In this paper,by utilizing the Marcinkiewicz-Zygmund inequality and Rosenthal-type inequality of negatively superadditive dependent(NSD)random arrays and truncated method,we investigate the complete f-moment convergen...In this paper,by utilizing the Marcinkiewicz-Zygmund inequality and Rosenthal-type inequality of negatively superadditive dependent(NSD)random arrays and truncated method,we investigate the complete f-moment convergence of NSD random variables.We establish and improve a general result on the complete f-moment convergence for Sung’s type randomly weighted sums of NSD random variables under some general assumptions.As an application,we show the complete consistency for the randomly weighted estimator in a nonparametric regression model based on NSD errors.展开更多
Assume that{a_(i),−∞<i<∞}is an absolutely summable sequence of real numbers.We establish the complete q-order moment convergence for the partial sums of moving average processes{X_(n)=Σ_(i=−∞)^(∞)a_(i)Y_(i+...Assume that{a_(i),−∞<i<∞}is an absolutely summable sequence of real numbers.We establish the complete q-order moment convergence for the partial sums of moving average processes{X_(n)=Σ_(i=−∞)^(∞)a_(i)Y_(i+n),n≥1}under some proper conditions,where{Yi,-∞<i<∞}is a doubly infinite sequence of negatively dependent random variables under sub-linear expectations.These results extend and complement the relevant results in probability space.展开更多
In the paper, the strong convergence properties for two different weighted sums of negatively orthant dependent(NOD) random variables are investigated. Let {X, n ≥ 1}be a sequence of NOD random variables. The results...In the paper, the strong convergence properties for two different weighted sums of negatively orthant dependent(NOD) random variables are investigated. Let {X, n ≥ 1}be a sequence of NOD random variables. The results obtained in the paper generalize the corresponding ones for i.i.d. random variables and identically distributed NA random variables to the case of NOD random variables, which are stochastically dominated by a random variable X. As a byproduct, the Marcinkiewicz-Zygmund type strong law of large numbers for NOD random variables is also obtained.展开更多
A general result on the strong convergence rate and complete convergence for arrays of rowwise extended negatively dependent random variables is established. As applications, some well-known results on negatively depe...A general result on the strong convergence rate and complete convergence for arrays of rowwise extended negatively dependent random variables is established. As applications, some well-known results on negatively dependent random variables can be easily extended to the case of arrays of rowwise extended negatively dependent random variables.展开更多
Strong limit theorems are established for weighted sums of widely orthant dependent（WOD） random variables. As corollaries, the strong limit theorems for weighted sums of extended negatively orthant dependent（ENOD）...Strong limit theorems are established for weighted sums of widely orthant dependent（WOD） random variables. As corollaries, the strong limit theorems for weighted sums of extended negatively orthant dependent（ENOD） random variables are also obtained, which extend and improve the related known works in the literature.展开更多
By using Rosenthal type moment inequality for extended negatively de- pendent random variables, we establish the equivalent conditions of complete convergence for weighted sums of sequences of extended negatively depe...By using Rosenthal type moment inequality for extended negatively de- pendent random variables, we establish the equivalent conditions of complete convergence for weighted sums of sequences of extended negatively dependent random variables under more general conditions. These results complement and improve the corresponding results obtained by Li et al. （Li D L, RAO M B, Jiang T F, Wang X C. Complete convergence and almost sure convergence of weighted sums of random variables. J. Theoret. Probab., 1995, 8： 49-76） and Liang （Liang H Y. Complete convergence for weighted sums of negatively associated random variables. Statist. Probab. Lett., 2000, 48： 317-325）.展开更多
In the paper, the complete convergence for the maximum of weighted sums of negatively superadditive dependent(NSD, in short) random variables is investigated by using the Rosenthal type inequality. Some sufficient con...In the paper, the complete convergence for the maximum of weighted sums of negatively superadditive dependent(NSD, in short) random variables is investigated by using the Rosenthal type inequality. Some sufficient conditions are presented to prove the complete convergence. The result obtained in the paper generalizes some corresponding ones for independent random variables and negatively associated random variables.展开更多
In this paper,an exponential inequality for weighted sums of identically distributed NOD （negatively orthant dependent） random variables is established,by which we obtain the almost sure convergence rate of which re...In this paper,an exponential inequality for weighted sums of identically distributed NOD （negatively orthant dependent） random variables is established,by which we obtain the almost sure convergence rate of which reaches the available one for independent random variables in terms of Berstein type inequality. As application,we obtain the relevant exponential inequality for Priestley-Chao estimator of nonparametric regression estimate under NOD samples,from which the strong consistency rate is also obtained.展开更多
Understanding the thermal stability of the proteins in human serum is essential since human serum is the important source of pharmaceutical proteins. Near-infrared（NIR） spectroscopy was applied to the investigation ...Understanding the thermal stability of the proteins in human serum is essential since human serum is the important source of pharmaceutical proteins. Near-infrared（NIR） spectroscopy was applied to the investigation of thermal changes in secondary structure and hydration of human serum proteins.However, as a multicomponent system, the overlap of the broad NIR bands makes the structural analysis very difficult directly using the spectra of serum samples. Therefore, continuous wavelet transform（CWT） was used to improve the resolution of NIR spectra, and Monte Carlo-uninformative variable elimination（MC-UVE） method was applied to the selection of the variables associated with the proteins for the structural analysis. The variables（5956, 5867, 5815, 5747, 4525, 4401, 4359 and 4328 cm^-1） related to protein secondary structures and those（7074, 6951, 6827 and 6700 cm 1） connected with water species were selected. Then, the thermal stability was analyzed through the intensity variations of the selected variables with temperature from 30℃ to 80 ℃. It was found that the variation of the spectral variables related to both a-helix and b-sheet changes apparently around 60 ℃, indicating the beginning of the thermal denaturation and the transition from a-helix to b-sheet. Moreover, an obvious change was found around 60℃for the content of the water specie S3, i.e., the water cluster containing three hydrogen bonds. The result demonstrates that MC-UVE can identify the protein-related NIR spectral variables, and the water species may be a marker for investigation of the structural change of proteins in biochemical systems.展开更多
In this paper, by using some inequalities of negatively orthant dependent(NOD,in short) random variables and the truncated method of random variables, we investigate the nonparametric regression model. The complete co...In this paper, by using some inequalities of negatively orthant dependent(NOD,in short) random variables and the truncated method of random variables, we investigate the nonparametric regression model. The complete consistency result for the estimator of g(x) is presented.展开更多
Let {X_(nk), k ≥ 1, n ≥ 1} be an array of rowwise negatively superadditive dependent random variables and {a_n, n ≥ 1} be a sequence of positive real numbers such that a_n↑∞. Under some suitable conditions,L_r co...Let {X_(nk), k ≥ 1, n ≥ 1} be an array of rowwise negatively superadditive dependent random variables and {a_n, n ≥ 1} be a sequence of positive real numbers such that a_n↑∞. Under some suitable conditions,L_r convergence of 1/an max 1≤j≤n |j∑k=1 X_(nk)| is studied. The results obtained in this paper generalize and improve some corresponding ones for negatively associated random variables and independent random variables.展开更多
The bounded and smooth solitary wave solutions of 10 nonlinear evolution equations with a positive fractional power term of dependent variable are successfully obtained by homogeneous balance principle and with the ai...The bounded and smooth solitary wave solutions of 10 nonlinear evolution equations with a positive fractional power term of dependent variable are successfully obtained by homogeneous balance principle and with the aid of sub-ODEs that admits a solution of sech-power or tanh-power type.In the special cases that the fractional power equals to 1 and 2,the solitary wave solutions of more than 10 important model equations arisen from mathematical physics are easily rediscovered.展开更多
The determination of material formula needs try-and-error experiment,and consumes large amount of time and fund.In order to solve the problem,a comprehensive method is established,via the experiment of artificial-simi...The determination of material formula needs try-and-error experiment,and consumes large amount of time and fund.In order to solve the problem,a comprehensive method is established,via the experiment of artificial-similar material formula of a mine slope.We controlled the samples by the compactness,and arranged the formula of the test group with the method of the uniform formula experiment.The physical and mechanical parameters of these samples were analyzed using the method of the partial least-squares regression(PLS).And a mathematical model of the indexes of physical and mechanics parameters relating to the factors of formulation constituents was established eventually.We used the model to analyze the effect of each formulation constituent on physical and mechanics parameters of samples.The experiment results and analysis illustrates that1)in the formulation of similar material,the effect of raw materials on the internal friction angleφand cohesion C is opposite;2)The method can highly facilitate the process of the of preparing artificial-similar materials,more economic and effective.展开更多
Corporate restructuring has become a major component in the financial and economic environment all over the world. Industrial restructuring has raised important issues for business decisions as well as for public poli...Corporate restructuring has become a major component in the financial and economic environment all over the world. Industrial restructuring has raised important issues for business decisions as well as for public policy formulation. Since 1991, Indian industries have been increasingly exposed to both domestic and international competition and competitiveness. The companies started restructuring there operations around their core business there M ＆ A. But M ＆ A is an area of potential good and harm in corporate strategy including manufacturing industry. Therefore, an attempt has been made to analyze the security returns and to find out the net wealth increase or decrease to the shareholders of acquiring firms. In India, there are totally 58 manufacturing companies which have undergone mergers and acquisitions during 2000, 2001 ＆ 2002. Thirty percentage from the total population was taken as sample size （i.e., 17 companies out of 58）. The present study is mainly based on secondary data. The Market Model and Market Adjusted Returns Model analysis are used as tools of analysis.展开更多
In this paper, we establish a complete convergence result and a complete moment convergence result for weighted sums of widely orthant dependent random variables under mild conditions. As corollaries, the correspondin...In this paper, we establish a complete convergence result and a complete moment convergence result for weighted sums of widely orthant dependent random variables under mild conditions. As corollaries, the corresponding results for weighted sums of extended negatively orthant dependent random variables are also obtained, which generalize and improve the related known works in the literature.展开更多
In this paper, complete moment convergence for widely orthant dependent random vari- ables is investigated under some mild conditions. For arrays of rowwise widely orthant dependent random variables, the main results ...In this paper, complete moment convergence for widely orthant dependent random vari- ables is investigated under some mild conditions. For arrays of rowwise widely orthant dependent random variables, the main results extend recent results on complete convergence to complete moment convergence. These results on complete moment convergence are shown to yield new results on complete integral convergence.展开更多
In the paper,we establish some exponential inequalities for non-identically distributed negatively orthant dependent(NOD,for short)random variables.In addition,we also establish some exponential inequalities for the p...In the paper,we establish some exponential inequalities for non-identically distributed negatively orthant dependent(NOD,for short)random variables.In addition,we also establish some exponential inequalities for the partial sum and the maximal partial sum of identically distributed NOD random variables.As an application,the Kolmogorov strong law of large numbers for identically distributed NOD random variables is obtained.Our results partially generalize or improve some known results.展开更多
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 a...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.展开更多
Let fX;Xn;n≥1g be a sequence of identically distributed pairwise negative quadrant dependent(PNQD)random variables and fan;n1g be a sequence of positive constants with an=f(n)and f(θ^k)=f(θ^k-1)for all large posit...Let fX;Xn;n≥1g be a sequence of identically distributed pairwise negative quadrant dependent(PNQD)random variables and fan;n1g be a sequence of positive constants with an=f(n)and f(θ^k)=f(θ^k-1)for all large positive integers k,where 1<θ≤βand f(x)>0(x≥1)is a non-decreasing function on[b;+1)for some b≥1:In this paper,we obtain the strong law of large numbers and complete convergence for the sequence fX;Xn;n≥1g,which are equivalent to the general moment conditionΣ∞n=1P(|X|>an)<1.Our results extend and improve the related known works in Baum and Katz[1],Chen at al.[3],and Sung[14].展开更多
We give the conditionally residual h-integrability with exponent r for an array of random variables and establish the conditional mean convergence of conditionally negatively quadrant dependent and conditionally negat...We give the conditionally residual h-integrability with exponent r for an array of random variables and establish the conditional mean convergence of conditionally negatively quadrant dependent and conditionally negative associated random variables under this integrability. These results generalize and improve the known ones.展开更多
基金supported by the National Social Science Fundation(Grant No.21BTJ040)the Project of Outstanding Young People in University of Anhui Province(Grant Nos.2023AH020037,SLXY2024A001).
文摘In this paper,by utilizing the Marcinkiewicz-Zygmund inequality and Rosenthal-type inequality of negatively superadditive dependent(NSD)random arrays and truncated method,we investigate the complete f-moment convergence of NSD random variables.We establish and improve a general result on the complete f-moment convergence for Sung’s type randomly weighted sums of NSD random variables under some general assumptions.As an application,we show the complete consistency for the randomly weighted estimator in a nonparametric regression model based on NSD errors.
基金Supported by the Academic Achievement Re-cultivation Projects of Jingdezhen Ceramic University(Grant Nos.215/20506341215/20506277)the Doctoral Scientific Research Starting Foundation of Jingdezhen Ceramic University(Grant No.102/01003002031)。
文摘Assume that{a_(i),−∞<i<∞}is an absolutely summable sequence of real numbers.We establish the complete q-order moment convergence for the partial sums of moving average processes{X_(n)=Σ_(i=−∞)^(∞)a_(i)Y_(i+n),n≥1}under some proper conditions,where{Yi,-∞<i<∞}is a doubly infinite sequence of negatively dependent random variables under sub-linear expectations.These results extend and complement the relevant results in probability space.
基金Supported by the National Natural Science Foundation of China(11671012,11501004,11501005)the Natural Science Foundation of Anhui Province(1508085J06)+2 种基金the Key Projects for Academic Talent of Anhui Province(gxbj ZD2016005)the Quality Engineering Project of Anhui Province(2016jyxm0047)the Graduate Academic Innovation Research Project of Anhui University(yfc100004)
文摘In the paper, the strong convergence properties for two different weighted sums of negatively orthant dependent(NOD) random variables are investigated. Let {X, n ≥ 1}be a sequence of NOD random variables. The results obtained in the paper generalize the corresponding ones for i.i.d. random variables and identically distributed NA random variables to the case of NOD random variables, which are stochastically dominated by a random variable X. As a byproduct, the Marcinkiewicz-Zygmund type strong law of large numbers for NOD random variables is also obtained.
基金Supported by the National Natural Science Foundation of China（11201001） Supported by the Natural Science Foundation of Anhui Province（1208085QA03, 1308085QA03）+1 种基金 Supported by the Research Teaching Model Curriculum of Anhui University（xjyjkc1407） Supported by the Students Science Research Training Program of Anhui University（KYXL2014017）
Acknowledgement The authors are most grateful to the editor and anonymous referees for careful reading of the manuscript and valuable suggestions which helped in significantly improving an earlier version of this paper.
文摘A general result on the strong convergence rate and complete convergence for arrays of rowwise extended negatively dependent random variables is established. As applications, some well-known results on negatively dependent random variables can be easily extended to the case of arrays of rowwise extended negatively dependent random variables.
基金Supported by the National Natural Science Foundation of China (Grant No.11271161)
文摘Strong limit theorems are established for weighted sums of widely orthant dependent（WOD） random variables. As corollaries, the strong limit theorems for weighted sums of extended negatively orthant dependent（ENOD） random variables are also obtained, which extend and improve the related known works in the literature.
基金The NSF(11271020 and 11201004)of Chinathe NSF(10040606Q30 and 1208085MA11)of Anhui Provincethe NSF(KJ2012ZD01)of Education Department of Anhui Province
文摘By using Rosenthal type moment inequality for extended negatively de- pendent random variables, we establish the equivalent conditions of complete convergence for weighted sums of sequences of extended negatively dependent random variables under more general conditions. These results complement and improve the corresponding results obtained by Li et al. （Li D L, RAO M B, Jiang T F, Wang X C. Complete convergence and almost sure convergence of weighted sums of random variables. J. Theoret. Probab., 1995, 8： 49-76） and Liang （Liang H Y. Complete convergence for weighted sums of negatively associated random variables. Statist. Probab. Lett., 2000, 48： 317-325）.
基金Supported by the Natural Science Foundation of Anhui Province(1508085J06)Supported by the Research Teaching Model Curriculum of Anhui University(xjyjkc1407)Supported by the Students Innovative Training Project of Anhui University(201510357118)
文摘In the paper, the complete convergence for the maximum of weighted sums of negatively superadditive dependent(NSD, in short) random variables is investigated by using the Rosenthal type inequality. Some sufficient conditions are presented to prove the complete convergence. The result obtained in the paper generalizes some corresponding ones for independent random variables and negatively associated random variables.
基金Supported by the National Natural Science Foundation of China ( 11061007)
文摘In this paper,an exponential inequality for weighted sums of identically distributed NOD （negatively orthant dependent） random variables is established,by which we obtain the almost sure convergence rate of which reaches the available one for independent random variables in terms of Berstein type inequality. As application,we obtain the relevant exponential inequality for Priestley-Chao estimator of nonparametric regression estimate under NOD samples,from which the strong consistency rate is also obtained.
基金supported by National Natural Science Foundation of China(No.21475068)
文摘Understanding the thermal stability of the proteins in human serum is essential since human serum is the important source of pharmaceutical proteins. Near-infrared（NIR） spectroscopy was applied to the investigation of thermal changes in secondary structure and hydration of human serum proteins.However, as a multicomponent system, the overlap of the broad NIR bands makes the structural analysis very difficult directly using the spectra of serum samples. Therefore, continuous wavelet transform（CWT） was used to improve the resolution of NIR spectra, and Monte Carlo-uninformative variable elimination（MC-UVE） method was applied to the selection of the variables associated with the proteins for the structural analysis. The variables（5956, 5867, 5815, 5747, 4525, 4401, 4359 and 4328 cm^-1） related to protein secondary structures and those（7074, 6951, 6827 and 6700 cm 1） connected with water species were selected. Then, the thermal stability was analyzed through the intensity variations of the selected variables with temperature from 30℃ to 80 ℃. It was found that the variation of the spectral variables related to both a-helix and b-sheet changes apparently around 60 ℃, indicating the beginning of the thermal denaturation and the transition from a-helix to b-sheet. Moreover, an obvious change was found around 60℃for the content of the water specie S3, i.e., the water cluster containing three hydrogen bonds. The result demonstrates that MC-UVE can identify the protein-related NIR spectral variables, and the water species may be a marker for investigation of the structural change of proteins in biochemical systems.
基金Supported by the Research Teaching Model Curriculum of Anhui University(xjyjkc1407)Supported by the Students Innovative Training Project of Anhui University(201310357004,201410357117,201410357249)Supported by the Quality Improvement Projects for Undergraduate Education of Anhui University(ZLTS2015035)
文摘In this paper, by using some inequalities of negatively orthant dependent(NOD,in short) random variables and the truncated method of random variables, we investigate the nonparametric regression model. The complete consistency result for the estimator of g(x) is presented.
基金Supported by the Provincial Natural Science Research Project of Anhui Colleges(KJ2015A018)Supported by the Students Science Research Training Program of Anhui University(kyxl2013003)+2 种基金Supported by the Students Innovative Training Project of Anhui University(201410357118)Supported by the Quality Engineering Project of Anhui Province(2015jyxm045)Supported by the Quality Improvement Project for Undergraduate Education of Anhui University(ZLTS2015035)
文摘Let {X_(nk), k ≥ 1, n ≥ 1} be an array of rowwise negatively superadditive dependent random variables and {a_n, n ≥ 1} be a sequence of positive real numbers such that a_n↑∞. Under some suitable conditions,L_r convergence of 1/an max 1≤j≤n |j∑k=1 X_(nk)| is studied. The results obtained in this paper generalize and improve some corresponding ones for negatively associated random variables and independent random variables.
基金Supported by the Natural Science Foundation of Education Department of Henan Province of China under Grant No.2011B110013
文摘The bounded and smooth solitary wave solutions of 10 nonlinear evolution equations with a positive fractional power term of dependent variable are successfully obtained by homogeneous balance principle and with the aid of sub-ODEs that admits a solution of sech-power or tanh-power type.In the special cases that the fractional power equals to 1 and 2,the solitary wave solutions of more than 10 important model equations arisen from mathematical physics are easily rediscovered.
基金Projects(41372312,51379194)supported by the National Natural Science Foundation of ChinaProject(CUGL140817)supported by the Fundamental Research Funds for the Central Universities of China University of Geosciences(Wuhan)+1 种基金Project(2014CFB894)supported by the Natural Science Foundation of Hubei Province of ChinaProject(2014M552113)supported by the China Postdoctoral Science Foundation
文摘The determination of material formula needs try-and-error experiment,and consumes large amount of time and fund.In order to solve the problem,a comprehensive method is established,via the experiment of artificial-similar material formula of a mine slope.We controlled the samples by the compactness,and arranged the formula of the test group with the method of the uniform formula experiment.The physical and mechanical parameters of these samples were analyzed using the method of the partial least-squares regression(PLS).And a mathematical model of the indexes of physical and mechanics parameters relating to the factors of formulation constituents was established eventually.We used the model to analyze the effect of each formulation constituent on physical and mechanics parameters of samples.The experiment results and analysis illustrates that1)in the formulation of similar material,the effect of raw materials on the internal friction angleφand cohesion C is opposite;2)The method can highly facilitate the process of the of preparing artificial-similar materials,more economic and effective.
文摘Corporate restructuring has become a major component in the financial and economic environment all over the world. Industrial restructuring has raised important issues for business decisions as well as for public policy formulation. Since 1991, Indian industries have been increasingly exposed to both domestic and international competition and competitiveness. The companies started restructuring there operations around their core business there M ＆ A. But M ＆ A is an area of potential good and harm in corporate strategy including manufacturing industry. Therefore, an attempt has been made to analyze the security returns and to find out the net wealth increase or decrease to the shareholders of acquiring firms. In India, there are totally 58 manufacturing companies which have undergone mergers and acquisitions during 2000, 2001 ＆ 2002. Thirty percentage from the total population was taken as sample size （i.e., 17 companies out of 58）. The present study is mainly based on secondary data. The Market Model and Market Adjusted Returns Model analysis are used as tools of analysis.
基金Supported by National Natural Science Foundation of China(Grant No.11271161)
文摘In this paper, we establish a complete convergence result and a complete moment convergence result for weighted sums of widely orthant dependent random variables under mild conditions. As corollaries, the corresponding results for weighted sums of extended negatively orthant dependent random variables are also obtained, which generalize and improve the related known works in the literature.
基金Supported by the National Natural Science Foundation of China(Grant Nos.11671012,11501004 and 11501005)the Natural Science Foundation of Anhui Province(Grant No.1508085J06)+1 种基金the Key Projects for Academic Talent of Anhui Province(Grant No.gxbjZD2016005)the Research Teaching Model Curriculum of Anhui University(Grant No.xjyjkc1407)
文摘In this paper, complete moment convergence for widely orthant dependent random vari- ables is investigated under some mild conditions. For arrays of rowwise widely orthant dependent random variables, the main results extend recent results on complete convergence to complete moment convergence. These results on complete moment convergence are shown to yield new results on complete integral convergence.
基金This paper is supported by the National Natural Science Foundation of China(Nos.11671012,11871072,11701004,11701005)the Natural Science Foundation of Anhui Province(Nos.1808085QA03,1908085QA01,1908085QA07)and the Provincial Natural Science Research Project of Anhui Colleges(KJ2019A0001,KJ2019A0003).
文摘In the paper,we establish some exponential inequalities for non-identically distributed negatively orthant dependent(NOD,for short)random variables.In addition,we also establish some exponential inequalities for the partial sum and the maximal partial sum of identically distributed NOD random variables.As an application,the Kolmogorov strong law of large numbers for identically distributed NOD random variables is obtained.Our results partially generalize or improve some known results.
基金Supported by the National Natural Science Foundation of China (10671149,60574002)
文摘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.
基金Supported by the National Natural Science Foundation of China(No.11271161).
文摘Let fX;Xn;n≥1g be a sequence of identically distributed pairwise negative quadrant dependent(PNQD)random variables and fan;n1g be a sequence of positive constants with an=f(n)and f(θ^k)=f(θ^k-1)for all large positive integers k,where 1<θ≤βand f(x)>0(x≥1)is a non-decreasing function on[b;+1)for some b≥1:In this paper,we obtain the strong law of large numbers and complete convergence for the sequence fX;Xn;n≥1g,which are equivalent to the general moment conditionΣ∞n=1P(|X|>an)<1.Our results extend and improve the related known works in Baum and Katz[1],Chen at al.[3],and Sung[14].
基金Acknowledgements The authors thank Editor Lu and two anonymous referees for their constructive suggestions and comments which helped in significantly improving an earlier version of this paper. This work is supported by the National Natural Science Foundation of China （11171001, 11201001, 11426032）, the Natural Science Foundation of Anhui Province （1308085QA03, 1408085QA02）, the Science Fund for Distinguished Young Scholars of Anhui Province （1508085J06）, and Introduction Projects of Anhui University Academic and Technology Leaders.
文摘We give the conditionally residual h-integrability with exponent r for an array of random variables and establish the conditional mean convergence of conditionally negatively quadrant dependent and conditionally negative associated random variables under this integrability. These results generalize and improve the known ones.
