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时滞随机系统的微分博弈理论及应用

书 名: 时滞随机系统的微分博弈理论及应用
英 文 名: DIFFERENTIAL GAME THEORY OF STOCHASTIC TIME-DELAY SYSTEMS WITH ITS APPLICATION
作 者: 朱怀念
I S B N: 978-7-5201-4078-2
关 键 词:  微分博弈 时滞随机系统 Stackelbery博弈 Pareto策略
出版日期: 2019-01-01

中文摘要

该书以工程和经济金融领域中广泛使用的时滞随机系统为研究对象,利用动态优化理论中的随机最大值原理和动态规划等方法,系统研究时滞随机系统的微分博弈问题,得到了博弈系统的鞍点均衡策略、纳什均衡策略、Stackelberg均衡策略及Pareto均衡策略的存在条件和显式表达,并将所得结果应用于现代鲁棒控制理论中的随机H2/H∞控制以及数理金融中的投资与消费选择问题,丰富了博弈论的相关研究。

该书可作为高等院校经济管理类以及理工类其他专业研究生学习微分博弈的参考书,也可作为工程技术人员和经济管理干部的参考用书。

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CommonID:DIR_70569372,ID:10560720,SiteID:14,Type:formerAidText,Code:null,ParentId:0,InnerCode:633259,name:前言,ShortName:null,SubName:null,EnTitle:null,EnShortTitle:null,EnSubTitle:null,Level:0,BookId:10560104,AbstractCH:null,AbstractEN:null,KeyWords:null,EKeyWords:null,SubjectWords:null,LiteratureId:10560718,Fileref:null,OrderFlag:0,IsLeaf:Y,PubDate:null,FindDate:null,IssueDate:null,DocType:null,ProductSeries:null,Doi:null,InstanceID:0,MinNodeSearch:null,XmlID:null,Prop1:null,Prop2:null,Prop3:null,prop4:null,AddUser:wanghan,AddTime:2019-02-15 17:13:02.0,ModifyUser:Admin,ModifyTime:2022-09-24 22:19:23.0,HitCount:0,ShowType:putong,LogoID:0,PdfID:0,DownCount:0,AuthorInfos:null,BookPublishDate:2019-01-01 00:00:00.0,SearchTitle:前言,ISBN:978-7-5201-4078-2,BookTitle:时滞随机系统的微分博弈理论及应用,BookStatus:7,AllowDownload:Y,BookVersionNum:null,researchorg:null,CopyRightDate:null,ExcellentPeriod:null,PrizeLevel:null,IsExcellence:null,ContentClass:null,IsDisabled:N,SearchTitle_2:前言,_RowNo:1
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CommonID:DIR_70569374,ID:10560733,SiteID:14,Type:chapter,Code:null,ParentId:0,InnerCode:633261,name:第1章 绪论,ShortName:,SubName:,EnTitle:,EnShortTitle:,EnSubTitle:,Level:0,BookId:10560104,AbstractCH:本文主要介绍了本选题的研究背景和意义,回顾了国内外学者在时滞随机系统微分博弈理论及应用研究方面的相关成果。,AbstractEN:,KeyWords:630331,630330,630337,EKeyWords:630335,630334,630338,SubjectWords:,LiteratureId:10560731,Fileref:null,OrderFlag:0,IsLeaf:N,PubDate:null,FindDate:null,IssueDate:null,DocType:null,ProductSeries:null,Doi:null,InstanceID:0,MinNodeSearch:Y,XmlID:b120190102X20183395001_001,Prop1:null,Prop2:null,Prop3:null,prop4:null,AddUser:wanghan,AddTime:2019-02-15 17:13:02.0,ModifyUser:Admin,ModifyTime:2022-09-24 22:19:23.0,HitCount:23,ShowType:putong,LogoID:0,PdfID:10560734,DownCount:13,AuthorInfos:,BookPublishDate:2019-01-01 00:00:00.0,SearchTitle:时滞随机系统微分博弈总论,ISBN:978-7-5201-4078-2,BookTitle:时滞随机系统的微分博弈理论及应用,BookStatus:7,AllowDownload:Y,BookVersionNum:,researchorg:,CopyRightDate:null,ExcellentPeriod:,PrizeLevel:,IsExcellence:N,ContentClass:,IsDisabled:N,SearchTitle_2:时滞随机系统微分博弈总论,_RowNo:3
CommonID:DIR_70569382,ID:10560738,SiteID:14,Type:chapter,Code:null,ParentId:0,InnerCode:633262,name:第2章 时滞线性随机系统的Nash微分博弈,ShortName:,SubName:,EnTitle:,EnShortTitle:,EnSubTitle:,Level:0,BookId:10560104,AbstractCH:本文主要研究了扩散项中包含状态和控制的时滞线性随机系统的Nash微分博弈问题。首先,回顾了时滞线性随机系统二次控制问题的相关结论,然后在此基础上,建立了时滞线性随机系统的两人Nash微分博弈模型。借助随机最大值原理给出了均衡策略的存在条件,得到了均衡策略的显式表达,拓展了已有的Nash随机微分博弈的研究成果。,AbstractEN:,KeyWords:630339,630340,630341,EKeyWords:630342,630343,630344,SubjectWords:,LiteratureId:10560737,Fileref:null,OrderFlag:0,IsLeaf:N,PubDate:null,FindDate:null,IssueDate:null,DocType:null,ProductSeries:null,Doi:null,InstanceID:0,MinNodeSearch:Y,XmlID:b120190102X20183395001_002,Prop1:null,Prop2:null,Prop3:null,prop4:null,AddUser:wanghan,AddTime:2019-02-15 17:13:03.0,ModifyUser:Admin,ModifyTime:2022-09-24 22:19:23.0,HitCount:14,ShowType:putong,LogoID:0,PdfID:10560739,DownCount:13,AuthorInfos:,BookPublishDate:2019-01-01 00:00:00.0,SearchTitle:时滞线性随机系统的Nash微分博弈,ISBN:978-7-5201-4078-2,BookTitle:时滞随机系统的微分博弈理论及应用,BookStatus:7,AllowDownload:Y,BookVersionNum:,researchorg:,CopyRightDate:null,ExcellentPeriod:,PrizeLevel:,IsExcellence:N,ContentClass:,IsDisabled:N,SearchTitle_2:时滞线性随机系统的Nash微分博弈,_RowNo:4
CommonID:DIR_70569398,ID:10560743,SiteID:14,Type:chapter,Code:null,ParentId:0,InnerCode:633263,name:第3章 时滞线性随机系统的Stackelberg博弈,ShortName:,SubName:,EnTitle:,EnShortTitle:,EnSubTitle:,Level:0,BookId:10560104,AbstractCH:本文主要研究了时滞线性随机系统的Stackelberg博弈问题。首先,针对系统中不存在时滞的情形,借助随机最大值原理研究了无时滞动态系统的Stackelberg博弈问题。然后在此基础上,采用类似的方法研究了时滞线性随机系统的Stackelberg博弈问题,得到了均衡策略的存在条件,给出了均衡策略的显式表达,拓展了已有关于Stackelberg随机微分博弈的研究成果。 ,AbstractEN:,KeyWords:630339,630330,330739,EKeyWords:630342,630334,330742,SubjectWords:,LiteratureId:10560742,Fileref:null,OrderFlag:0,IsLeaf:N,PubDate:null,FindDate:null,IssueDate:null,DocType:null,ProductSeries:null,Doi:null,InstanceID:0,MinNodeSearch:Y,XmlID:b120190102X20183395001_003,Prop1:null,Prop2:null,Prop3:null,prop4:null,AddUser:wanghan,AddTime:2019-02-15 17:13:03.0,ModifyUser:Admin,ModifyTime:2022-09-24 22:19:23.0,HitCount:11,ShowType:putong,LogoID:0,PdfID:10560745,DownCount:13,AuthorInfos:,BookPublishDate:2019-01-01 00:00:00.0,SearchTitle:时滞线性随机系统的Stackelberg博弈,ISBN:978-7-5201-4078-2,BookTitle:时滞随机系统的微分博弈理论及应用,BookStatus:7,AllowDownload:Y,BookVersionNum:,researchorg:,CopyRightDate:null,ExcellentPeriod:,PrizeLevel:,IsExcellence:N,ContentClass:,IsDisabled:N,SearchTitle_2:时滞线性随机系统的Stackelberg博弈,_RowNo:5
CommonID:DIR_70569409,ID:10560748,SiteID:14,Type:chapter,Code:null,ParentId:0,InnerCode:633264,name:第4章 时滞线性随机系统微分博弈的Pareto策略,ShortName:,SubName:,EnTitle:,EnShortTitle:,EnSubTitle:,Level:0,BookId:10560104,AbstractCH:本文主要考虑了时滞线性随机系统微分博弈的Pareto策略问题。首先,针对无时滞博弈的Pareto策略问题,借助配方法,得到了连续时间系统和离散时间系统Pareto策略存在的条件和显式表达。然后,利用此方法研究带时滞博弈的Pareto策略问题,推导证明了Pareto策略存在的条件等价于矩阵不等式存在解,同时得到了Pareto策略的显式解和最优值函数的一个上界。 ,AbstractEN:,KeyWords:630339,630330,630333,EKeyWords:630342,630334,630336,SubjectWords:,LiteratureId:10560747,Fileref:null,OrderFlag:0,IsLeaf:N,PubDate:null,FindDate:null,IssueDate:null,DocType:null,ProductSeries:null,Doi:null,InstanceID:0,MinNodeSearch:Y,XmlID:b120190102X20183395001_004,Prop1:null,Prop2:null,Prop3:null,prop4:null,AddUser:wanghan,AddTime:2019-02-15 17:13:03.0,ModifyUser:Admin,ModifyTime:2022-09-24 22:19:23.0,HitCount:12,ShowType:putong,LogoID:0,PdfID:10560749,DownCount:13,AuthorInfos:,BookPublishDate:2019-01-01 00:00:00.0,SearchTitle:时滞线性随机系统微分博弈的Pareto策略,ISBN:978-7-5201-4078-2,BookTitle:时滞随机系统的微分博弈理论及应用,BookStatus:7,AllowDownload:Y,BookVersionNum:,researchorg:,CopyRightDate:null,ExcellentPeriod:,PrizeLevel:,IsExcellence:N,ContentClass:,IsDisabled:N,SearchTitle_2:时滞线性随机系统微分博弈的Pareto策略,_RowNo:6
CommonID:DIR_70569418,ID:10560752,SiteID:14,Type:chapter,Code:null,ParentId:0,InnerCode:633265,name:第五章 基于Nash博弈的时滞线性系统随机H2/H控制,ShortName:,SubName:,EnTitle:,EnShortTitle:,EnSubTitle:,Level:0,BookId:10560104,AbstractCH:本文借助于时滞线性随机系统Nash博弈的结果,将控制策略设计者视为博弈的一方记为博弈人P1,将随机性干扰视为博弈的另一方记为 “自然博弈人”P2,从而将鲁棒控制问题转化为两人博弈问题,即博弈人P1如何在预期到 “自然人”P2的各种干扰策略情况下设计自己的策略,既实现与“自然人”的均衡又使自己的目标最优。解决了噪声同时依赖于状态、控制和干扰的时滞线性随机系统的混合H2/H控制问题,证明了控制器的存在性,并借助正倒向随机微分方程给出了反馈控制策略的解析表达。,AbstractEN:,KeyWords:630339,630345,630330,EKeyWords:630342,630346,630334,SubjectWords:,LiteratureId:10560750,Fileref:null,OrderFlag:0,IsLeaf:N,PubDate:null,FindDate:null,IssueDate:null,DocType:null,ProductSeries:null,Doi:null,InstanceID:0,MinNodeSearch:Y,XmlID:b120190102X20183395001_005,Prop1:null,Prop2:null,Prop3:null,prop4:null,AddUser:wanghan,AddTime:2019-02-15 17:13:03.0,ModifyUser:Admin,ModifyTime:2022-09-24 22:19:23.0,HitCount:12,ShowType:putong,LogoID:0,PdfID:10560754,DownCount:14,AuthorInfos:,BookPublishDate:2019-01-01 00:00:00.0,SearchTitle:基于Nash博弈的时滞线性系统随机H2/H控制,ISBN:978-7-5201-4078-2,BookTitle:时滞随机系统的微分博弈理论及应用,BookStatus:7,AllowDownload:Y,BookVersionNum:,researchorg:,CopyRightDate:null,ExcellentPeriod:,PrizeLevel:,IsExcellence:N,ContentClass:,IsDisabled:N,SearchTitle_2:基于Nash博弈的时滞线性系统随机H2/H控制,_RowNo:7
CommonID:DIR_70569430,ID:10560758,SiteID:14,Type:chapter,Code:null,ParentId:0,InnerCode:633266,name:第6章 广义时滞线性随机系统的多人Nash微分博弈,ShortName:,SubName:,EnTitle:,EnShortTitle:,EnSubTitle:,Level:0,BookId:10560104,AbstractCH:本文主要研究了广义时滞线性随机系统的多人Nash微分博弈问题。首先,针对无时滞情形下的广义线性随机系统,讨论了其在有限时间和无限时间域内的N人Nash微分博弈问题,借助一组推广的耦合Riccati方程得到了Nash均衡策略存在的充分条件,即耦合Riccati方程如果存在解,Nash均衡策略就存在,同时给出了Nash均衡策略的显式表达。然后,将相关结果拓展至广义时滞线性随机系统的多人Nash微分博弈问题中,得到了Nash均衡策略的存在条件等价于一组矩阵不等式存在解。最后, 将所得到的广义时滞线性随机系统的多人Nash微分博弈结果应用于随机H2/H控制中,得到了随机H2/H控制的存在条件和显式表示。,AbstractEN:,KeyWords:630347,630348,630340,EKeyWords:630349,630350,630343,SubjectWords:,LiteratureId:10560757,Fileref:null,OrderFlag:0,IsLeaf:N,PubDate:null,FindDate:null,IssueDate:null,DocType:null,ProductSeries:null,Doi:null,InstanceID:0,MinNodeSearch:Y,XmlID:b120190102X20183395001_006,Prop1:null,Prop2:null,Prop3:null,prop4:null,AddUser:wanghan,AddTime:2019-02-15 17:13:04.0,ModifyUser:Admin,ModifyTime:2022-09-24 22:19:23.0,HitCount:13,ShowType:putong,LogoID:0,PdfID:10560760,DownCount:13,AuthorInfos:,BookPublishDate:2019-01-01 00:00:00.0,SearchTitle:广义时滞线性随机系统的多人Nash微分博弈,ISBN:978-7-5201-4078-2,BookTitle:时滞随机系统的微分博弈理论及应用,BookStatus:7,AllowDownload:Y,BookVersionNum:,researchorg:,CopyRightDate:null,ExcellentPeriod:,PrizeLevel:,IsExcellence:N,ContentClass:,IsDisabled:N,SearchTitle_2:广义时滞线性随机系统的多人Nash微分博弈,_RowNo:8
CommonID:DIR_70569444,ID:10560764,SiteID:14,Type:chapter,Code:null,ParentId:0,InnerCode:633267,name:第7章 时滞非线性随机系统Nash微分博弈,ShortName:,SubName:,EnTitle:,EnShortTitle:,EnSubTitle:,Level:0,BookId:10560104,AbstractCH:本文研究了时滞非线性随机系统的Nash微分博弈问题。针对一类噪声依赖于状态和控制的时滞非线性随机系统,研究了无限时间域内的两人Nash微分博弈问题,借助四个耦合的Hamilton-Jacobi方程组(HJEs)得到了Nash均衡策略存在的充分条件,即耦合HJEs如果存在解,Nash均衡策略就存在,同时给出了Nash均衡策略的显式表达。最后,通过一个数值算例验证了所得结论的有效性。 ,AbstractEN:,KeyWords:630351,630352,630353,EKeyWords:630354,630355,630356,SubjectWords:,LiteratureId:10560763,Fileref:null,OrderFlag:0,IsLeaf:N,PubDate:null,FindDate:null,IssueDate:null,DocType:null,ProductSeries:null,Doi:null,InstanceID:0,MinNodeSearch:Y,XmlID:b120190102X20183395001_007,Prop1:null,Prop2:null,Prop3:null,prop4:null,AddUser:wanghan,AddTime:2019-02-15 17:13:04.0,ModifyUser:Admin,ModifyTime:2022-09-24 22:19:23.0,HitCount:9,ShowType:putong,LogoID:0,PdfID:10560766,DownCount:13,AuthorInfos:,BookPublishDate:2019-01-01 00:00:00.0,SearchTitle:时滞非线性随机系统Nash微分博弈,ISBN:978-7-5201-4078-2,BookTitle:时滞随机系统的微分博弈理论及应用,BookStatus:7,AllowDownload:Y,BookVersionNum:,researchorg:,CopyRightDate:null,ExcellentPeriod:,PrizeLevel:,IsExcellence:N,ContentClass:,IsDisabled:N,SearchTitle_2:时滞非线性随机系统Nash微分博弈,_RowNo:9
CommonID:DIR_70569450,ID:10560770,SiteID:14,Type:chapter,Code:null,ParentId:0,InnerCode:633268,name:第8章 时滞非线性随机系统的H2/H控制:无限时间情形,ShortName:,SubName:,EnTitle:,EnShortTitle:,EnSubTitle:,Level:0,BookId:10560104,AbstractCH:本文研究了一类噪声依赖于状态、控制和干扰的无限时间域内的时滞非线性随机系统混合H2/H控制问题。首先,借助于四个耦合的Hamilton-Jacobi方程组得到了带时滞的非线性随机系统H2/H控制存在的充分性条件。然后,基于T-S模糊模型给出了噪声依赖状态和控制的时滞非线性随机系统H2/H控制器的设计方案。控制器的设计可通过求解一组线性矩阵不等式获得,从而避开了求解耦合HJEs的困难。最后,数值仿真算例验证了结论的有效性。,AbstractEN:,KeyWords:630351,630330,630357,EKeyWords:630354,630334,630358,SubjectWords:,LiteratureId:10560768,Fileref:null,OrderFlag:0,IsLeaf:N,PubDate:null,FindDate:null,IssueDate:null,DocType:null,ProductSeries:null,Doi:null,InstanceID:0,MinNodeSearch:Y,XmlID:b120190102X20183395001_008,Prop1:null,Prop2:null,Prop3:null,prop4:null,AddUser:wanghan,AddTime:2019-02-15 17:13:04.0,ModifyUser:Admin,ModifyTime:2022-09-24 22:19:23.0,HitCount:16,ShowType:putong,LogoID:0,PdfID:10560772,DownCount:14,AuthorInfos:,BookPublishDate:2019-01-01 00:00:00.0,SearchTitle:时滞非线性随机系统的H2/H控制:无限时间情形,ISBN:978-7-5201-4078-2,BookTitle:时滞随机系统的微分博弈理论及应用,BookStatus:7,AllowDownload:Y,BookVersionNum:,researchorg:,CopyRightDate:null,ExcellentPeriod:,PrizeLevel:,IsExcellence:N,ContentClass:,IsDisabled:N,SearchTitle_2:时滞非线性随机系统的H2/H控制:无限时间情形,_RowNo:10
CommonID:DIR_70569457,ID:10560776,SiteID:14,Type:chapter,Code:null,ParentId:0,InnerCode:633269,name:第9章 时滞随机系统微分博弈在数理金融中的应用,ShortName:,SubName:,EnTitle:,EnShortTitle:,EnSubTitle:,Level:0,BookId:10560104,AbstractCH:本文针对投资组合选择问题,将自然看成博弈的“虚拟”对手,在投资者与自然之间构建了一个两人零和随机微分博弈模型,投资者选择一个投资策略最大化其终止时刻财富期望效用,而市场选择一个概率测度代表的投资环境最小化投资者的最大化终止时刻期望财富效用。利用最大值原理得到了投资者的最优投资策略的显式解。针对生产和消费选择问题,构建了雇主和雇员之间的一个两人非零和微分博弈模型,利用随机最大值原理获得了两个博弈参与人的最优策略。,AbstractEN:,KeyWords:630331,630330,630359,EKeyWords:630335,630334,630360,SubjectWords:,LiteratureId:10560774,Fileref:null,OrderFlag:0,IsLeaf:N,PubDate:null,FindDate:null,IssueDate:null,DocType:null,ProductSeries:null,Doi:null,InstanceID:0,MinNodeSearch:Y,XmlID:b120190102X20183395001_009,Prop1:null,Prop2:null,Prop3:null,prop4:null,AddUser:wanghan,AddTime:2019-02-15 17:13:05.0,ModifyUser:Admin,ModifyTime:2022-09-24 22:19:23.0,HitCount:13,ShowType:putong,LogoID:0,PdfID:10560778,DownCount:13,AuthorInfos:,BookPublishDate:2019-01-01 00:00:00.0,SearchTitle:时滞随机系统微分博弈在数理金融中的应用,ISBN:978-7-5201-4078-2,BookTitle:时滞随机系统的微分博弈理论及应用,BookStatus:7,AllowDownload:Y,BookVersionNum:,researchorg:,CopyRightDate:null,ExcellentPeriod:,PrizeLevel:,IsExcellence:N,ContentClass:,IsDisabled:N,SearchTitle_2:时滞随机系统微分博弈在数理金融中的应用,_RowNo:11
CommonID:DIR_70569466,ID:10560785,SiteID:14,Type:backAidText,Code:null,ParentId:0,InnerCode:633270,name:结论与展望,ShortName:,SubName:,EnTitle:,EnShortTitle:,EnSubTitle:,Level:0,BookId:10560104,AbstractCH:本文主要讨论以下几个问题,第一,讨论了时滞线性随机系统的Nash博弈问题;第二,讨论了扩散项中包含系统状态和控制的时滞线性随机系统的Stackelbery博弈问题;第三,讨论了时滞线性随机系统微分博弈的Pareto策略问题;第四,研究了基于 Nash博弈的时滞线性随机系统的H2/H鲁棒控制问题;第五,讨论了广义时滞线性随机系统的多人Nash微分博弈问题;第六,讨论了无限时间域内时滞非线性随机系统的Nash微分博弈问题;第七,讨论了一类噪声依赖于状态、控制和干扰的时滞非线性随机系统的H2/H控制问题;第八,运用随机微分博弈的方法讨论了数理金融中的投资组合选择问题与生产和消费选择问题。 ,AbstractEN:,KeyWords:630331,630340,630332,EKeyWords:630361,630343,330742,SubjectWords:,LiteratureId:10560783,Fileref:null,OrderFlag:0,IsLeaf:Y,PubDate:null,FindDate:null,IssueDate:null,DocType:null,ProductSeries:null,Doi:null,InstanceID:0,MinNodeSearch:Y,XmlID:null,Prop1:null,Prop2:null,Prop3:null,prop4:null,AddUser:wanghan,AddTime:2019-02-15 17:13:05.0,ModifyUser:Admin,ModifyTime:2022-09-24 22:19:23.0,HitCount:4,ShowType:putong,LogoID:0,PdfID:13985465,DownCount:10,AuthorInfos:,BookPublishDate:2019-01-01 00:00:00.0,SearchTitle:时滞随机系统微分博弈结论与展望,ISBN:978-7-5201-4078-2,BookTitle:时滞随机系统的微分博弈理论及应用,BookStatus:7,AllowDownload:Y,BookVersionNum:,researchorg:,CopyRightDate:null,ExcellentPeriod:,PrizeLevel:,IsExcellence:N,ContentClass:,IsDisabled:N,SearchTitle_2:时滞随机系统微分博弈结论与展望,_RowNo:12
CommonID:DIR_70569467,ID:10560790,SiteID:14,Type:backAidText,Code:null,ParentId:0,InnerCode:633271,name:致谢,ShortName:null,SubName:null,EnTitle:null,EnShortTitle:null,EnSubTitle:null,Level:0,BookId:10560104,AbstractCH:null,AbstractEN:null,KeyWords:null,EKeyWords:null,SubjectWords:null,LiteratureId:10560788,Fileref:null,OrderFlag:0,IsLeaf:Y,PubDate:null,FindDate:null,IssueDate:null,DocType:null,ProductSeries:null,Doi:null,InstanceID:0,MinNodeSearch:null,XmlID:null,Prop1:null,Prop2:null,Prop3:null,prop4:null,AddUser:wanghan,AddTime:2019-02-15 17:13:05.0,ModifyUser:Admin,ModifyTime:2022-09-24 22:19:23.0,HitCount:0,ShowType:putong,LogoID:0,PdfID:0,DownCount:0,AuthorInfos:null,BookPublishDate:2019-01-01 00:00:00.0,SearchTitle:致谢,ISBN:978-7-5201-4078-2,BookTitle:时滞随机系统的微分博弈理论及应用,BookStatus:7,AllowDownload:Y,BookVersionNum:null,researchorg:null,CopyRightDate:null,ExcellentPeriod:null,PrizeLevel:null,IsExcellence:null,ContentClass:null,IsDisabled:N,SearchTitle_2:致谢,_RowNo:13
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