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Acta Mathematica Sinica,English Series 2009年第8期25卷 1289-1296页

作者： yun hu Department of Mathematics Soochow University Suzhou 215006 P. R. China

We study the fixed point sets of subgroups of modular groups acting on Teichmiiller spaces.

关键词： Teichmiiller space modular group allowable mapping

Improved Hardy–Littlewood–Sobolev Inequality on S^(n)under Constraints

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Acta Mathematica Sinica,English Series 2023年第11期39卷 2149-2163页

作者： yun yun hu Jing Bo DOU School of Mathematics and Statistics Shaanxi Normal UniversityXi’an 710119P.R.China

In this paper,we establish an improved Hardy–Littlewood–Sobolev inequality on Snunder higher-order moments ***,by constructing precise test functions,using improved Hardy–Littlewood–Sobolev inequality on S^(n),we show such inequality is almost optimal in critical *** an application,we give a simpler proof of the existence of the maximizer for conformal Hardy–Littlewood–Sobolev inequality.

关键词： Hardy–Littlewood–Sobolev inequality higher-order moments constraint concentration compactness principle almost optimal

Isomorphisms of fiber spaces over Teichmüller spaces

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Science China Mathematics 2006年第7期49卷 877-892页

作者： hu yun SHEN Yuliang Department of Mathematics Suzhou University Suzhou 215006 China Department of Mathematics Suzhou University Suzhou 215006 China

We will be mainly concerned with some important fiber spaces over Teichmuller spaces, including the Bers fiber space and Teichmuller curve, establishing an isomorphism theorem between 'punctured' Teichmuller curves an... 详细信息

关键词： Teichmuller space Bers fiber space 'punctured' fiber space Teichmuller curve 'punctured' Teichmuller curve biholomorphic isomorphism.

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On Strebel points

Science China Mathematics 2009年第9期52卷 2019-2026页

作者： hu yun SHEN YuLiang Department of Mathematics Soochow UniversitySuzhou 215006China

Any Beltrami coefficient μ on a hyperbolic Riemann surface X of infinite type represents a point [μ]T in the Teichmüller space T (X) and a point [μ]B in the tangent space of T (X) at the base point as well. The paper deals with the problem of determining whether that [μ]T is a Strebel point is equivalent to that [μ]B is an infinitesimal Strebel point.

关键词： Teichmüller space Strebel point infinitesimal Strebel point 32G15 30C62 30F60

EFFECT OF SULPhuRIZING-OXIDIZING ENVIRONMENT ON CREEP CRACK GROWTH OF Ni-BASE SUPERALLOY GH30

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Acta Metallurgica Sinica(English Letters) 1992年第1期5卷 43-47页

作者： ZHANG Yuanhu ZHANG yun hu Shanghai Jiaotong Univ Shanghai China

An investigation was made on the creep crack growth behaviour under static load at 1023 K for Ni-base superalloy GH30 exposed to air and air+10% SO_*** results showed that in the region of low stress intensity factor,the creep crack growth rate is higher in air+10% SO_2 than in air only,while in the high region,it is *** fractograph of specimens has been analyzed,and the mechanism of creep crack growth together with the influences of sul- phur and oxygen has been discussed as well.

关键词： Ni-base superalloy creep crack growth environment

Correspondence between quantum-optical transform and classical-optical transform explored by developing Dirac＇s symbolic method

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Frontiers of physics 2012年第3期7卷 261-310页

作者： Hong-yi Fan Li-yun hu Department of Physics Shanghai Jiao Tong UniversityShanghai 200030China College of Physics&Communication Electronics Jiangxi Normal UniversityNanchang 330022China Department of Material Science and Engineering University of Science and Technology of China Hefei 230026 China

By virtue of the new technique of performing integration over Dirac＇s ket-bra operators, we ex- plore quantum optical version of classical optical transformations such as optical Fresnel transform, Hankel transform, fractional Fourier transform, Wigner transform, wavelet transform and Fresnel- Hadmard combinatorial transform etc. In this way one may gain benefit for developing classical optics theory from the research in quantum optics, or vice-versa. We cannot only find some new quantum mechanical unitary operators which correspond to the known optical transformations, de- riving a new theorem for calculating quantum tomogram of density operators, but also can reveal some new classical optical transformations. For examples, we find the generalized Fresnel opera- tor （GFO） to correspond to the generalized Fresnel transform （GFT） in classical optics. We derive GFO＇s normal product form and its canonical coherent state representation and find that GFO is the loyal representation of symplectic group multiplication rule. We show that GFT is just the transformation matrix element of GFO in the coordinate representation such that two successive GFTs is still a GFT. The ABCD rule of the Gaussian beam propagation is directly demonstrated in the context of quantum optics. Especially, the introduction of quantum mechanical entangled state representations opens up a new area in finding new classical optical transformations. The complex wavelet transform and the condition of mother wavelet are studied in the context of quantum op- tics too. Throughout our discussions, the coherent state, the entangled state representation of the two-mode squeezing operators and the technique of integration within an ordered product （IWOP） of operators are fully used. All these have confirmed Dirac＇s assertion：＂...for a quantum dynamic system that has a classical analogue, unitary transformation in the quantum theory is the analogue of contact transformation in the classical theory＂.

关键词： Dirac's symbolic method IWOP technique entangled state of continuum variables entangled Fresnel transform Collins formula Generalized Fresnel operator complex wavelet trans-form complex Wigner transform complex fractional Fourier transform symplectic wavelet trans-form entangled symplectic wavelet transform Symplectic-dilation mixed wavelet transform frac-tional Radon transform new eigenmodes of fractional Fourier transform

New Approach for Solving Master Equations in Quantum Optics and Quantum Statistics by Virtue of Thermo-Entangled State Representation

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Communications in Theoretical Physics 2009年第4期51卷 729-742页

作者： FAN Hong-Yi hu Li-yun Department of Physics Shanghai Jiao Tong University Shanghai 200030 China Department of Material Science and Engineering University of Science and Technology of China Hefei 230026 China

By introducing a fictitious mode to be a counterpart mode of the system mode under review we introduce the entangled state representation （η｜, which can arrange master equations of density operators p（t） in quantum statistics as state-vector evolution equations due to the elegant properties of （η｜. In this way many master equations （respectively describing damping oscillator, laser, phase sensitive, and phase diffusion processes with different initial density operators） can be concisely solved. Specially, for a damping process characteristic of the decay constant k we find that the matrix element of p（t） at time t in 〈η｜ representation is proportional to that of the initial po in the decayed entangled state （ηe^-kt｜ representation, accompanying with a Gaussian damping factor. Thus we have a new insight about the nature of the dissipative process. We also set up the so-called thermo-entangled state representation of density operators, ρ = f（d^2η/π）（η｜ρ〉D（η）, which is different from all the previous known representations.

关键词： master equation fictitious mode thermo-entangled state representation damping oscillator and laser phase sensitive and phase diffusion processes

Teleportation of Squeezed Entangled State

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Communications in Theoretical Physics 2007年第5期47卷 805-810页

作者： hu Li-yun ZHOU Nan-Run Department of Physics Shanghai Jiao Tong University Shanghai 200030 China Department of Electronics Information Engineering Nanchang University Nanchang 330029 China

Based on the coherent entangled state ｜a, x〉 we introduce the squeezed entangled state （SES）. Then we propose a teleportation protocol for the SES by using Einstein-Podolsky-Rosen entangled state ｜η〉 as a quantum channel. The calculation is greatly simplified by virtue of the Schmidt decompositions of both ｜a, x〉 and ｜η〉. Any bipartite states that can be expanded in terms of ｜a, x〉 may be teleported in this way due to the completeness of ｜a, x〉.

关键词： squeezed entangled state continuous variables EPR state teleportation

Two-Variable Hermite Polynomial Excitation of Two-Mode Squeezed Vacuum State as Squeezed Two-Mode Number State

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Communications in Theoretical Physics 2008年第10期50卷 965-970页

作者： hu Li-yun FAN Hong-Yi Department of Physics Shanghai Jiao Tong University Shanghai 200030 China

We find that the squeezed two-mode number state is just a two-variable Hermite polynomial excitation of thetwo-mode squeezed vacuum state (THPES).We find that the Wigner function of THPES and its marginal distributionsare just related to two-variable Hermite polynomials (or Laguerre polynomials) and that the tomogram of THPES canbe expressed by one-mode Hermite polynomial.

关键词： Two variable Hermite polynomial excitation state Wigner function marginal distribution tomgram

Efficient multi-event monitoring using built-in search engines

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Frontiers of Computer Science 2016年第2期10卷 281-291页

作者： Zhaoman ZHONG Zongtian LIU yun hu Cunhua LI School of Computer Engineering Huaihai Institute of Technology Lianyungang 222006 China School of Computer Engineering and Science Shanghai University Shanghai 200072 China

Users of the internet often wish to follow certain news events, and the interests of these users often overlap. General search engines （GSEs） cannot be used to achieve this task due to incomplete coverage and lack of freshness. Instead, a broker is used to regularly query the built-in search engines （BSEs） of news and social media sites. Each user defines an event profile consisting of a set of query rules called event rules （ERs）. To ensure that queries match the semantics of BSEs, ERs are transformed into a disjunctive normal form, and separated into conjunctive clauses （atomic event rules, AERs）. It is slow to process all AERs on BSEs, and can violate query submission rate limits. Accordingly, the set of AERs is reduced to eliminate AERs that are duplicates, or logically contained by other AERs. Five types of event are selected for experimental comparison and analysis, including natural disasters, accident disasters, public health events, social security events, and negative events of public servants. Using 12 BSEs, 85 ERs for five types of events are defined by five users. Experimental comparison is conducted on three aspects： event rule reduction ratio, number of collected events, and that of related events. Experimental results in this paper show that event rule reduction effectively enhances the efficiency of crawling.

关键词： information retrieval event retrieval event monitoring BSEs event rule reduction