T' that is present in all previously re- ported sequences. Conclusions: These HCV variants, evolved or re- mained in this area, may be of great significance in diagnosis and treatment of hepatitis C patients.

Diffusion tensor imaging of spinal microstructure in healthy adults： improved resolution with the readout segmentation of long variable echo-trains

Diffusion tensor imaging plays an important role in the accurate diagnosis and prognosis of spinal cord diseases. However, because of technical limitations, the imaging sequences used in this technique cannot reveal the fine structure of the spinal cord with precision. We used the readout segmentation of long variable echo-trains（RESOLVE） sequence in this cross-sectional study of 45 healthy volunteers aged 20 to 63 years. We found that the RESOLVE sequence significantly increased the resolution of the diffusion images and improved the median signal-to-noise ratio of the middle（C4–6） and lower（C7–T1） cervical segments to the level of the upper cervical segment. In addition, the values of fractional anisotropy and radial diffusivity were significantly higher in white matter than in gray matter. Our study verified that the RESOLVE sequence could improve resolution of diffusion tensor imaging in clinical applications and provide accurate baseline data for the diagnosis and treatment of cervical spinal cord diseases.

Some Remarks for Sequences of Pairwise NQD Random Variables

We first obtain the Petrov theorem for pairwise NQD（negative quadrant dependent） random variables which may have different distributions.Some well-known results are improved and extended.Next,we give an example to clarify one of the important properties of sequences of pairwise NQD random variables,so that we can point out some mistakes that have appeared in recent published papers.

ON THE STRONG LAW OF LARGE NUMBERS

This paper introduces the concept of BC sequences and investigates some conditions which imply the strong law of large numbers for these sequences. The authors also study the strong law of large numbers for general random variable sequences. As applications of the result the authors characterize p-smoothableness of Banach space. Some generalizations of Petrov theorem, the Marcinkiewicz-Zygmund theorem and Hoffmann-J(?)rgensen and Pisier theorem are obtained.

On a Conjecture of an Invariance Principle for Sequences of Associated Random Variables

A finite collection of random variables, X1} —, Xm, is said to be associated if any two coordinatewise nondecreasing functions /i and /a on Rm such that Jt = fj(Xi} , Xm~) has finite variance for j = l, 2, Oov(/i,fa)>0; an infinite collection is said to be associated if every finite subcollection is. associated. Thus the concept of "association" is introduced as dependence in probability (Esary, Proschan and Walkup (1967)). It is relative to a lot of practical models, such as the percolation models, the Ising models of statistical mechanics. Therefore, some people are

THE GROWTH AND BOREL POINTS OF RANDOM ALGEBROID FUNCTIONS IN THE UNIT DISC

In this paper,we construct k-valued random analytic algebroid functions for the first time.By combining the properties of random series,we study the growth and Bor el points of random analytic algebroid functions in the unit disc and obtain some interesting theorems.

Long-term photometric behavior of the PMS stars V977 Cep and V982 Cep in the vicinity of NGC 7129

Long-term BVRI photometric light curves of the pre-main sequence stars V977 Cep and V982 Cep during the period from 2000 October to 2016 August are presented. The stars are located in the vicinity of the reflection nebula NGC 7129. Our photometric data show that both stars exhibit strong photometric variability in all optical passbands, which is typical for Classical T Tauri stars. Using our observational data we analyze the reasons for the observed brightness variations. In the case of V977 Cep we identify previously unknown periodicity in its light curve.

Strong Stability of Linear Forms in φ-Mixing Random Variables

In this paper some new results of strong stability of linear forms in φ-mixing random variables are given. It is mainly proved that for a sequence of φ-mixing random variables {xn,n≥1} and two sequences of positive numbers {an,n≥1} and {bn,n≥1} there exist d dn∈R,n = 1,2,..., such that bn^-1∑i=1^naixi-dn→0 a.s.under some suitable conditions. The results extend and improve the corresponding theorems for independent identically distributed random variables.

Rosenthal Inequality for NOD Sequences and Its Applications

Rosenthal inequality for NOD （negatively＇ orthant dependent） random variable sequences is established. As its applications, two theorems of complete convergence of weighted sums for arrays of NOD random variables are given, which extend the corresponding known results.

Laws of the Iterated Logarithm for-mixing Random Variables with Normal Distribution

Consider a ρ-mixing sequence of identically distributed random variables with the underlying dis- tribution in the domain of attraction of the normal distribution. This paper proves that law of the iterated logarithm holds for ρ-mixing sequences of random variables. Our results generalize and improve Theorems 1.2-1.3 of Qi and Cheng （1996） from the i.i.d, case to ρ-mixing sequences.