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Discretization error of irregular sampling approximations of stochastic integrals

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Applied Mathematics(A Journal of Chinese Universities) 2016年第3期31卷 296-306页

作者： ZHOU Li-kai su zhong-gen Department of Mathematics Zhejiang University

This paper studies the limit distributions for discretization error of irregular sam- pling approximations of stochastic integral. The irregular sampling approximation was first presented in Hayashi et al.[3], which was more general than the sampling approximation in Lindberg and Rootzen [10]. As applications, we derive the asymptotic distribution of hedging error and the Euler scheme of stochastic differential equation respectively.

关键词： Euler scheme irregular sampling stochastic integral weak convergence hedging error

Tracy-Widom distribution, Airy2 process and its sample path properties

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Applied Mathematics(A Journal of Chinese Universities) 2021年第1期36卷 128-158页

作者： su zhong-gen LEI Yu-huan SHEN Tian School of Mathematical Sciences Zhejiang UniversityHangzhou 310027China

Tracy-Widom distribution was rst discovered in the study of largest eigenvalues of high dimensional Gaussian unitary ensembles(GUE),and since then it has appeared in a number of apparently distinct research *** is believed that Tracy-Widom distribution have a universal feature like classic normal ***2 process is de ned through nite dimensional distributions with Tracy-Widom distribution as its marginal *** this introductory survey,we will briey review some basic notions,intuitive background and fundamental properties concerning Tracy-Widom distribution and Airy2 *** sake of reading,the paper starts with some simple and well-known facts about normal distributions,Gaussian processes and their sample path properties.

关键词： Airy2 process Dyson Brownian motion Tracy-Widom distribution sample path property.

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随机配置问题的概率分析

数学进展 2005年第2期34卷 133-144页

作者：苏中根浙江大学数学系杭州浙江310027

假设(ti,j)1≤i,j≤n是一个n×n的具有独立同分布,参数为1的指数费用矩阵.考虑最优配置费用Ane=:minπsumfromi=1ton=1ti,π(i),其中π=(π(1),…,π(n))为1,2,…,n的排列.本文目的是对最近关于平均最优配置费用EAne的研究进展作些评论... 详细信息

假设(ti,j)1≤i,j≤n是一个n×n的具有独立同分布,参数为1的指数费用矩阵.考虑最优配置费用Ane=:minπsumfromi=1ton=1ti,π(i),其中π=(π(1),…,π(n))为1,2,…,n的排列.本文目的是对最近关于平均最优配置费用EAne的研究进展作些评论,特别关注Aldous的目标方法和局部弱收敛性,以及著名的Parisi猜想和证明.文章结尾包含了一些尚未解决的问题,值得进一步研究.

关键词：渐近本质唯一性目标方法 PaLrisi猜想随机配置

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柴油机缸盖微区域高效节能化冷却研究

内燃机工程 2015年第3期36卷 92-99页

作者：林育兹郑伟苏忠根厦门大学厦门361005 厦门大学嘉庚学院漳州363105 温州大学瓯江学院温州325035

为实现柴油机缸盖高热密度区节能化高效冷却,通过外部施加交变磁场改善缸盖内部磁纳米流冷却液的流动与传热,并对比了该方法与采用传统乙二醇冷却液、Cu-乙二醇纳米流冷却液缸盖高热密度区传热效果的差异。研究结果表明:交变磁场有助于... 详细信息

为实现柴油机缸盖高热密度区节能化高效冷却,通过外部施加交变磁场改善缸盖内部磁纳米流冷却液的流动与传热,并对比了该方法与采用传统乙二醇冷却液、Cu-乙二醇纳米流冷却液缸盖高热密度区传热效果的差异。研究结果表明:交变磁场有助于加强磁纳米流内部纳米粒子的扰动,可增强传热效果。在适宜磁场交变频率下,被测热源温度值最大下降幅度提升17.2%。在柴油机缸盖鼻梁微区域的实际应用冷却试验表明:标定工况点下测点温度值最大下降幅度达12.4%,外特性工况下测点平均温度下降3%左右。同时瞬态工况测试结果表明,与采用传统乙二醇冷却液和Cu-乙二醇纳米流冷却液相比,采用优化控制策略后的冷却系统匹配交变磁场影响下的磁纳米流冷却液时,柴油机预热时间分别缩短了8.4%和7.1%。能耗率计算结果表明:采用外部施加交变磁场方式加强磁纳米流冷却液高效传热的方式在达到相同冷却液温度时,可节能6.7%。

关键词：内燃机缸盖局部冷却传热磁性纳米流试验节能

LIL for the Length of the Longest Increasing subsequences

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Acta Mathematicae Applicatae Sinica 2020年第2期36卷 283-293页

作者： zhong-gen su School of Mathematcial Sciences Zhejiang UniversityHangzhou 310027China

Let X1,X2,…,Xn,…be a sequence of *** variables uniformly distributed on[0;1],and denote by Ln the length of the longest increasing subsequences of X1,X2,…,*** the poissonized version Hn based on Hammersley’s representation in the 2-dimensional space.A law of the iterated logarithm for Hn is established using the well-known subsequence method and Borel-Cantelli *** key technical ingredients in the argument include superadditivity,increment independence and precise tail estimates for the Hn’*** work was motivated by recent works due to Ledoux(***.31,(2018)).It remains open to establish an analog for the Ln itself.

关键词： Borel-Cantelli lemma Hammersley's representation law of the iterated logarithm longest increasing subsequences

电控EGR对农用ZS1110型柴油机性能影响的研究

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拖拉机与农用运输车 2011年第5期38卷 43-45页

作者：苏忠根郑伟温州大学浙江温州325035

设计了一款应用在柴油机上的电控EGR系统,并进行了不同EGR率对柴油机经济性的影响研究和稳态十三工况下的排放性研究。试验结果表明:采用电控EGR技术后,试验柴油机比油耗在不同工况下有不同程度的升高,尤其在高负荷区域内;NOx排放有着... 详细信息

设计了一款应用在柴油机上的电控EGR系统,并进行了不同EGR率对柴油机经济性的影响研究和稳态十三工况下的排放性研究。试验结果表明:采用电控EGR技术后,试验柴油机比油耗在不同工况下有不同程度的升高,尤其在高负荷区域内;NOx排放有着较为明显的下降,微粒有一定程度的升高,HC排放总体上变化不大。

关键词：柴油机排放废气再循环

Transition Distributions of Young Diagrams Under Periodically Weighted Plancherel Measures

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Acta Mathematicae Applicatae Sinica 2009年第4期25卷 655-674页

作者： zhong-gen su Department of Mathematics Zhejiang University Hangzhou 310027 China

Kerov[16,17] proved that Wigner＇s semi-circular law in Gauss[an unitary ensembles is the transition distribution of the omega curve discovered by Vershik and Kerov[34] for the limit shape of random partitions under the Plancherel measure. This establishes a close link between random Plancherel partitions and Gauss[an unitary ensembles, In this paper we aim to consider a general problem, namely, to characterize the transition distribution of the limit shape of random Young diagrams under Poissonized Plancherel measures in a periodic potential, which naturally arises in Nekrasov＇s partition functions and is further studied by Nekrasov and Okounkov[25] and Okounkov[28,29]. We also find an associated matrix mode[ for this transition distribution. Our argument is based on a purely geometric analysis on the relation between matrix models and SeibergWitten differentials.

关键词： Limit shape Limiting density of eigenvalues Poissonized Plancherel measures in a periodic potential Transition distributions Unitary invariant matrix models

On Increasing subsequences of Minimal ErdSs-Szekeres Permutations

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Acta Mathematica Sinica,English Series 2011年第8期27卷 1573-1580页

作者： zhong gen su Department of Mathematics Zhejiang University Hangzhou 310027 P. R. China

Let π be a minimal ErdSs-Szekeres permutation of 1, 2,..., n^2, and let ln,k be the length of the longest increasing subsequence in the segment （πr（1）,...,π（k））. Under uniform measure we establish an exponentially decaying bound of the upper tail probability for ln,k, and as a consequence we obtain a complete convergence, which is an improvement of Romik＇s recent result. We also give a precise lower exponential tail for ln,k.

关键词： Large deviation minimal Erd6s-Szekeres permutation Robinson-Schensted-Knuth cor- respondence Young tableaux

Precise Asymptotics for Random Matrices and Random Growth Models

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Acta Mathematica Sinica,English Series 2008年第6期24卷 971-982页

作者： zhong gen su Department of Mathematics Zhejiang University Hangzhou 310027 P. R. China

The author considers the largest eigenvaiues of random matrices from Gaussian unitary ensemble and Laguerre unitary ensemble, and the rightmost charge in certain random growth models. We obtain some precise asymptotics results, which are in a sense similar to the precise asymptotics for sums of independent random variables in the context of the law of large numbers and complete convergence. Our proofs depend heavily upon the upper and lower tail estimates for random matrices and random growth models. The Tracy-Widom distribution plays a central role as well.

关键词： Gaussian unitary ensemble Laguerre unitary ensemble largest eigenvalues random growth models Tracy-Widom distribution