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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

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

Wavefunction of Coupled Quantum—Classical Oscillator

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Chinese Physics Letters 2003年第5期20卷 600-601页

作者： HEWei-zhong XULiu-su ZOUFeng-Wu DepartmentofInformaitonandComputingScience GuangxiUniversityofTechmologyLiuzhou545005

Considering classical environment to be a classical oscillator, we describe the dynamics of a system consisting of a quantum oscillator coupled to classical oscillator. Using the Born-Oppenheimer approximation and the method of adiabatic invariants, we derive the classically effective Hamiltonian describing the complete dynamics of the system and the wavefunction of quantum part of the system. We also present a new method for investigating the dynamics of the quantum system in classical environment.

关键词：波动函数量子振荡器经典振荡器哈密顿函数近似计算动力学系统

Invariant measures for the strong-facilitated exclusion process

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Applied Mathematics(A Journal of Chinese Universities) 2023年第3期38卷 317-337页

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

Consider a generalized model of the facilitated exclusion process, which is a onedimensional exclusion process with a dynamical constraint that prevents the particle at site x from jumping to x+1 (or x-1) if the sites x-1, x-2 (or x+1, x+2) are empty. It is nongradient and lacks invariant measures of product form. The purpose of this paper is to identify the invariant measures and to show that they satisfy both exponential decay of correlations and equivalence of ensembles. These properties will play a pivotal role in deriving the hydrodynamic limit.

关键词： equivalence of ensembles exclusion process facilitated dynamic invariant measure

On K_(0)-groups of operator algebras on Banach spaces

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Science China Mathematics 2006年第2期49卷 233-244页

作者： ZHANG Yunnan zhong Huaijie su Weigang School of Mathematics and Computer Science Fujian Normal University Fuzhou 350007 China School of Mathematics and Computer Science Fujian Normal University Fuzhou 350007 China School of Mathematics and Computer Science Fujian Normal University Fuzhou 350007 China

This paper merges some classifications of G-M-type Banach spaces simplifically, discusses the condition of K0(B(X)) = 0 for operator algebra B(X) on a Banach space X, and obtains a result to improve Laustsen's suffici... 详细信息

关键词： Banach space operator Banach algebra K0-group.

Control of static unstable airframes

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Journal of Systems Engineering and Electronics 2010年第6期21卷 1063-1071页

作者： Junfang Fan Defu Lin zhong su Qing Li School of Automation Beijing Information Science and Technology University Beijing 100101 E R. China School of Aerospace Engineering Beijing Institute of Technology Beijing 100081 P. R. China

The challenge and control problems of static unstable missiles are presented. The steady-state benefits of static instability are illustrated, while the corresponding control challenge is described both by the characteristic lag of airframe and the increment of necessary control usage. Control limitation led by unstable zero-pole pair is analyzed for preliminary design and evaluation. Linear control strategy is examined wherein two and three loop acceleration autopilots with different control usages are developed using an optimal control approach combined with frequency domain constraint. The weights selection and relation with system performance are detailed. Then the nonlinear backstepping recursive method is detailed to determine how well it is able to follow command and its engineering feasibility. The results show that a static unstable missile is controllable, while the actuator bandwidth is the crucial limited factor. There should be a compromise between overall performance and actuator payment.

关键词： missile control static instability optimal control backstepping weight matrix unstable zero-pole pair.

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

Generating Even-Photon State via Resonant Interaction Between Ladder-Type Three-Level Atoms with a Single-Mode Field

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Communications in Theoretical Physics 2008年第1期49卷 221-224页

作者： zhong Zhi-Rong su Wan-Jun Department of Electronic Science and Applied Physics Puzhou University Puzhou 350002 China

A scheme is presented to generate even-photon state based on resonant interaction between ladder-type three-level atoms with a single-mode field. In the scheme, a sequence of suitably prepared ladder-type three-level atoms are orderly sent through a single-mode cavity initiaJly in vacuum state. The detection of a J1 the atoms in the ground states collapses the cavity to the desired state. The scheme is based on the resonant interaction of atoms with the cavity, and thus the required interaction time can be greatly shortened. This is important in view of decoherence.

关键词： even photon state resonant interaction ladder-type atom