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Conditional central limit theorems for a sequence of conditional independent random variables
De-Mei Yuan,Li-Ran Wei,Lan Lei 대한수학회 2014 대한수학회지 Vol.51 No.1
A conditional version of the classical central limit theorem is derived rigorously by using conditional characteristic functions, and a more general version of conditional central limit theorem for the case of conditionally independent but not necessarily conditionally identically distributed random variables is established. These are done anticipating that the field of conditional limit theory will prove to be of significant applicability.
SOME RESULTS ON CONDITIONALLY UNIFORMLY STRONG MIXING SEQUENCES OF RANDOM VARIABLES
Yuan, De-Mei,Hu, Xue-Mei,Tao, Bao Korean Mathematical Society 2014 대한수학회지 Vol.51 No.3
From the ordinary notion of uniformly strong mixing for a sequence of random variables, a new concept called conditionally uniformly strong mixing is proposed and the relation between uniformly strong mixing and conditionally uniformly strong mixing is answered by examples, that is, uniformly strong mixing neither implies nor is implied by conditionally uniformly strong mixing. A couple of equivalent definitions and some of basic properties of conditionally uniformly strong mixing random variables are derived, and several conditional covariance inequalities are obtained. By means of these properties and conditional covariance inequalities, a conditional central limit theorem stated in terms of conditional characteristic functions is established, which is a conditional version of the earlier result under the non-conditional case.
CONDITIONAL CENTRAL LIMIT THEOREMS FOR A SEQUENCE OF CONDITIONAL INDEPENDENT RANDOM VARIABLES
Yuan, De-Mei,Wei, Li-Ran,Lei, Lan Korean Mathematical Society 2014 대한수학회지 Vol.51 No.1
A conditional version of the classical central limit theorem is derived rigorously by using conditional characteristic functions, and a more general version of conditional central limit theorem for the case of conditionally independent but not necessarily conditionally identically distributed random variables is established. These are done anticipating that the field of conditional limit theory will prove to be of significant applicability.
De Peng Yuan,Xiao Feng Xu,Hong Woo-Jong,Si Ting Wang,Xin Tong Jia,Yang Liu,Shuang Li,Zhi Min Li,Qian Sun,Qiong Mei,Shuai Li,정기홍,Song Hong Wei,Yuan Hu Xuan 한국식물생명공학회 2020 Plant biotechnology reports Vol.14 No.5
Sheath blight disease (ShB) severely afects rice production; however, the details of defense against ShB remain unclear. To understand the rice defense mechanism against ShB, an RNA sequencing analysis was performed using Rhizoctonia solani inoculated rice leaves after 48 h of inoculation. Among them, 3417 genes were upregulated and 2532 were downregulated when compared with the control group (>twofold or<1/2). In addition, the diferentially expressed genes were classifed via Gene Ontology (GO), Kyoto Encyclopedia of Genes and Genomes (KEGG), and MapMan analyses. Fifty-nine GO terms and seven KEGG pathways were signifcantly enriched. A MapMan analysis demonstrated that the phytohormone and metabolic pathways were signifcantly altered. Interestingly, the expression levels of 359 transcription factors, including WRKY, MYB, and NAC family members, as well as 239 transporter genes, including ABC, MFS, and SWEET, were signifcantly changed in response to R. solani AG1-IA inoculation. Additionally, OsWRKY53 and OsAKT1 negatively regulate the defense response in rice against R. solani via gain of function study for OsWRKY53 and loss of function study for OsAKT1, respectively. Furthermore, several diferentially expressed genes contain R. solani-responsive cis acting regulatory elements in their promoter regions. Taken together, our analyses provide valuable information for the additional study of the defense mechanisms against ShB, and the candidate genes identifed in this study will be useful resource for future breeding to enhance resistance against ShB.
Yuan, De-Mei,Li, Shun-Jing Korean Mathematical Society 2015 대한수학회지 Vol.52 No.2
Extensions of the Kolmogorov convergence criterion and the Marcinkiewicz-Zygmund inequalities from independent random variables to conditional independent ones are derived. As their applications, a conditional version of the Marcinkiewicz-Zygmund strong law of large numbers and a result on convergence in $L^p$ for conditionally independent and conditionally identically distributed random variables are established, respectively.
Yuan, De-Mei Korean Mathematical Society 2016 대한수학회지 Vol.53 No.6
The Marcinkiewicz-Zygmund strong law of large numbers for conditionally independent and conditionally identically distributed random variables is an existing, but merely qualitative result. In this paper, for the more general cases where the conditional order of moment belongs to (0, ${\infty}$) instead of (0, 2), we derive results on convergence rates which are quantitative ones in the sense that they tell us how fast convergence is obtained. Furthermore, some conditional probability inequalities are of independent interest.
SOME RESULTS ON CONDITIONALLY UNIFORMLY STRONG MIXING SEQUENCES OF RANDOM VARIABLES
De-Mei Yuan,Xue-Mei Hu,Bao Tao 대한수학회 2014 대한수학회지 Vol.51 No.3
From the ordinary notion of uniformly strong mixing for a se- quence of random variables, a new concept called conditionally uniformly strong mixing is proposed and the relation between uniformly strong mix- ing and conditionally uniformly strong mixing is answered by examples, that is, uniformly strong mixing neither implies nor is implied by condi- tionally uniformly strong mixing. A couple of equivalent definitions and some of basic properties of conditionally uniformly strong mixing ran- dom variables are derived, and several conditional covariance inequalities are obtained. By means of these properties and conditional covariance inequalities, a conditional central limit theorem stated in terms of condi- tional characteristic functions is established, which is a conditional version of the earlier result under the non-conditional case.
De-Mei Yuan 대한수학회 2016 대한수학회지 Vol.53 No.6
The Marcinkiewicz-Zygmund strong law of large numbers for conditionally independent and conditionally identically distributed random variables is an existing, but merely qualitative result. In this paper, for the more general cases where the conditional order of moment belongs to $\left({0,\infty } \right)$ instead of $\left( {0,2} \right)$, we derive results on convergence rates which are quantitative ones in the sense that they tell us how fast convergence is obtained. Furthermore, some conditional probability inequalities are of independent interest.
De-Mei Yuan,Shun-Jing Li 대한수학회 2015 대한수학회지 Vol.52 No.2
Extensions of the Kolmogorov convergence criterion and the Marcinkiewicz-Zygmund inequalities from independent random variables to conditional independent ones are derived. As their applications, a conditional version of the Marcinkiewicz-Zygmund strong law of large numbers and a result on convergence in Lp for conditionally independent and conditionally identically distributed random variables are established, respectively.
Transformation of nitrogen-containing compounds in atmospheric residue by hydrotreating
Mei Liu,Lin-Zhou Zhang,Cheng Zhang,Sheng-Hua Yuan,De-Zhi Zhao,Lin-Hai Duan 한국화학공학회 2018 Korean Journal of Chemical Engineering Vol.35 No.2
Atmospheric residue from Saudi Arabia light crude oil was subjected to the hydrotreating process in a continuous fixed-bed reactor with hydrodesulfurization (HDS) and hydrodenitrogenation (HDN) catalysts. The detailed molecular composition of the polar heteroatom species in the feedstock and products was determined by electrospray ionization (ESI) Fourier transform ion cyclotron resonance mass spectrometry (FT-ICR MS) combined with other analytical methods. The ESI FT-ICR MS analysis indicates that the N1 class species have the highest relative abundance. In the hydrotreating process, small neutral N1 class species with high aromaticity and short side chains showed the highest relative abundance and were defined as easily removable compounds. High aromaticity and small molecule basic N1 compounds exhibited higher catalytic activity towards hydrogenation. The N1S1 class species were converted to the N1 class species, or even hydrocarbons, by the preferential removal of the sulfur atoms. Most of the N1O1 class species were difficult to remove, because of their stable chemical structure.