A Note on the Almost Sure Central Limit Theorem for Partial Sums of ρ^(−)-Mixing Sequences

Let be a strictly stationary sequence of ρ?-mixing random variables. We proved the almost sure central limit theorem, containing the general weight sequences, for the partial sums , where , . The result generalizes and improves the previous results.

Complete Convergence Properties of the Sums for -mixing Sequences of Random Variables

This paper discusses complete convergence properties of the sums of -mixing random sequences.As a result,we improve the corresponding results of Wu Qunying(2001). And extended the Baum and Katz complete convergence to the case of -mixing random sequences by moment inequality and truncating without necessarily adding any extra conditions.

COMPLETE CONVERGENCE FOR A CLASS OF MIXING SEQUENCES

Under some conditions on probability, the author obtains some results on the complete convergence for partial sums of not necessary identically distributed p-mixing se- quences, and the complete convergence for partial sums of B-valued martingale differences is also studied. As application the author gives the corresponding results on the complete convergence for randomly indexed partial sums.

An Almost Sure Central Limit Theorem for Weighted Sums of Mixing Sequences

In this paper, we prove an almost sure central limit theorem for weighted sums of mixing sequences of random variables without stationary assumptions. We no longer restrict to logarithmic averages, but allow rather arbitrary weight sequences. This extends the earlier work on mixing random variables

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.

Complete Convergence and Weak Law of Large Numbers for <i><span style="text-decoration:overline;">ρ</span></i>-Mixing Sequences of Random Variables

In this paper, the complete convergence and weak law of large numbers are established for ρ-mixing sequences of random variables. Our results extend and improve the Baum and Katz complete convergence theorem and the classical weak law of large numbers, etc. from independent sequences of random variables to ρ-mixing sequences of random variables without necessarily adding any extra conditions.

Upper Large Deviations for Mixing Random Sequence

In this article, we prove upper large deviations for the empirical measure generated by stationary mixing random sequence under some suitable assumptions and upper large deviations for the mixing random sequence.

Tracing surface seawater mixing and nutrient transport by^(222)Rn on the northern coast of Beibu Gulf,China

The transport and diffusion of substances in seawater are limited by the mixing motion of water bodies,while the main forms of mixing in offshore water bodies are advection and eddy diffusion.The eddy diffusion process of water indicates the possible transport direction of dissolved substances.However,the complex environment in the coastal zone makes it difficult to quantitatively assess the water diffusion process.^(222)Rn is a useful tool to trace the diffusion process of water bodies.However,studies on the^(222)Rn distribution and its behavior in the Beibu Gulf are scarce.In this study,the activity distribution characteristics of^(222)Rn in surface seawater of the Guangxi shelf area of the Beibu Gulf were measured.Based on the one-dimensional,steady-state model,the vorticity diffusion coefficient of^(222)Rn in the horizontal direction was calculated as(0.42−2.13)×10^(8) m^(2)/d,and the offshore fluxes of^(222)Rn under the influence of water mixing were calculated as 2.00×10^(12) Bq/d.Correspondingly,the horizontal transport fluxes of silicate,phosphate,nitrite and nitrate were 6.28×10^(−3)mol/(m^(2)·d),0.10×10^(−3)mol/(m^(2)·d),0.20×10^(−3)mol/(m^(2)·d)and 4.15×10^(−3)mol/(m^(2)·d),respectively.These results indicate that the study of eddy current diffusion in offshore marine water facilitates a deeper understanding of the water mixing process and nutrient transport and migration.

Complete Convergence for Weighted Sums of φ-mixing Sequence

In this paper, the complete convergence and strong law of large numbers for weighted sums of φ-mixing sequence with different distribution are investigated under some weaker moment conditions. Our results extend ones of independent sequence with identical distribution to the case of φ-mixing sequence with different distribution.

非同分布φ-mixing序列的完全收敛性

设为随机变量序列，文章在较弱的混合速度且非同分布的条件 下证明了其完全 收敛性的一个结果.

Mixing Deposition of Upper Carboniferous in Jiangshan,Zhejiang Province and its Tectonic Significance

The Outangdi Formation in Jiangshan, Zhejiang, is the mixing deposit of terrigenous clastics and carbonates in Weiningian of the late Carboniferous. The mixing deposits include interbeddings, which constitute a series of alternated clastic and carbonate beds and mixing within the same bed which forms ＂hunji rock＂. The Outangdi Formation has the features of intercalated marine and terrestrial deposits with the progradational sequences, which are lower fine and upper coarse sedimentary granularity in the section. Hunji rock is formed in a seashore environment. It is a mixed carbonate sediment found in beaches or tideland facies with quartz sand taken from a bayou or beach by coastwise flow and circumfluence. There are two kinds of hunji sequences： （1） interbeds of sandstone and carbonate rock in seashore environments; and （2） interbeds of clastics in river facies and carbonate rock in ocean facies. It is indicated that mixing depositions belong to ＂facies mixing＂, affected mainly by regional tectonic uplift, rise of the global sea level, and the dynamics of water medium in the basin. Regional sea level periodic changes and progradational sequences probably resulted from the intense uplift of the old land called Cathaysia. The classification and name of mixed sediments are also discussed in the present study. Interbeds and alternated beds of clastic and carbonate beds are named ＂hunji sequence＂, a new genetic term. It is suggested that hunji rock means a special sediment event of mixing terrigenous clastics and carbonates instead of a name of a specific rock.

Sequencing of Mixed Model Assembly Lines Based on Improved Shuffled Frog Leaping Algorithm

Shuffled frog leaping algorithm( SFLA) was used to solve multi-objective sequencing problem of mixed model assembly line( MMAL). Local convergence can be avoided and optimal solution can be obtained to a certain extent. However,the multi-objective sequencing problem of MMAL is an non-deterministic polynomial hard( NP-hard) problem and the shortcomings are slow convergence rate and low precision. To solve the shortcomings for optimization objectives of minimizing total utility time and keeping average consumption rate of parts, a chaos differential evolution SFLA( CDESFLA) is proposed in this study. Because SFLA is easy to fall into local optimum,the evolution operator of differential evolution algorithms is introduced in SFLA as a local search strategy,and differential mutation operator is introduced in chaotic sequence to prevent premature convergence. The examples show that the proposed CDESFLA is better for convergence accuracy than SFLA,genetic algorithm( GA) and particle swarm optimization( PSO)

Some Convergence Results for Arbitrary Sequences under Moment Condition

Let {X n , n ≥ 1} be an arbitrary sequence of random variables. Some convergence results for the partial sums of arbitrary sequence of random variables are obtained, which generalize the known results for independent sequences, NA sequences, ρ-mixing sequences and φ-mixing sequences, and so on.

LARGE DEVIATIONS FOR SOME DEPENDENT SEQUENCES

Let （Xi） be a martingale difference sequence and Sn=∑^ni=1Xi Suppose （Xi） i=1 is bounded in L^p. In the case p ≥2, Lesigne and Volny （Stochastic Process. Appl. 96 （2001） 143） obtained the estimation μ（Sn 〉 n） ≤ cn^-p/2, Yulin Li （Statist. Probab. Lett. 62 （2003） 317） generalized the result to the case when p ∈ （1,2] and obtained μ（Sn 〉 n） ≤ cn^l-p, these are optimal in a certain sense. In this article, the authors study the large deviation of Sn for some dependent sequences and obtain the same order optimal upper bounds for μ（Sn 〉 n） as those for martingale difference sequence.

Sequencing Mixed-model Production Systems by Modified Multi-objective Genetic Algorithms

As two independent problems,scheduling for parts fabrication line and sequencing for mixed-model assembly line have been addressed respectively by many researchers.However,these two problems should be considered simultaneously to improve the efficiency of the whole fabrication/assembly systems.By far,little research effort is devoted to sequencing problems for mixed-model fabrication/assembly systems.This paper is concerned about the sequencing problems in pull production systems which are composed of one mixed-model assembly line with limited intermediate buffers and two flexible parts fabrication flow lines with identical parallel machines and limited intermediate buffers.Two objectives are considered simultaneously：minimizing the total variation in parts consumption in the assembly line and minimizing the total makespan cost in the fabrication/assembly system.The integrated optimization framework,mathematical models and the method to construct the complete schedules for the fabrication lines according to the production sequences for the first stage in fabrication lines are presented.Since the above problems are non-deterministic polynomial-hard（NP-hard）,a modified multi-objective genetic algorithm is proposed for solving the models,in which a method to generate the production sequences for the fabrication lines from the production sequences for the assembly line and a method to generate the initial population are put forward,new selection,crossover and mutation operators are designed,and Pareto ranking method and sharing function method are employed to evaluate the individuals＇ fitness.The feasibility and efficiency of the multi-objective genetic algorithm is shown by computational comparison with a multi-objective simulated annealing algorithm.The sequencing problems for mixed-model production systems can be solved effectively by the proposed modified multi-objective genetic algorithm.

Development characteristics of the third-order sequence of Upper Devonian–Lower Carboniferous shore-mixed shelf in Tarim Basin, NW China

Based on the study of stratigraphic sedimentary facies of the prototype sedimentary basin formed in the Late Devonian to Permian Period in the Tarim Basin, the prototype sedimentary basin are divided into five order sequences according to the theory of sequence stratigraphy. It is considered that the Upper Devonian–Lower Carboniferous shore-mixing shelf in the lower part of the prototype sedimentary basin is a typical third-order sequence and a sequence development model is established. The third-order sequence is actually a transgression systems tract and highstand systems tract cycle assemblage, and the type I sequence(no lowstand systems tract) is a typical developmental mode of the third order sequence, and the identification mark is the existence of huge mudstone and limestone wedges from sea to land. The fifth-order parasequence is the basic sequence, which is a single cycle sequence. The thin layer limestone isochronous sediments, which are easy to be identified in the mixed shelf areas, are the isochronous sediments of the largest or secondary marine-flooding surface. The mixed shelf area belongs to the equilibrium sedimentary profile of internal and external sediments, and there is no condensed section. The inclined deposition phenomenon of extraneous source sediments in the sea area weakens or disappears in the mixed shelf area. The paleogeomorphology at the bottom of the third-order sequence is a terrace-slope break zone. This paleogeomorphological feature is not only the main reason for the sedimentary diachronism of Donghe sandstone, but also the main reason for the formation of the transgression-highstand fourth-order cyclic sequences of the Donghe sandstone section and its upper gravel-bearing sandstone section.

STUDY ON THE SEQUENCE STRUCTURE OF BUTADIENE-STYRENE RUBBER BY ^(13)C-NMR METHOD V.CALCULATION METHOD OF DIAD COMPOSITION

The calculating equations which could be used to obtain diad composition from the peakintensities of carbon spectra were derived. The result of the microstructure calculated from thediad compositions was in good agreement with that obtained through IR or;H-NMR measurement.

Convergence of Iterative Sequence with Mixed Errors for Uniformly Quasi-Lipschitzian Mappings

In convex metric spaces, the sufficient and necessary conditions for Ishikawa iterative sequences of uniformly quasi-Lipschitzian mapping T with mixed errors to converge to a fixed point ate proved, and as a special case, in which T need not be continuous. The results of this paper improve and extend some recent results.

STUDY ON THE SEQUENCE STRUCTURE OF SBR BY ^(13)C—NMR METHOD Ⅰ. ASSIGNMENT FOR UNSATURAT CARBONS SPECTRA

The sequence structures of emulsion-processed SBR and solution-processed (by lithium catalyst) SBR were investigated by ^(13)C-NMR spectroscopy. Seventeen peaks within unsaturated carbon region were recorded under the adopted experimental conditions. Assignments for these peaks were made by empirical-parameter-evaluation method.

Convergence Rate of Estimator forNonparametric Regression Model under ρ-mixing Errors

In this paper, we investigate the nonparametric regression model based on ρ-mixing errors, which are stochastically dominated by a nonnegative random variable. Weobtain the convergence rate for the weighted estimator of unknown function g（x） in pth-mean, which yields the convergence rate in probability. Moreover, an example of the nearestneighbor estimator is also illustrated and the convergence rates of estimator are presented.