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BLOW UP OF SOLUTIONS TO THE CAUCHY PROBLEM FOR NONLINEAR WAVE EQUATIONS

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Chinese Annals of mathematics,Series B 2001年第3期22卷 275-280页

作者： zhou yi institute of mathematics, fudan university,{2., China institute of mathematics Fudan University Shanghai 200433 China

The author proves blow up of solutions to the Cauchy problem of certain nonlinear equations and, also, estimates the time when the blow up occurs.

关键词： Cauchy problem Nonlinear wave equation Blow up

PARAMETERS OF DARBOUX TRANSFORMATION FOR REDUCED AKNS,KAUP-NEWELL AND PCF SYSTEMS

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Chinese Annals of mathematics,Series B 1999年第2期20卷 195-204页

作者： zhou ZIXIANG(institute of {2., fudan university, shanghai 2.043.) fudan Univ Inst Math Shanghai 200433 Peoples R China

FOr the integrable system with u(p, q) reduction, there is a well-known sufficient conditionto choose the parameters: the spectral parameters only take two mutually conjugate valuesand the solutions of the Lax pair should satisfy certain orthogonal relations. In this paper, theauthor proves that, for the AKNS system, the Kaup-Newed system and the principal chiralfield (PCF), this condition is also necessary for generic potentials with the u(p, q) *** some other reductions, sufficiency and necessity of more constraints are proved.

关键词： Darboux transformation Spectral parameters u(p q) reduction

General properties of the spectral form factor in open quantum systems

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Frontiers of physics 2024年第3期19卷 229-237页

作者： yi-Neng zhou Tian-Gang zhou Pengfei Zhang institute for Advanced Study Tsinghua UniversityBeijing 100084China Department of Physics Fudan UniversityShanghai 200438China

The spectral form factor(SFF)can probe the eigenvalue statistic at different energy scales as its time variable *** closed quantum chaotic systems,the SFF exhibits a universal dip-ramp-plateau behavior,which reflects the spectrum rigidity of the *** this work,we explore the general properties of SFF in open quantum *** find that in open systems the SFF first decays exponentially,followed by a linear increase at some intermediate time scale,and finally decreases to a saturated plateau *** derive general relations between(i)the early-time decay exponent and Lindblad operators;(ii)the long-time plateau value and the number of steady *** also explain the effective field theory perspective of general *** verify our theoretical predictions by numerically simulating the Sachdev−Ye−Kitaev(SYK)model,random matrix theory(RMT),and the Bose−Hubbard model.

关键词： spectral form factor open quantum system quantum chaos

Remarks on the Global Existence for Incompressible Navier-Stokes Equations

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Chinese Annals of mathematics,Series B 2024年第4期45卷 529-536页

作者： Sheng WANG Zexian ZHANG yi zhou shanghai Center for Mathematical Sciences Fudan UniversityShanghai 200433China School of mathematics Science Fudan UniversityShanghai 200433China

In this article,the authors use the special structure of helicity for the threedimensional incompressible Navier-Stokes equations to construct a family of finite energy smooth solutions to the Navier-Stokes equations ... 详细信息

关键词： Navier-Stokes euqations Helicity Global existence Critical norm

Ultrahigh spatiotemporal resolution beam signal reconstruction with bunch phase compensation

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Nuclear Science and Techniques 2024年第5期35卷 99-108页

作者： You-Ming Deng Yong-Bin Leng Xing-yi Xu Jian Chen yi-Mei {2. shanghai institute of Applied Physics Chinese Academy of SciencesShanghai 201800China university of the Chinese Academy of Sciences Beijing 100049China shanghai Synchrotron Radiation Facility Chinese Academy of SciencesShanghai 201204China university of Science and Technology of China Hefei 230026China shanghai Advanced Research institute Chinese Academy of SciencesShanghai 201204China

Various electromagnetic signals are excited by the beam in the acceleration and beam-diagnostic elements of a particle *** is important to obtain time-domain waveforms of these signals with high temporal resolution for research,such as the study of beam–cavity interactions and bunch-by-bunch parameter ***,a signal reconstruction algorithm with ultrahigh spatiotemporal resolution and bunch phase compensation based on equivalent sampling is proposed in this *** with traditional equivalent sampling,the use of phase compensation and setting the bunch signal zero-crossing point as the time reference can construct a more accurate reconstructed *** basic principles of the method,simulation,and experimental comparison are also *** on the beam test platform of the shanghai Synchrotron Radiation Facility(SSRF)and the method of experimental verification,the factors that affect the reconstructed signal quality are analyzed and discussed,including the depth of the sampled data,quantization noise of analog-to-digital converter,beam transverse oscillation,and longitudinal *** results of the beam experiments show that under the user operation conditions of the SSRF,a beam excitation signal with an amplitude uncertainty of 2.can be reconstructed.

关键词： Turn-by-turn bunch phase compensation technique Equivalent sampling Signal reconstruction algorithm Ultrahigh spatiotemporal resolution SSRF

THE MODULI SPACE OF COMPLEX LAGRANGIAN SUBMANIFOLDS IN THE HYPER-KAEHLER MANIFOLD

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Chinese Annals of mathematics,Series B 1999年第4期20卷 393-400页

作者： FU JIXIANG(institute of mathematics,{2., shanghai 2.043., China) fudan Univ Inst Math Shanghai 200433 Peoples R China

The deformation of a compact complex Lagrangian submanifold in a hyper-Kaehler manifold and the moduli space are studied. It is proved that the moduli space Mc1 is a special Kaehler manifold, where special means that there is a real flat torsionfree symplectic connection satisfying dI = 0 (I is a complex structure of Mcl). Thus, following [4], one knows thatT*Mcl is a hyper-Kaehler manifold and then that Mcl is a complex Lagrangian submanifold in T* Mcl.

关键词： Moduli space Complex Lagrangian submanifold Hyper-Kaehler manifold Special Lagrangian submanifold Special Kaehler manifold Deformation

THE OCCUPATION DENSITY FIELD FOR THE CATALYTIC SUPER-BROWNIAN MOTION

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Chinese Annals of mathematics,Series B 1999年第4期20卷 447-454页

作者： HONG WENMING(institute of mathematics,{2. shanghai 2.043., China) fudan Univ Inst Math Shanghai 200433 Peoples R China

It is proved that the occupation time of the catalytic super-Brownian motion is absolutely continuous for d = 1, and the occupation density field is jointly continuous and jointly Holder continuous.

关键词： Branching rate functional Brownian collision local time Catalytic super-Brownian motion Occupation time Occupation density field

Efficient photocatalytic NADH regeneration with Rh-loaded Z-scheme mediator-free system

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Chinese Chemical Letters 2024年第2期35卷 496-500页

作者： yi zhou yiling He Ming Gao Ningkai Ding Juying Lei Yanbo zhou State Environmental Protection Key Laboratory of Environmental Risk Assessment and Control on Chemical Process East China University of Science and TechnologyShanghai 200237China National Engineering Research Center of Industrial Wastewater Detoxication and Resource Recovery East China University of Science and TechnologyShanghai 200237China shanghai Engineering Research Center for Multi-media Environmental Catalysis and Resource Utilization East China University of Science and TechnologyShanghai 200237China shanghai institute of Pollution Control and Ecological Security Shanghai 200092China

Nicotinamide adenine dinucleotide(NADH)regeneration is necessary for the sustainable application of enzymatic *** Rh-based complex[Cp^(*)Rh(bpy)(H)]+has been widely used as an important mediator in NADH regeneration systems,but it is limited by complexity and high ***,a Z-scheme was constructed by loading Rh onto carbon nitride nanosheets/carbon nitride quantum dots(CN-CNQD).The resultant catalyst achieved a high yield of NADH in a mediator-free(M-free)system of 0.2.3 mmol L^(−1) g^(−1) min^(−1),which is 5.2. times that of pure *** enzyme introduction experiments confirmed that the enzyme active product 1,4-NADH could reach 34.2.%selectivity in the M-free *** research revealed that the heterojunction between CNs and CNQDs improved the NADH regeneration activity in the traditional M-involved system,while Rh loading was proved to optimize the yield and selectivity of 1,4-NADH in M-free *** immobilized Rh shows more competitiveness than[Cp^(*)Rh(bpy)(H)]^(+).This study contributes to the construction of an M-free system for further application in greener,lower-cost enzymatic processes.

关键词： Photocatalysis NADH regeneration Mediator-free Carbon nitride Z-scheme

Determining beam transverse absolute position by triangulation of multi-electrode signal phase differences

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Nuclear Science and Techniques 2024年第8期35卷 38-47页

作者： Xing Yang Hong‑Shuang Wang yi‑Mei zhou Yong‑Bin Leng shanghai institute of Applied Physics Chinese Academy of SciencesShanghai 201800China university of Chinese Academy of Sciences Beijing 100049China shanghai Advanced Research institute Chinese Academy of SciencesShanghai 201204China university of Science and Technology of China Hefei 230026China

Accurate measurement of the transverse position of a beam is crucial in particle accelerators because it plays a key role in determining the beam *** methods for beam-position measurement rely on the detection of image currents induced on electrodes or narrow-band wake field induced by a beam passing through a cavity-type ***,these methods have *** indirect measurement of multiple parameters is computationally complex,requiring external calibration to determine the system parameters in ***,the utilization of the beam signal information is ***,this study proposes a novel method for measuring the absolute electron beam transverse *** utilizing the geometric relationship between the center position of the measured electron beam and multiple detection electrodes and by analyzing the differences in the arrival times of the beam signals detected by these electrodes,the absolute transverse position of the electron beam crossing the electrode plane can be *** method features absolute position measurement,a position sensitivity coefficient independent of vacuum chamber apertures,and no requirement for a symmetrical detector electrode *** feasibility of this method is validated through numerical simulations and beam experiments.

关键词： Electron beam bunch-by bunch diagnostics Bunch position measurement Triangulation method Bunch phase Bunch-by-bunch Transverse position Pickup signal